Chapter 1: Whole Numbers to One Billion
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Whole Numbers to One Billion with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Rational Number (a number that can be written as a fraction of integers with a nonzero denominator)
- Prime Number (a whole number greater than 1 with exactly two positive factors)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
1.1 Whole numbers to 1 billion
Whole numbers to 1 billion is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the value of the first digit in 487,305,219.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Whole numbers to 1 billion is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 400,000,000
Worked Example 2
Problem: Identify the value of the first digit in 73,040,506.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Whole numbers to 1 billion is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 70,000,000
Worked Example 3
Problem: Identify the value of the first digit in 905,600,012.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Whole numbers to 1 billion is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 900,000,000
Worked Example 4
Problem: Identify the value of the first digit in 1,000,000,000.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Whole numbers to 1 billion is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1,000,000,000
Worked Example 5
Problem: Identify the value of the first digit in 268,999,450.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Whole numbers to 1 billion is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 200,000,000
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Whole numbers to 1 billion. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.2 Place value
Place value (the value of a digit because of its position) increases by a factor of 10 as you move one place left. This topic focuses on Place value .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the value of the first digit in 487,305,219.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Place value (the value of a digit because of its position) increases by a factor of 10 as you move one place left. This topic focuses on Place value .
Answer: 400,000,000
Worked Example 2
Problem: Identify the value of the first digit in 73,040,506.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Place value (the value of a digit because of its position) increases by a factor of 10 as you move one place left. This topic focuses on Place value .
Answer: 70,000,000
Worked Example 3
Problem: Identify the value of the first digit in 905,600,012.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Place value (the value of a digit because of its position) increases by a factor of 10 as you move one place left. This topic focuses on Place value .
Answer: 900,000,000
Worked Example 4
Problem: Identify the value of the first digit in 1,000,000,000.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Place value (the value of a digit because of its position) increases by a factor of 10 as you move one place left. This topic focuses on Place value .
Answer: 1,000,000,000
Worked Example 5
Problem: Identify the value of the first digit in 268,999,450.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Place value (the value of a digit because of its position) increases by a factor of 10 as you move one place left. This topic focuses on Place value .
Answer: 200,000,000
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Place value. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.3 Reading large numbers
Reading large numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the value of the first digit in 487,305,219.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Reading large numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 400,000,000
Worked Example 2
Problem: Identify the value of the first digit in 73,040,506.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Reading large numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 70,000,000
Worked Example 3
Problem: Identify the value of the first digit in 905,600,012.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Reading large numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 900,000,000
Worked Example 4
Problem: Identify the value of the first digit in 1,000,000,000.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Reading large numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1,000,000,000
Worked Example 5
Problem: Identify the value of the first digit in 268,999,450.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Reading large numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 200,000,000
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Reading large numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.4 Writing large numbers in standard form
Writing large numbers in standard form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the value of the first digit in 487,305,219.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Writing large numbers in standard form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 400,000,000
Worked Example 2
Problem: Identify the value of the first digit in 73,040,506.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Writing large numbers in standard form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 70,000,000
Worked Example 3
Problem: Identify the value of the first digit in 905,600,012.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Writing large numbers in standard form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 900,000,000
Worked Example 4
Problem: Identify the value of the first digit in 1,000,000,000.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Writing large numbers in standard form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1,000,000,000
Worked Example 5
Problem: Identify the value of the first digit in 268,999,450.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Writing large numbers in standard form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 200,000,000
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Writing large numbers in standard form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.5 Expanded form
Expanded form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 487,305,219 in expanded form.
- Break the number into the value of each nonzero digit.
Very beginner explanation: Expanded form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 400000000 + 80000000 + 7000000 + 300000 + 5000 + 200 + 10 + 9
Worked Example 2
Problem: Write 73,040,506 in expanded form.
- Break the number into the value of each nonzero digit.
Very beginner explanation: Expanded form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 70000000 + 3000000 + 40000 + 500 + 6
Worked Example 3
Problem: Write 905,600,012 in expanded form.
- Break the number into the value of each nonzero digit.
Very beginner explanation: Expanded form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 900000000 + 5000000 + 600000 + 10 + 2
Worked Example 4
Problem: Write 1,000,000,000 in expanded form.
- Break the number into the value of each nonzero digit.
Very beginner explanation: Expanded form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1000000000
Worked Example 5
Problem: Write 268,999,450 in expanded form.
- Break the number into the value of each nonzero digit.
Very beginner explanation: Expanded form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 200000000 + 60000000 + 8000000 + 900000 + 90000 + 9000 + 400 + 50
Worked Example 6
Problem: Write 638,420,715 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 600,000,000 + 30,000,000 + 8,000,000 + 400,000 + 20,000 + 700 + 10 + 5
Worked Example 7
Problem: Write 92,305,004 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 90,000,000 + 2,000,000 + 300,000 + 5,000 + 4
Worked Example 8
Problem: Write 704,090,650 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 700,000,000 + 4,000,000 + 90,000 + 600 + 50
Worked Example 9
Problem: Write 18,765,432 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 10,000,000 + 8,000,000 + 700,000 + 60,000 + 5,000 + 400 + 30 + 2
Worked Example 10
Problem: Write 999,500,001 in expanded form.
- Read each non-zero digit by place value.
- Write each place-value amount separately.
- Join the parts with plus signs.
Very beginner explanation: Expanded form shows exactly what each digit contributes to the number.
Answer: 900,000,000 + 90,000,000 + 9,000,000 + 500,000 + 1
Practice Exercise
Create one new question about Expanded form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.6 Word form
Word form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the value of the first digit in 487,305,219.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Word form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 400,000,000
Worked Example 2
Problem: Identify the value of the first digit in 73,040,506.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Word form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 70,000,000
Worked Example 3
Problem: Identify the value of the first digit in 905,600,012.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Word form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 900,000,000
Worked Example 4
Problem: Identify the value of the first digit in 1,000,000,000.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Word form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1,000,000,000
Worked Example 5
Problem: Identify the value of the first digit in 268,999,450.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Word form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 200,000,000
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Word form. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.7 Comparing whole numbers
Comparing whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 487,305,219 and 487,292,874.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Comparing whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 487,305,219 > 487,292,874
Worked Example 2
Problem: Compare 73,040,506 and 73,015,816.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Comparing whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 73,040,506 > 73,015,816
Worked Example 3
Problem: Compare 905,600,012 and 905,562,977.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Comparing whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 905,600,012 > 905,562,977
Worked Example 4
Problem: Compare 1,000,000,000 and 999,950,620.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Comparing whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1,000,000,000 > 999,950,620
Worked Example 5
Problem: Compare 268,999,450 and 268,937,725.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Comparing whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 268,999,450 > 268,937,725
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Comparing whole numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.8 Ordering whole numbers
Ordering whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 487,305,219 and 487,292,874.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Ordering whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 487,305,219 > 487,292,874
Worked Example 2
Problem: Compare 73,040,506 and 73,015,816.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Ordering whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 73,040,506 > 73,015,816
Worked Example 3
Problem: Compare 905,600,012 and 905,562,977.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Ordering whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 905,600,012 > 905,562,977
Worked Example 4
Problem: Compare 1,000,000,000 and 999,950,620.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Ordering whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1,000,000,000 > 999,950,620
Worked Example 5
Problem: Compare 268,999,450 and 268,937,725.
- Compare digits from the greatest place value toward the right.
Very beginner explanation: Ordering whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 268,999,450 > 268,937,725
Worked Example 6
Problem: What is the value of the first digit in 638,420,715?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 600,000,000
Worked Example 7
Problem: What is the value of the first digit in 92,305,004?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 90,000,000
Worked Example 8
Problem: What is the value of the first digit in 704,090,650?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 700,000,000
Worked Example 9
Problem: What is the value of the first digit in 18,765,432?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 10,000,000
Worked Example 10
Problem: What is the value of the first digit in 999,500,001?
- Find the position of the first digit.
- Multiply the digit by its place value.
Very beginner explanation: Place value tells the value of a digit because of where it is located.
Answer: 900,000,000
Practice Exercise
Create one new question about Ordering whole numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.9 Number lines
Number lines is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Number lines: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Number lines is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Number lines: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Number lines is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Number lines: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Number lines is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Number lines: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Number lines is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Number lines: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Number lines is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Which is farther right on a number line: 3,000 or 3,750?
- Numbers get larger as you move right.
- 3,750 is greater than 3,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 3,750
Worked Example 7
Problem: Which is farther right on a number line: 4,000 or 4,750?
- Numbers get larger as you move right.
- 4,750 is greater than 4,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 4,750
Worked Example 8
Problem: Which is farther right on a number line: 5,000 or 5,750?
- Numbers get larger as you move right.
- 5,750 is greater than 5,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 5,750
Worked Example 9
Problem: Which is farther right on a number line: 6,000 or 6,750?
- Numbers get larger as you move right.
- 6,750 is greater than 6,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 6,750
Worked Example 10
Problem: Which is farther right on a number line: 7,000 or 7,750?
- Numbers get larger as you move right.
- 7,750 is greater than 7,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 7,750
Practice Exercise
Create one new question about Number lines. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.10 Rounding to different places
Rounding to different places is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Round 487,305,219 to the nearest 10.
- Find the 10 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Rounding to different places is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 487,305,220
Worked Example 2
Problem: Round 73,040,506 to the nearest 100.
- Find the 100 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Rounding to different places is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 73,040,500
Worked Example 3
Problem: Round 905,600,012 to the nearest 1,000.
- Find the 1,000 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Rounding to different places is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 905,600,000
Worked Example 4
Problem: Round 1,000,000,000 to the nearest 10,000.
- Find the 10,000 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Rounding to different places is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1,000,000,000
Worked Example 5
Problem: Round 268,999,450 to the nearest 100,000.
- Find the 100,000 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Rounding to different places is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 269,000,000
Worked Example 6
Problem: Round 638,420,715 to the nearest 10.
- Locate the 10 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 638,420,720
Worked Example 7
Problem: Round 92,305,004 to the nearest 100.
- Locate the 100 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 92,305,000
Worked Example 8
Problem: Round 704,090,650 to the nearest 1,000.
- Locate the 1,000 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 704,091,000
Worked Example 9
Problem: Round 18,765,432 to the nearest 10,000.
- Locate the 10,000 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 18,770,000
Worked Example 10
Problem: Round 999,500,001 to the nearest 100,000.
- Locate the 100,000 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 999,500,000
Practice Exercise
Create one new question about Rounding to different places. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.11 Estimation
Estimation is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Round 487,305,219 to the nearest 10.
- Find the 10 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Estimation is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 487,305,220
Worked Example 2
Problem: Round 73,040,506 to the nearest 100.
- Find the 100 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Estimation is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 73,040,500
Worked Example 3
Problem: Round 905,600,012 to the nearest 1,000.
- Find the 1,000 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Estimation is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 905,600,000
Worked Example 4
Problem: Round 1,000,000,000 to the nearest 10,000.
- Find the 10,000 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Estimation is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1,000,000,000
Worked Example 5
Problem: Round 268,999,450 to the nearest 100,000.
- Find the 100,000 place.
- Look at the digit immediately to its right.
- Round down for 0–4 and up for 5–9.
Very beginner explanation: Estimation is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 269,000,000
Worked Example 6
Problem: Round 638,420,715 to the nearest 10.
- Locate the 10 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 638,420,720
Worked Example 7
Problem: Round 92,305,004 to the nearest 100.
- Locate the 100 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 92,305,000
Worked Example 8
Problem: Round 704,090,650 to the nearest 1,000.
- Locate the 1,000 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 704,091,000
Worked Example 9
Problem: Round 18,765,432 to the nearest 10,000.
- Locate the 10,000 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 18,770,000
Worked Example 10
Problem: Round 999,500,001 to the nearest 100,000.
- Locate the 100,000 place.
- Look at the next digit to the right.
- 0–4: keep the target digit; 5–9: increase it by 1.
- Replace lower places with zeros.
Very beginner explanation: Rounding gives a nearby value that is easier to use while staying close to the original number.
Answer: 999,500,000
Practice Exercise
Create one new question about Estimation. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
1.12 Real-life large-number problems
Real-life large-number problems is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Identify the value of the first digit in 487,305,219.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Real-life large-number problems is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 400,000,000
Worked Example 2
Problem: Identify the value of the first digit in 73,040,506.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Real-life large-number problems is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 70,000,000
Worked Example 3
Problem: Identify the value of the first digit in 905,600,012.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Real-life large-number problems is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 900,000,000
Worked Example 4
Problem: Identify the value of the first digit in 1,000,000,000.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Real-life large-number problems is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1,000,000,000
Worked Example 5
Problem: Identify the value of the first digit in 268,999,450.
- Locate the first digit.
- Multiply it by its place value.
Very beginner explanation: Real-life large-number problems is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 200,000,000
Worked Example 6
Problem: Explain Real-life large-number problems in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Real-life large-number problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Real-life large-number problems and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Real-life large-number problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Real-life large-number problems using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Real-life large-number problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Real-life large-number problems problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Real-life large-number problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Real-life large-number problems could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Real-life large-number problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Real-life large-number problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Whole numbers to 1 billion . Show your reasoning and check your answer.
- Create and solve a new question about Place value . Show your reasoning and check your answer.
- Create and solve a new question about Reading large numbers . Show your reasoning and check your answer.
- Create and solve a new question about Writing large numbers in standard form . Show your reasoning and check your answer.
- Create and solve a new question about Expanded form . Show your reasoning and check your answer.
- Create and solve a new question about Word form . Show your reasoning and check your answer.
- Create and solve a new question about Comparing whole numbers . Show your reasoning and check your answer.
- Create and solve a new question about Ordering whole numbers . Show your reasoning and check your answer.
- Create and solve a new question about Number lines . Show your reasoning and check your answer.
- Create and solve a new question about Rounding to different places . Show your reasoning and check your answer.
- Create and solve a new question about Estimation . Show your reasoning and check your answer.
- Create and solve a new question about Real-life large-number problems . Show your reasoning and check your answer.
Common Mistakes
- Ignoring place value or signs.
- Using an operation before checking what the question asks.
- Skipping estimation and accepting an unreasonable result.
- Forgetting the correct order of operations.
30 Review Questions and Answers
Q1. What is important to remember about Whole numbers to 1 billion?
Answer: Whole numbers to 1 billion is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q2. What is important to remember about Place value?
Answer: Place value (the value of a digit because of its position) increases by a factor of 10 as you move one place left. This topic focuses on Place value.
Q3. What is important to remember about Reading large numbers?
Answer: Reading large numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q4. What is important to remember about Writing large numbers in standard form?
Answer: Writing large numbers in standard form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q5. What is important to remember about Expanded form?
Answer: Expanded form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Word form?
Answer: Word form is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q7. What is important to remember about Comparing whole numbers?
Answer: Comparing whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Ordering whole numbers?
Answer: Ordering whole numbers is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q9. What is important to remember about Number lines?
Answer: Number lines is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Rounding to different places?
Answer: Rounding to different places is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q11. What is important to remember about Estimation?
Answer: Estimation is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Real-life large-number problems?
Answer: Real-life large-number problems is an important Grade 7 idea in Whole Numbers to One Billion. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q13. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q14. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q15. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q16. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q17. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q18. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q19. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q20. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q21. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q22. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q23. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q24. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q25. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q26. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q27. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q28. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q29. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.
Q30. Why should sources be checked in data problems?
Answer: Reliable sources and fair collection methods make conclusions more trustworthy.