Chapter 13: Rational Numbers
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Rational Numbers 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)
- Integer (a positive whole number, negative whole number, or zero)
- Prime Number (a whole number greater than 1 with exactly two positive factors)
- Ratio (a comparison of two quantities)
- 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.
13.1 Meaning of rational number
A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Meaning of rational number .
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: Show why 3/4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Meaning of rational number .
Answer: 3/4 = 0.75
Worked Example 2
Problem: Show why -2 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Meaning of rational number .
Answer: -2 = -2/1
Worked Example 3
Problem: Show why 0.4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Meaning of rational number .
Answer: 0.4 = 2/5
Worked Example 4
Problem: Show why 0.333… is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Meaning of rational number .
Answer: 0.333… = 1/3
Worked Example 5
Problem: Show why 1.25 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Meaning of rational number .
Answer: 1.25 = 5/4
Worked Example 6
Problem: Show why 3/5 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 3/5 = 0.6
Worked Example 7
Problem: Show why -7 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: -7 = -7/1
Worked Example 8
Problem: Show why 0.25 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.25 = 1/4
Worked Example 9
Problem: Show why 0.666… is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.666… = 2/3
Worked Example 10
Problem: Show why 1.4 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 1.4 = 7/5
Practice Exercise
Create one new question about Meaning of rational number. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.2 Integers as rational numbers
An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers as rational numbers .
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: Place -7 on a number line.
- Start at 0.
- Move 7 units left.
Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers as rational numbers .
Answer: -7 is negative.
Worked Example 2
Problem: Place 4 on a number line.
- Start at 0.
- Move 4 units right.
Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers as rational numbers .
Answer: 4 is positive.
Worked Example 3
Problem: Place -6 on a number line.
- Start at 0.
- Move 6 units left.
Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers as rational numbers .
Answer: -6 is negative.
Worked Example 4
Problem: Place 12 on a number line.
- Start at 0.
- Move 12 units right.
Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers as rational numbers .
Answer: 12 is positive.
Worked Example 5
Problem: Place -15 on a number line.
- Start at 0.
- Move 15 units left.
Very beginner explanation: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers as rational numbers .
Answer: -15 is negative.
Worked Example 6
Problem: Calculate -8 + (5).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -3
Worked Example 7
Problem: Calculate 7 + (-12).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -5
Worked Example 8
Problem: Calculate -4 + (-9).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -13
Worked Example 9
Problem: Calculate 15 + (-6).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: 9
Worked Example 10
Problem: Calculate -20 + (13).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -7
Practice Exercise
Create one new question about Integers as rational numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.3 Fractions as rational numbers
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions as rational numbers .
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 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions as rational numbers .
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions as rational numbers .
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions as rational numbers .
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions as rational numbers .
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions as rational numbers .
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Fractions as rational numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.4 Decimals as rational numbers
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Decimals as rational numbers .
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 tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Decimals as rational numbers .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Decimals as rational numbers .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Decimals as rational numbers .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Decimals as rational numbers .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Decimals as rational numbers .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 3.8
Worked Example 7
Problem: Round 8.4 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 8.4
Worked Example 8
Problem: Round 12.05 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 12.1
Worked Example 9
Problem: Round 0.96 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 1
Worked Example 10
Problem: Round 5.125 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 5.1
Practice Exercise
Create one new question about Decimals as rational numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.5 Positive rational numbers
A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Positive rational numbers .
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: Show why 3/4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Positive rational numbers .
Answer: 3/4 = 0.75
Worked Example 2
Problem: Show why -2 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Positive rational numbers .
Answer: -2 = -2/1
Worked Example 3
Problem: Show why 0.4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Positive rational numbers .
Answer: 0.4 = 2/5
Worked Example 4
Problem: Show why 0.333… is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Positive rational numbers .
Answer: 0.333… = 1/3
Worked Example 5
Problem: Show why 1.25 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Positive rational numbers .
Answer: 1.25 = 5/4
Worked Example 6
Problem: Show why 3/5 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 3/5 = 0.6
Worked Example 7
Problem: Show why -7 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: -7 = -7/1
Worked Example 8
Problem: Show why 0.25 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.25 = 1/4
Worked Example 9
Problem: Show why 0.666… is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.666… = 2/3
Worked Example 10
Problem: Show why 1.4 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 1.4 = 7/5
Practice Exercise
Create one new question about Positive rational numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.6 Negative rational numbers
A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Negative rational numbers .
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: Show why 3/4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Negative rational numbers .
Answer: 3/4 = 0.75
Worked Example 2
Problem: Show why -2 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Negative rational numbers .
Answer: -2 = -2/1
Worked Example 3
Problem: Show why 0.4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Negative rational numbers .
Answer: 0.4 = 2/5
Worked Example 4
Problem: Show why 0.333… is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Negative rational numbers .
Answer: 0.333… = 1/3
Worked Example 5
Problem: Show why 1.25 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Negative rational numbers .
Answer: 1.25 = 5/4
Worked Example 6
Problem: Show why 3/5 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 3/5 = 0.6
Worked Example 7
Problem: Show why -7 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: -7 = -7/1
Worked Example 8
Problem: Show why 0.25 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.25 = 1/4
Worked Example 9
Problem: Show why 0.666… is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.666… = 2/3
Worked Example 10
Problem: Show why 1.4 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 1.4 = 7/5
Practice Exercise
Create one new question about Negative rational numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.7 Terminating decimals
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Terminating decimals .
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 tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Terminating decimals .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Terminating decimals .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Terminating decimals .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Terminating decimals .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Terminating decimals .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 3.8
Worked Example 7
Problem: Round 8.4 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 8.4
Worked Example 8
Problem: Round 12.05 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 12.1
Worked Example 9
Problem: Round 0.96 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 1
Worked Example 10
Problem: Round 5.125 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 5.1
Practice Exercise
Create one new question about Terminating decimals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.8 Repeating decimals
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Repeating decimals .
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 tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Repeating decimals .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Repeating decimals .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Repeating decimals .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Repeating decimals .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Repeating decimals .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 3.8
Worked Example 7
Problem: Round 8.4 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 8.4
Worked Example 8
Problem: Round 12.05 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 12.1
Worked Example 9
Problem: Round 0.96 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 1
Worked Example 10
Problem: Round 5.125 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 5.1
Practice Exercise
Create one new question about Repeating decimals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.9 Rational numbers on number lines
A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Rational numbers on number lines .
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: Show why 3/4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Rational numbers on number lines .
Answer: 3/4 = 0.75
Worked Example 2
Problem: Show why -2 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Rational numbers on number lines .
Answer: -2 = -2/1
Worked Example 3
Problem: Show why 0.4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Rational numbers on number lines .
Answer: 0.4 = 2/5
Worked Example 4
Problem: Show why 0.333… is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Rational numbers on number lines .
Answer: 0.333… = 1/3
Worked Example 5
Problem: Show why 1.25 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Rational numbers on number lines .
Answer: 1.25 = 5/4
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 Rational numbers on number lines. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.10 Comparing rational numbers
A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Comparing rational numbers .
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: Show why 3/4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Comparing rational numbers .
Answer: 3/4 = 0.75
Worked Example 2
Problem: Show why -2 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Comparing rational numbers .
Answer: -2 = -2/1
Worked Example 3
Problem: Show why 0.4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Comparing rational numbers .
Answer: 0.4 = 2/5
Worked Example 4
Problem: Show why 0.333… is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Comparing rational numbers .
Answer: 0.333… = 1/3
Worked Example 5
Problem: Show why 1.25 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Comparing rational numbers .
Answer: 1.25 = 5/4
Worked Example 6
Problem: Show why 3/5 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 3/5 = 0.6
Worked Example 7
Problem: Show why -7 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: -7 = -7/1
Worked Example 8
Problem: Show why 0.25 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.25 = 1/4
Worked Example 9
Problem: Show why 0.666… is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.666… = 2/3
Worked Example 10
Problem: Show why 1.4 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 1.4 = 7/5
Practice Exercise
Create one new question about Comparing rational numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.11 Ordering rational numbers
A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Ordering rational numbers .
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: Show why 3/4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Ordering rational numbers .
Answer: 3/4 = 0.75
Worked Example 2
Problem: Show why -2 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Ordering rational numbers .
Answer: -2 = -2/1
Worked Example 3
Problem: Show why 0.4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Ordering rational numbers .
Answer: 0.4 = 2/5
Worked Example 4
Problem: Show why 0.333… is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Ordering rational numbers .
Answer: 0.333… = 1/3
Worked Example 5
Problem: Show why 1.25 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Ordering rational numbers .
Answer: 1.25 = 5/4
Worked Example 6
Problem: Show why 3/5 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 3/5 = 0.6
Worked Example 7
Problem: Show why -7 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: -7 = -7/1
Worked Example 8
Problem: Show why 0.25 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.25 = 1/4
Worked Example 9
Problem: Show why 0.666… is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.666… = 2/3
Worked Example 10
Problem: Show why 1.4 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 1.4 = 7/5
Practice Exercise
Create one new question about Ordering rational numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.12 Equivalent rational forms
A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Equivalent rational forms .
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: Show why 3/4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Equivalent rational forms .
Answer: 3/4 = 0.75
Worked Example 2
Problem: Show why -2 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Equivalent rational forms .
Answer: -2 = -2/1
Worked Example 3
Problem: Show why 0.4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Equivalent rational forms .
Answer: 0.4 = 2/5
Worked Example 4
Problem: Show why 0.333… is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Equivalent rational forms .
Answer: 0.333… = 1/3
Worked Example 5
Problem: Show why 1.25 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Equivalent rational forms .
Answer: 1.25 = 5/4
Worked Example 6
Problem: Show why 3/5 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 3/5 = 0.6
Worked Example 7
Problem: Show why -7 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: -7 = -7/1
Worked Example 8
Problem: Show why 0.25 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.25 = 1/4
Worked Example 9
Problem: Show why 0.666… is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.666… = 2/3
Worked Example 10
Problem: Show why 1.4 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 1.4 = 7/5
Practice Exercise
Create one new question about Equivalent rational forms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
13.13 Real-life rational-number problems
A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Real-life rational-number problems .
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: Show why 3/4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Real-life rational-number problems .
Answer: 3/4 = 0.75
Worked Example 2
Problem: Show why -2 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Real-life rational-number problems .
Answer: -2 = -2/1
Worked Example 3
Problem: Show why 0.4 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Real-life rational-number problems .
Answer: 0.4 = 2/5
Worked Example 4
Problem: Show why 0.333… is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Real-life rational-number problems .
Answer: 0.333… = 1/3
Worked Example 5
Problem: Show why 1.25 is rational.
- Write it as a fraction of integers.
Very beginner explanation: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Real-life rational-number problems .
Answer: 1.25 = 5/4
Worked Example 6
Problem: Show why 3/5 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 3/5 = 0.6
Worked Example 7
Problem: Show why -7 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: -7 = -7/1
Worked Example 8
Problem: Show why 0.25 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.25 = 1/4
Worked Example 9
Problem: Show why 0.666… is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 0.666… = 2/3
Worked Example 10
Problem: Show why 1.4 is a rational number.
- A rational number can be written as a fraction of integers.
- Rewrite the given number as a fraction if needed.
Very beginner explanation: If a number can be written as a/b where a and b are integers and b is not zero, it is rational.
Answer: 1.4 = 7/5
Practice Exercise
Create one new question about Real-life rational-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 Meaning of rational number . Show your reasoning and check your answer.
- Create and solve a new question about Integers as rational numbers . Show your reasoning and check your answer.
- Create and solve a new question about Fractions as rational numbers . Show your reasoning and check your answer.
- Create and solve a new question about Decimals as rational numbers . Show your reasoning and check your answer.
- Create and solve a new question about Positive rational numbers . Show your reasoning and check your answer.
- Create and solve a new question about Negative rational numbers . Show your reasoning and check your answer.
- Create and solve a new question about Terminating decimals . Show your reasoning and check your answer.
- Create and solve a new question about Repeating decimals . Show your reasoning and check your answer.
- Create and solve a new question about Rational numbers on number lines . Show your reasoning and check your answer.
- Create and solve a new question about Comparing rational numbers . Show your reasoning and check your answer.
- Create and solve a new question about Ordering rational numbers . Show your reasoning and check your answer.
- Create and solve a new question about Equivalent rational forms . Show your reasoning and check your answer.
Common Mistakes
- Changing only one part of an equivalent fraction or ratio.
- Moving a decimal point without a mathematical reason.
- Using the new amount instead of the original amount for percent change.
- Mixing units when comparing rates or scale.
30 Review Questions and Answers
Q1. What is important to remember about Meaning of rational number?
Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Meaning of rational number.
Q2. What is important to remember about Integers as rational numbers?
Answer: An integer (a positive whole number, a negative whole number, or zero) is useful for temperatures, elevations, gains, and losses. This topic focuses on Integers as rational numbers.
Q3. What is important to remember about Fractions as rational numbers?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions as rational numbers.
Q4. What is important to remember about Decimals as rational numbers?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Decimals as rational numbers.
Q5. What is important to remember about Positive rational numbers?
Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Positive rational numbers.
Q6. What is important to remember about Negative rational numbers?
Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Negative rational numbers.
Q7. What is important to remember about Terminating decimals?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Terminating decimals.
Q8. What is important to remember about Repeating decimals?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Repeating decimals.
Q9. What is important to remember about Rational numbers on number lines?
Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Rational numbers on number lines.
Q10. What is important to remember about Comparing rational numbers?
Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Comparing rational numbers.
Q11. What is important to remember about Ordering rational numbers?
Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Ordering rational numbers.
Q12. What is important to remember about Equivalent rational forms?
Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Equivalent rational forms.
Q13. What is important to remember about Real-life rational-number problems?
Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. This topic focuses on Real-life rational-number problems.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q26. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q27. 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.
Q28. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q29. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q30. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.