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Chapter 28: Multi-Term Equations

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Multi-Term Equations in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Meaning of multiple terms (A multiple is a result found by multiplying a number by a whole number.)
  • Combining like terms (Combining like terms introduction is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Equations such as 2x plus 3x equals 20 (An equation states that two mathematical expressions have the same value.)
  • Equations with a variable term and constant (A variable is a symbol used to represent a number that may change or may be unknown.)
  • Simplifying before solving (Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Equations with decimal tenths (A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

28.1 Meaning of multiple terms

A multiple is a result found by multiplying a number by a whole number. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: List the first five positive multiples of 17.

  1. Multiply 17 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 17, 34, 51, 68, 85

Worked Example 2

Problem: List the first five positive multiples of 89.

  1. Multiply 89 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 89, 178, 267, 356, 445

Worked Example 3

Problem: List the first five positive multiples of 43.

  1. Multiply 43 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 43, 86, 129, 172, 215

Worked Example 4

Problem: List the first five positive multiples of 14.

  1. Multiply 14 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 14, 28, 42, 56, 70

Worked Example 5

Problem: List the first five positive multiples of 82.

  1. Multiply 82 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 82, 164, 246, 328, 410

Worked Example 6

Problem: List the first five positive multiples of 38.

  1. Multiply 38 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 38, 76, 114, 152, 190

Worked Example 7

Problem: List the first five positive multiples of 52.

  1. Multiply 52 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 52, 104, 156, 208, 260

Worked Example 8

Problem: List the first five positive multiples of 63.

  1. Multiply 63 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 63, 126, 189, 252, 315

Worked Example 9

Problem: List the first five positive multiples of 75.

  1. Multiply 75 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 75, 150, 225, 300, 375

Worked Example 10

Problem: List the first five positive multiples of 89.

  1. Multiply 89 by 1, 2, 3, 4, and 5.

Very beginner explanation: Multiples come from repeated multiplication by whole numbers.

Answer: 89, 178, 267, 356, 445

Practice Exercise

Create one new Grade 6 problem about Meaning of multiple terms. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

28.2 Combining like terms introduction

Combining like terms introduction is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate 3x + 4 when x = 5.

  1. Replace x with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 2

Problem: Evaluate 2n + 7 when n = 6.

  1. Replace n with 6.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 3

Problem: Evaluate 5a - 3 when a = 4.

  1. Replace a with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 17

Worked Example 4

Problem: Evaluate 4p + 1 when p = 8.

  1. Replace p with 8.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 33

Worked Example 5

Problem: Evaluate 6m - 5 when m = 3.

  1. Replace m with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 13

Worked Example 6

Problem: Evaluate 2.5x + 1 when x = 4.

  1. Replace x with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 11

Worked Example 7

Problem: Evaluate 7q + 2 when q = 2.

  1. Replace q with 2.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 16

Worked Example 8

Problem: Evaluate 3r - 1 when r = 9.

  1. Replace r with 9.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 9

Problem: Evaluate 4y + 6 when y = 5.

  1. Replace y with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 10

Problem: Evaluate 8k - 4 when k = 3.

  1. Replace k with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 20

Practice Exercise

Create one new Grade 6 problem about Combining like terms introduction. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

28.3 Equations such as 2x plus 3x equals 20

An equation states that two mathematical expressions have the same value. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Solve x + 7 = 18.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 11

Worked Example 2

Problem: Solve x - 9 = 14.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 23

Worked Example 3

Problem: Solve 4x = 28.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 7

Worked Example 4

Problem: Solve x ÷ 5 = 6.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 30

Worked Example 5

Problem: Solve 2x + 3x = 25.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Worked Example 6

Problem: Solve 3x + 4 = 19.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Worked Example 7

Problem: Solve 5x - 2 = 23.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Worked Example 8

Problem: Solve 0.5x + 2 = 6.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 8

Worked Example 9

Problem: Solve 4x + 1 = 2x + 13.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 6

Worked Example 10

Problem: Solve 6x - 3 = 3x + 12.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Practice Exercise

Create one new Grade 6 problem about Equations such as 2x plus 3x equals 20. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is changing only one side of a relationship or forgetting to check the solution.

28.4 Equations with a variable term and constant

A variable is a symbol used to represent a number that may change or may be unknown. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate 3x + 4 when x = 5.

  1. Replace x with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 2

Problem: Evaluate 2n + 7 when n = 6.

  1. Replace n with 6.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 3

Problem: Evaluate 5a - 3 when a = 4.

  1. Replace a with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 17

Worked Example 4

Problem: Evaluate 4p + 1 when p = 8.

  1. Replace p with 8.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 33

Worked Example 5

Problem: Evaluate 6m - 5 when m = 3.

  1. Replace m with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 13

Worked Example 6

Problem: Evaluate 2.5x + 1 when x = 4.

  1. Replace x with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 11

Worked Example 7

Problem: Evaluate 7q + 2 when q = 2.

  1. Replace q with 2.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 16

Worked Example 8

Problem: Evaluate 3r - 1 when r = 9.

  1. Replace r with 9.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 9

Problem: Evaluate 4y + 6 when y = 5.

  1. Replace y with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 10

Problem: Evaluate 8k - 4 when k = 3.

  1. Replace k with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 20

Practice Exercise

Create one new Grade 6 problem about Equations with a variable term and constant. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is changing only one side of a relationship or forgetting to check the solution.

28.5 Balancing multi-term equations

An equation states that two mathematical expressions have the same value. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate 3x + 4 when x = 5.

  1. Replace x with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 2

Problem: Evaluate 2n + 7 when n = 6.

  1. Replace n with 6.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 3

Problem: Evaluate 5a - 3 when a = 4.

  1. Replace a with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 17

Worked Example 4

Problem: Evaluate 4p + 1 when p = 8.

  1. Replace p with 8.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 33

Worked Example 5

Problem: Evaluate 6m - 5 when m = 3.

  1. Replace m with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 13

Worked Example 6

Problem: Evaluate 2.5x + 1 when x = 4.

  1. Replace x with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 11

Worked Example 7

Problem: Evaluate 7q + 2 when q = 2.

  1. Replace q with 2.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 16

Worked Example 8

Problem: Evaluate 3r - 1 when r = 9.

  1. Replace r with 9.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 9

Problem: Evaluate 4y + 6 when y = 5.

  1. Replace y with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 10

Problem: Evaluate 8k - 4 when k = 3.

  1. Replace k with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 20

Practice Exercise

Create one new Grade 6 problem about Balancing multi-term equations. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is changing only one side of a relationship or forgetting to check the solution.

28.6 Simplifying before solving

Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Simplifying before solving to analyze the values 16 and 12. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Simplifying before solving to analyze the values 12 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Simplifying before solving to analyze the values 4 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Simplifying before solving to analyze the values 12 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Simplifying before solving to analyze the values 6 and 9. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Simplifying before solving to analyze the values 27 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Simplifying before solving to analyze the values 9 and 12. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Simplifying before solving to analyze the values 12 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Simplifying before solving to analyze the values 10 and 9. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Simplifying before solving to analyze the values 21 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Simplifying before solving. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

28.7 Equations with decimal tenths

A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: What digit is in the tenths place of 82.825?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 8

Worked Example 2

Problem: What digit is in the tenths place of 81.384?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 3

Worked Example 3

Problem: What digit is in the tenths place of 44.166?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 1

Worked Example 4

Problem: What digit is in the tenths place of 22.1?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 1

Worked Example 5

Problem: What digit is in the tenths place of 23.781?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 7

Worked Example 6

Problem: What digit is in the tenths place of 33.796?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 7

Worked Example 7

Problem: What digit is in the tenths place of 1.665?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 6

Worked Example 8

Problem: What digit is in the tenths place of 35.138?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 1

Worked Example 9

Problem: What digit is in the tenths place of 47.214?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 2

Worked Example 10

Problem: What digit is in the tenths place of 18.459?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 4

Practice Exercise

Create one new Grade 6 problem about Equations with decimal tenths. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is lining up the last digits instead of lining up decimal points and place values.

28.8 Checking multi-term solutions

Checking multi-term solutions is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate 3x + 4 when x = 5.

  1. Replace x with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 2

Problem: Evaluate 2n + 7 when n = 6.

  1. Replace n with 6.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 3

Problem: Evaluate 5a - 3 when a = 4.

  1. Replace a with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 17

Worked Example 4

Problem: Evaluate 4p + 1 when p = 8.

  1. Replace p with 8.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 33

Worked Example 5

Problem: Evaluate 6m - 5 when m = 3.

  1. Replace m with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 13

Worked Example 6

Problem: Evaluate 2.5x + 1 when x = 4.

  1. Replace x with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 11

Worked Example 7

Problem: Evaluate 7q + 2 when q = 2.

  1. Replace q with 2.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 16

Worked Example 8

Problem: Evaluate 3r - 1 when r = 9.

  1. Replace r with 9.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 9

Problem: Evaluate 4y + 6 when y = 5.

  1. Replace y with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 10

Problem: Evaluate 8k - 4 when k = 3.

  1. Replace k with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 20

Practice Exercise

Create one new Grade 6 problem about Checking multi-term solutions. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

28.9 Writing multi-term equations from situations

An equation states that two mathematical expressions have the same value. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate 3x + 4 when x = 5.

  1. Replace x with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 2

Problem: Evaluate 2n + 7 when n = 6.

  1. Replace n with 6.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 3

Problem: Evaluate 5a - 3 when a = 4.

  1. Replace a with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 17

Worked Example 4

Problem: Evaluate 4p + 1 when p = 8.

  1. Replace p with 8.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 33

Worked Example 5

Problem: Evaluate 6m - 5 when m = 3.

  1. Replace m with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 13

Worked Example 6

Problem: Evaluate 2.5x + 1 when x = 4.

  1. Replace x with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 11

Worked Example 7

Problem: Evaluate 7q + 2 when q = 2.

  1. Replace q with 2.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 16

Worked Example 8

Problem: Evaluate 3r - 1 when r = 9.

  1. Replace r with 9.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 9

Problem: Evaluate 4y + 6 when y = 5.

  1. Replace y with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 10

Problem: Evaluate 8k - 4 when k = 3.

  1. Replace k with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 20

Practice Exercise

Create one new Grade 6 problem about Writing multi-term equations from situations. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is changing only one side of a relationship or forgetting to check the solution.

28.10 Area and perimeter equations

An equation states that two mathematical expressions have the same value. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Solve x + 7 = 18.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 11

Worked Example 2

Problem: Solve x - 9 = 14.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 23

Worked Example 3

Problem: Solve 4x = 28.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 7

Worked Example 4

Problem: Solve x ÷ 5 = 6.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 30

Worked Example 5

Problem: Solve 2x + 3x = 25.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Worked Example 6

Problem: Solve 3x + 4 = 19.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Worked Example 7

Problem: Solve 5x - 2 = 23.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Worked Example 8

Problem: Solve 0.5x + 2 = 6.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 8

Worked Example 9

Problem: Solve 4x + 1 = 2x + 13.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 6

Worked Example 10

Problem: Solve 6x - 3 = 3x + 12.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Practice Exercise

Create one new Grade 6 problem about Area and perimeter equations. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is changing only one side of a relationship or forgetting to check the solution.

28.11 Cost equations

An equation states that two mathematical expressions have the same value. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Solve x + 7 = 18.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 11

Worked Example 2

Problem: Solve x - 9 = 14.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 23

Worked Example 3

Problem: Solve 4x = 28.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 7

Worked Example 4

Problem: Solve x ÷ 5 = 6.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 30

Worked Example 5

Problem: Solve 2x + 3x = 25.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Worked Example 6

Problem: Solve 3x + 4 = 19.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Worked Example 7

Problem: Solve 5x - 2 = 23.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Worked Example 8

Problem: Solve 0.5x + 2 = 6.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 8

Worked Example 9

Problem: Solve 4x + 1 = 2x + 13.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 6

Worked Example 10

Problem: Solve 6x - 3 = 3x + 12.

  1. Simplify each side if needed.
  2. Use inverse operations to isolate the variable.
  3. Keep the relationship balanced.
  4. Substitute the answer to check.

Very beginner explanation: An equation is balanced when both sides have equal value.

Answer: x = 5

Practice Exercise

Create one new Grade 6 problem about Cost equations. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is changing only one side of a relationship or forgetting to check the solution.

28.12 Real-life multi-term equation problems

An equation states that two mathematical expressions have the same value. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Evaluate 3x + 4 when x = 5.

  1. Replace x with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 2

Problem: Evaluate 2n + 7 when n = 6.

  1. Replace n with 6.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 3

Problem: Evaluate 5a - 3 when a = 4.

  1. Replace a with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 17

Worked Example 4

Problem: Evaluate 4p + 1 when p = 8.

  1. Replace p with 8.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 33

Worked Example 5

Problem: Evaluate 6m - 5 when m = 3.

  1. Replace m with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 13

Worked Example 6

Problem: Evaluate 2.5x + 1 when x = 4.

  1. Replace x with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 11

Worked Example 7

Problem: Evaluate 7q + 2 when q = 2.

  1. Replace q with 2.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 16

Worked Example 8

Problem: Evaluate 3r - 1 when r = 9.

  1. Replace r with 9.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 9

Problem: Evaluate 4y + 6 when y = 5.

  1. Replace y with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 10

Problem: Evaluate 8k - 4 when k = 3.

  1. Replace k with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 20

Practice Exercise

Create one new Grade 6 problem about Real-life multi-term equation problems. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is changing only one side of a relationship or forgetting to check the solution.

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30 Review Questions and Answers

Q1. What is important to understand about Meaning of multiple terms?

Answer: A multiple is a result found by multiplying a number by a whole number.

Q2. What is important to understand about Combining like terms introduction?

Answer: Combining like terms introduction is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q3. What is important to understand about Equations such as 2x plus 3x equals 20?

Answer: An equation states that two mathematical expressions have the same value.

Q4. What is important to understand about Equations with a variable term and constant?

Answer: A variable is a symbol used to represent a number that may change or may be unknown.

Q5. What is important to understand about Balancing multi-term equations?

Answer: An equation states that two mathematical expressions have the same value.

Q6. What is important to understand about Simplifying before solving?

Answer: Simplifying before solving is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q7. What is important to understand about Equations with decimal tenths?

Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.

Q8. What is important to understand about Checking multi-term solutions?

Answer: Checking multi-term solutions is a Grade 6 mathematics idea in Multi-Term Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q9. What is important to understand about Writing multi-term equations from situations?

Answer: An equation states that two mathematical expressions have the same value.

Q10. What is important to understand about Area and perimeter equations?

Answer: An equation states that two mathematical expressions have the same value.

Q11. What is important to understand about Cost equations?

Answer: An equation states that two mathematical expressions have the same value.

Q12. What is important to understand about Real-life multi-term equation problems?

Answer: An equation states that two mathematical expressions have the same value.

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 help prevent incompatible quantities from being mixed.

Q16. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q17. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, a table, 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 and check copied values, operations, signs, units, rules, and calculations.

Q21. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q22. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q23. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q24. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q25. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q26. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q27. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.

Q28. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.

Q29. Why should you compare an exact answer with an estimate?

Answer: The estimate gives a quick reasonableness check for the exact calculation.

Q30. What does representing mathematics mean?

Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.