Chapter 27: Solving One-Step 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

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Chapter Overview

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

Key Technical Terms

Meaning of equation (An equation states that two mathematical expressions have the same value.)
Equality and balance (Equality and balance is a Grade 6 mathematics idea in Solving One-Step Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Inverse operations (A ratio compares two quantities by division.)
Equations with decimal tenths (A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.)
Checking solutions (Checking solutions is a Grade 6 mathematics idea in Solving One-Step Equations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)

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.

27.1 Meaning of equation

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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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 Meaning of equation. 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.

27.2 Equality and balance

Equality and balance is a Grade 6 mathematics idea in Solving One-Step 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: Solve x + 7 = 18.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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 Equality and balance. 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.

27.3 Inverse operations

A ratio compares two quantities by division. 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: Simplify the ratio 10:15.

Find the greatest common factor, 5.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 2:3

Worked Example 2

Problem: Simplify the ratio 10:3.

Find the greatest common factor, 1.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 10:3

Worked Example 3

Problem: Simplify the ratio 6:8.

Find the greatest common factor, 2.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 3:4

Worked Example 4

Problem: Simplify the ratio 11:7.

Find the greatest common factor, 1.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 11:7

Worked Example 5

Problem: Simplify the ratio 3:12.

Find the greatest common factor, 3.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 1:4

Worked Example 6

Problem: Simplify the ratio 4:13.

Find the greatest common factor, 1.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 4:13

Worked Example 7

Problem: Simplify the ratio 9:15.

Find the greatest common factor, 3.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 3:5

Worked Example 8

Problem: Simplify the ratio 10:13.

Find the greatest common factor, 1.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 10:13

Worked Example 9

Problem: Simplify the ratio 8:4.

Find the greatest common factor, 4.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 2:1

Worked Example 10

Problem: Simplify the ratio 3:6.

Find the greatest common factor, 3.
Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 1:2

Practice Exercise

Create one new Grade 6 problem about Inverse operations. 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.

27.4 Addition equations

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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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 Addition 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.

27.5 Subtraction equations

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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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 Subtraction 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.

27.6 Multiplication equations

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: Find 1% of 80.

Think of 1% as 1/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 0.8

Worked Example 2

Problem: Find 5% of 120.

Think of 5% as 5/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6

Worked Example 3

Problem: Find 10% of 64.

Think of 10% as 10/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6.4

Worked Example 4

Problem: Find 20% of 250.

Think of 20% as 20/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 50

Worked Example 5

Problem: Find 25% of 96.

Think of 25% as 25/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 24

Worked Example 6

Problem: Find 50% of 40.

Think of 50% as 50/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 20

Worked Example 7

Problem: Find 75% of 200.

Think of 75% as 75/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 150

Worked Example 8

Problem: Find 15% of 60.

Think of 15% as 15/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 9

Worked Example 9

Problem: Find 30% of 150.

Think of 30% as 30/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 45

Worked Example 10

Problem: Find 40% of 90.

Think of 40% as 40/100.
Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 36

Practice Exercise

Create one new Grade 6 problem about Multiplication 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.

27.7 Division equations

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: Calculate 780 ÷ 15.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 52

Worked Example 2

Problem: Calculate 1983 ÷ 15.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 132 remainder 3

Worked Example 3

Problem: Calculate 2484 ÷ 23.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 108

Worked Example 4

Problem: Calculate 619 ÷ 7.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 88 remainder 3

Worked Example 5

Problem: Calculate 249 ÷ 3.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 83

Worked Example 6

Problem: Calculate 792 ÷ 22.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 36

Worked Example 7

Problem: Calculate 1239 ÷ 21.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 59

Worked Example 8

Problem: Calculate 386 ÷ 20.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 19 remainder 6

Worked Example 9

Problem: Calculate 1140 ÷ 12.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 95

Worked Example 10

Problem: Calculate 676 ÷ 24.

Estimate the quotient.
Divide using place value.
Record any remainder.
Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 28 remainder 4

Practice Exercise

Create one new Grade 6 problem about Division 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.

27.8 Equations with whole numbers

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: In 610,451, what is the value of the digit 4 in the 100 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 400

Worked Example 2

Problem: In 963,584, what is the value of the digit 8 in the 10 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 80

Worked Example 3

Problem: In 663,748, what is the value of the digit 6 in the 10,000 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 60,000

Worked Example 4

Problem: In 565,480, what is the value of the digit 4 in the 100 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 400

Worked Example 5

Problem: In 47,051, what is the value of the digit 4 in the 10,000 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 40,000

Worked Example 6

Problem: In 294,668, what is the value of the digit 2 in the 100,000 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 200,000

Worked Example 7

Problem: In 650,780, what is the value of the digit 7 in the 100 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 700

Worked Example 8

Problem: In 665,376, what is the value of the digit 5 in the 1,000 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 5,000

Worked Example 9

Problem: In 70,320, what is the value of the digit 0 in the 100,000 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 0

Worked Example 10

Problem: In 168,093, what is the value of the digit 6 in the 10,000 place?

Locate the requested place.
Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 60,000

Practice Exercise

Create one new Grade 6 problem about Equations with whole numbers. 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.

27.9 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 56.609?

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 2

Problem: What digit is in the tenths place of 73.552?

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: 5

Worked Example 3

Problem: What digit is in the tenths place of 81.84?

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 4

Problem: What digit is in the tenths place of 18.526?

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: 5

Worked Example 5

Problem: What digit is in the tenths place of 95.976?

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: 9

Worked Example 6

Problem: What digit is in the tenths place of 9.65?

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 7

Problem: What digit is in the tenths place of 46.806?

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 8

Problem: What digit is in the tenths place of 95.122?

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 66.598?

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: 5

Worked Example 10

Problem: What digit is in the tenths place of 22.366?

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

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.

27.10 Checking solutions

Checking solutions is a Grade 6 mathematics idea in Solving One-Step 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 Checking solutions to analyze the values 3 and 11. What should be checked first?

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

Very beginner explanation: Checking solutions is a Grade 6 mathematics idea in Solving One-Step 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 Checking solutions to analyze the values 22 and 14. What should be checked first?

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

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

Worked Example 3

Problem: Use Checking solutions to analyze the values 12 and 11. What should be checked first?

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

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

Worked Example 4

Problem: Use Checking solutions to analyze the values 28 and 18. What should be checked first?

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

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

Worked Example 5

Problem: Use Checking solutions to analyze the values 12 and 9. What should be checked first?

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

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

Worked Example 6

Problem: Use Checking solutions to analyze the values 16 and 14. What should be checked first?

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

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

Worked Example 7

Problem: Use Checking solutions to analyze the values 23 and 7. What should be checked first?

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

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

Worked Example 8

Problem: Use Checking solutions to analyze the values 29 and 2. What should be checked first?

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

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

Worked Example 9

Problem: Use Checking solutions to analyze the values 17 and 14. What should be checked first?

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

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

Worked Example 10

Problem: Use Checking solutions to analyze the values 18 and 8. What should be checked first?

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

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

Practice Exercise

Create one new Grade 6 problem about Checking 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.

27.11 Writing equations from word problems

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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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 Writing equations from word 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.

27.12 Real-life one-step equations

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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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.

Simplify each side if needed.
Use inverse operations to isolate the variable.
Keep the relationship balanced.
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 Real-life one-step 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.

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30 Review Questions and Answers

Q1. What is important to understand about Meaning of equation?

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

Q2. What is important to understand about Equality and balance?

Answer: Equality and balance is a Grade 6 mathematics idea in Solving One-Step 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 Inverse operations?

Answer: A ratio compares two quantities by division.

Q4. What is important to understand about Addition equations?

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

Q5. What is important to understand about Subtraction equations?

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

Q6. What is important to understand about Multiplication equations?

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

Q7. What is important to understand about Division equations?

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

Q8. What is important to understand about Equations with whole numbers?

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

Q9. 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.

Q10. What is important to understand about Checking solutions?

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

Q11. What is important to understand about Writing equations from word problems?

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

Q12. What is important to understand about Real-life one-step equations?

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.