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Chapter 14: Percent Increase, Decrease, and Change

Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.

Grade 8Beginner Friendly5+ Examples Per TopicPractice30 Q&A
Estimated reading time0% read
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What this chapter covers

This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.

14.1 Original amount

Original amount is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Where is the point (2,3) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Worked Example 2

Problem: Where is the point (-4,5) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 3

Problem: Where is the point (-3,-2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 4

Problem: Where is the point (6,-1) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 5

Problem: Where is the point (0,4) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 6

Problem: Where is the point (5,0) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: on an axis

Worked Example 7

Problem: Where is the point (-7,2) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant II

Worked Example 8

Problem: Where is the point (1,-6) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant IV

Worked Example 9

Problem: Where is the point (-2,-8) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant III

Worked Example 10

Problem: Where is the point (8,7) located?

  1. Move horizontally using x.
  2. Move vertically using y.
  3. Identify the quadrant or axis.

Very beginner explanation: Ordered pairs are always written (x, y): horizontal first, vertical second.

Answer: Quadrant I

Practice exercise

Create one new Grade 8 problem involving Original amount. Show the important steps, include units when needed, and explain how you checked the answer.

14.2 New amount

New amount is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: New amount: Explain New amount in one simple sentence.

  1. Look at the words in “New amount”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: New amount is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: New amount: A student says, “I can use New amount without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: New amount: What is the first step when solving a problem about New amount?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: New amount: After solving a New amount problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: New amount: Give one way New amount could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: New amount can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: New amount: Which representation could help explain New amount: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: New amount: A student gets an answer for New amount but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: New amount: Why can estimation help before a detailed New amount calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: New amount: How can you test whether your rule for New amount works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: New amount: How would you teach New amount to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving New amount. Show the important steps, include units when needed, and explain how you checked the answer.

14.3 Amount of increase

Amount of increase is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Increase 80 by 10%.

  1. Find the increase: 0.1 × 80 = 8.
  2. Add it to the original: 80 + 8.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 88

Worked Example 2

Problem: Increase 60 by 25%.

  1. Find the increase: 0.25 × 60 = 15.
  2. Add it to the original: 60 + 15.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 75

Worked Example 3

Problem: Increase 120 by 15%.

  1. Find the increase: 0.15 × 120 = 18.
  2. Add it to the original: 120 + 18.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 138

Worked Example 4

Problem: Increase 250 by 5%.

  1. Find the increase: 0.05 × 250 = 12.5.
  2. Add it to the original: 250 + 12.5.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 262.5

Worked Example 5

Problem: Increase 75 by 13%.

  1. Find the increase: 0.13 × 75 = 9.75.
  2. Add it to the original: 75 + 9.75.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 84.75

Worked Example 6

Problem: Increase 140 by 35%.

  1. Find the increase: 0.35 × 140 = 49.
  2. Add it to the original: 140 + 49.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 189

Worked Example 7

Problem: Increase 500 by 8%.

  1. Find the increase: 0.08 × 500 = 40.
  2. Add it to the original: 500 + 40.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 540

Worked Example 8

Problem: Increase 45 by 60%.

  1. Find the increase: 0.6 × 45 = 27.
  2. Add it to the original: 45 + 27.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 72

Worked Example 9

Problem: Increase 320 by 2.5%.

  1. Find the increase: 0.025 × 320 = 8.
  2. Add it to the original: 320 + 8.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 328

Worked Example 10

Problem: Increase 64 by 125%.

  1. Find the increase: 1.25 × 64 = 80.
  2. Add it to the original: 64 + 80.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 144

Practice exercise

Create one new Grade 8 problem involving Amount of increase. Show the important steps, include units when needed, and explain how you checked the answer.

14.4 Amount of decrease

Amount of decrease is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Decrease 80 by 10%.

  1. Find the decrease: 0.1 × 80 = 8.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 72

Worked Example 2

Problem: Decrease 60 by 25%.

  1. Find the decrease: 0.25 × 60 = 15.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 45

Worked Example 3

Problem: Decrease 120 by 15%.

  1. Find the decrease: 0.15 × 120 = 18.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 102

Worked Example 4

Problem: Decrease 250 by 5%.

  1. Find the decrease: 0.05 × 250 = 12.5.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 237.5

Worked Example 5

Problem: Decrease 75 by 13%.

  1. Find the decrease: 0.13 × 75 = 9.75.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 65.25

Worked Example 6

Problem: Decrease 140 by 35%.

  1. Find the decrease: 0.35 × 140 = 49.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 91

Worked Example 7

Problem: Decrease 500 by 8%.

  1. Find the decrease: 0.08 × 500 = 40.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 460

Worked Example 8

Problem: Decrease 45 by 60%.

  1. Find the decrease: 0.6 × 45 = 27.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 18

Worked Example 9

Problem: Decrease 320 by 2.5%.

  1. Find the decrease: 0.025 × 320 = 8.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 312

Worked Example 10

Problem: Decrease 64 by 125%.

  1. Find the decrease: 1.25 × 64 = 80.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: -16

Practice exercise

Create one new Grade 8 problem involving Amount of decrease. Show the important steps, include units when needed, and explain how you checked the answer.

14.5 Percent increase

Percent means per hundred, so 35% means 35 out of 100. In this section, the focus is Percent increase.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Increase 80 by 10%.

  1. Find the increase: 0.1 × 80 = 8.
  2. Add it to the original: 80 + 8.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 88

Worked Example 2

Problem: Increase 60 by 25%.

  1. Find the increase: 0.25 × 60 = 15.
  2. Add it to the original: 60 + 15.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 75

Worked Example 3

Problem: Increase 120 by 15%.

  1. Find the increase: 0.15 × 120 = 18.
  2. Add it to the original: 120 + 18.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 138

Worked Example 4

Problem: Increase 250 by 5%.

  1. Find the increase: 0.05 × 250 = 12.5.
  2. Add it to the original: 250 + 12.5.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 262.5

Worked Example 5

Problem: Increase 75 by 13%.

  1. Find the increase: 0.13 × 75 = 9.75.
  2. Add it to the original: 75 + 9.75.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 84.75

Worked Example 6

Problem: Increase 140 by 35%.

  1. Find the increase: 0.35 × 140 = 49.
  2. Add it to the original: 140 + 49.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 189

Worked Example 7

Problem: Increase 500 by 8%.

  1. Find the increase: 0.08 × 500 = 40.
  2. Add it to the original: 500 + 40.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 540

Worked Example 8

Problem: Increase 45 by 60%.

  1. Find the increase: 0.6 × 45 = 27.
  2. Add it to the original: 45 + 27.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 72

Worked Example 9

Problem: Increase 320 by 2.5%.

  1. Find the increase: 0.025 × 320 = 8.
  2. Add it to the original: 320 + 8.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 328

Worked Example 10

Problem: Increase 64 by 125%.

  1. Find the increase: 1.25 × 64 = 80.
  2. Add it to the original: 64 + 80.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 144

Practice exercise

Create one new Grade 8 problem involving Percent increase. Show the important steps, include units when needed, and explain how you checked the answer.

14.6 Percent decrease

Percent means per hundred, so 35% means 35 out of 100. In this section, the focus is Percent decrease.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Decrease 80 by 10%.

  1. Find the decrease: 0.1 × 80 = 8.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 72

Worked Example 2

Problem: Decrease 60 by 25%.

  1. Find the decrease: 0.25 × 60 = 15.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 45

Worked Example 3

Problem: Decrease 120 by 15%.

  1. Find the decrease: 0.15 × 120 = 18.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 102

Worked Example 4

Problem: Decrease 250 by 5%.

  1. Find the decrease: 0.05 × 250 = 12.5.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 237.5

Worked Example 5

Problem: Decrease 75 by 13%.

  1. Find the decrease: 0.13 × 75 = 9.75.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 65.25

Worked Example 6

Problem: Decrease 140 by 35%.

  1. Find the decrease: 0.35 × 140 = 49.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 91

Worked Example 7

Problem: Decrease 500 by 8%.

  1. Find the decrease: 0.08 × 500 = 40.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 460

Worked Example 8

Problem: Decrease 45 by 60%.

  1. Find the decrease: 0.6 × 45 = 27.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 18

Worked Example 9

Problem: Decrease 320 by 2.5%.

  1. Find the decrease: 0.025 × 320 = 8.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 312

Worked Example 10

Problem: Decrease 64 by 125%.

  1. Find the decrease: 1.25 × 64 = 80.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: -16

Practice exercise

Create one new Grade 8 problem involving Percent decrease. Show the important steps, include units when needed, and explain how you checked the answer.

14.7 Finding final amount after increase

Finding final amount after increase is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Increase 80 by 10%.

  1. Find the increase: 0.1 × 80 = 8.
  2. Add it to the original: 80 + 8.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 88

Worked Example 2

Problem: Increase 60 by 25%.

  1. Find the increase: 0.25 × 60 = 15.
  2. Add it to the original: 60 + 15.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 75

Worked Example 3

Problem: Increase 120 by 15%.

  1. Find the increase: 0.15 × 120 = 18.
  2. Add it to the original: 120 + 18.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 138

Worked Example 4

Problem: Increase 250 by 5%.

  1. Find the increase: 0.05 × 250 = 12.5.
  2. Add it to the original: 250 + 12.5.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 262.5

Worked Example 5

Problem: Increase 75 by 13%.

  1. Find the increase: 0.13 × 75 = 9.75.
  2. Add it to the original: 75 + 9.75.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 84.75

Worked Example 6

Problem: Increase 140 by 35%.

  1. Find the increase: 0.35 × 140 = 49.
  2. Add it to the original: 140 + 49.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 189

Worked Example 7

Problem: Increase 500 by 8%.

  1. Find the increase: 0.08 × 500 = 40.
  2. Add it to the original: 500 + 40.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 540

Worked Example 8

Problem: Increase 45 by 60%.

  1. Find the increase: 0.6 × 45 = 27.
  2. Add it to the original: 45 + 27.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 72

Worked Example 9

Problem: Increase 320 by 2.5%.

  1. Find the increase: 0.025 × 320 = 8.
  2. Add it to the original: 320 + 8.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 328

Worked Example 10

Problem: Increase 64 by 125%.

  1. Find the increase: 1.25 × 64 = 80.
  2. Add it to the original: 64 + 80.

Very beginner explanation: Percent increase uses the original amount as the base.

Answer: 144

Practice exercise

Create one new Grade 8 problem involving Finding final amount after increase. Show the important steps, include units when needed, and explain how you checked the answer.

14.8 Finding final amount after decrease

Finding final amount after decrease is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Decrease 80 by 10%.

  1. Find the decrease: 0.1 × 80 = 8.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 72

Worked Example 2

Problem: Decrease 60 by 25%.

  1. Find the decrease: 0.25 × 60 = 15.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 45

Worked Example 3

Problem: Decrease 120 by 15%.

  1. Find the decrease: 0.15 × 120 = 18.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 102

Worked Example 4

Problem: Decrease 250 by 5%.

  1. Find the decrease: 0.05 × 250 = 12.5.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 237.5

Worked Example 5

Problem: Decrease 75 by 13%.

  1. Find the decrease: 0.13 × 75 = 9.75.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 65.25

Worked Example 6

Problem: Decrease 140 by 35%.

  1. Find the decrease: 0.35 × 140 = 49.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 91

Worked Example 7

Problem: Decrease 500 by 8%.

  1. Find the decrease: 0.08 × 500 = 40.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 460

Worked Example 8

Problem: Decrease 45 by 60%.

  1. Find the decrease: 0.6 × 45 = 27.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 18

Worked Example 9

Problem: Decrease 320 by 2.5%.

  1. Find the decrease: 0.025 × 320 = 8.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: 312

Worked Example 10

Problem: Decrease 64 by 125%.

  1. Find the decrease: 1.25 × 64 = 80.
  2. Subtract it from the original.

Very beginner explanation: Percent decrease means remove a percentage of the original amount.

Answer: -16

Practice exercise

Create one new Grade 8 problem involving Finding final amount after decrease. Show the important steps, include units when needed, and explain how you checked the answer.

14.9 Reverse-percent problems

Percent means per hundred, so 35% means 35 out of 100. In this section, the focus is Reverse-percent problems.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find 10% of 80.

  1. Convert 10% to decimal 0.1.
  2. Multiply 0.1 × 80.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 2

Problem: Find 25% of 60.

  1. Convert 25% to decimal 0.25.
  2. Multiply 0.25 × 60.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 15

Worked Example 3

Problem: Find 15% of 120.

  1. Convert 15% to decimal 0.15.
  2. Multiply 0.15 × 120.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 18

Worked Example 4

Problem: Find 5% of 250.

  1. Convert 5% to decimal 0.05.
  2. Multiply 0.05 × 250.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 12.5

Worked Example 5

Problem: Find 13% of 75.

  1. Convert 13% to decimal 0.13.
  2. Multiply 0.13 × 75.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 9.75

Worked Example 6

Problem: Find 35% of 140.

  1. Convert 35% to decimal 0.35.
  2. Multiply 0.35 × 140.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 49

Worked Example 7

Problem: Find 8% of 500.

  1. Convert 8% to decimal 0.08.
  2. Multiply 0.08 × 500.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 40

Worked Example 8

Problem: Find 60% of 45.

  1. Convert 60% to decimal 0.6.
  2. Multiply 0.6 × 45.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 27

Worked Example 9

Problem: Find 2.5% of 320.

  1. Convert 2.5% to decimal 0.025.
  2. Multiply 0.025 × 320.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 10

Problem: Find 125% of 64.

  1. Convert 125% to decimal 1.25.
  2. Multiply 1.25 × 64.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 80

Practice exercise

Create one new Grade 8 problem involving Reverse-percent problems. Show the important steps, include units when needed, and explain how you checked the answer.

14.10 Population change

A population is the entire group being studied. In this section, the focus is Population change.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find 10% of 80.

  1. Convert 10% to decimal 0.1.
  2. Multiply 0.1 × 80.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 2

Problem: Find 25% of 60.

  1. Convert 25% to decimal 0.25.
  2. Multiply 0.25 × 60.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 15

Worked Example 3

Problem: Find 15% of 120.

  1. Convert 15% to decimal 0.15.
  2. Multiply 0.15 × 120.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 18

Worked Example 4

Problem: Find 5% of 250.

  1. Convert 5% to decimal 0.05.
  2. Multiply 0.05 × 250.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 12.5

Worked Example 5

Problem: Find 13% of 75.

  1. Convert 13% to decimal 0.13.
  2. Multiply 0.13 × 75.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 9.75

Worked Example 6

Problem: Find 35% of 140.

  1. Convert 35% to decimal 0.35.
  2. Multiply 0.35 × 140.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 49

Worked Example 7

Problem: Find 8% of 500.

  1. Convert 8% to decimal 0.08.
  2. Multiply 0.08 × 500.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 40

Worked Example 8

Problem: Find 60% of 45.

  1. Convert 60% to decimal 0.6.
  2. Multiply 0.6 × 45.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 27

Worked Example 9

Problem: Find 2.5% of 320.

  1. Convert 2.5% to decimal 0.025.
  2. Multiply 0.025 × 320.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 10

Problem: Find 125% of 64.

  1. Convert 125% to decimal 1.25.
  2. Multiply 1.25 × 64.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 80

Practice exercise

Create one new Grade 8 problem involving Population change. Show the important steps, include units when needed, and explain how you checked the answer.

14.11 Attendance change

Attendance change is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find 10% of 80.

  1. Convert 10% to decimal 0.1.
  2. Multiply 0.1 × 80.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 2

Problem: Find 25% of 60.

  1. Convert 25% to decimal 0.25.
  2. Multiply 0.25 × 60.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 15

Worked Example 3

Problem: Find 15% of 120.

  1. Convert 15% to decimal 0.15.
  2. Multiply 0.15 × 120.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 18

Worked Example 4

Problem: Find 5% of 250.

  1. Convert 5% to decimal 0.05.
  2. Multiply 0.05 × 250.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 12.5

Worked Example 5

Problem: Find 13% of 75.

  1. Convert 13% to decimal 0.13.
  2. Multiply 0.13 × 75.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 9.75

Worked Example 6

Problem: Find 35% of 140.

  1. Convert 35% to decimal 0.35.
  2. Multiply 0.35 × 140.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 49

Worked Example 7

Problem: Find 8% of 500.

  1. Convert 8% to decimal 0.08.
  2. Multiply 0.08 × 500.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 40

Worked Example 8

Problem: Find 60% of 45.

  1. Convert 60% to decimal 0.6.
  2. Multiply 0.6 × 45.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 27

Worked Example 9

Problem: Find 2.5% of 320.

  1. Convert 2.5% to decimal 0.025.
  2. Multiply 0.025 × 320.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 10

Problem: Find 125% of 64.

  1. Convert 125% to decimal 1.25.
  2. Multiply 1.25 × 64.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 80

Practice exercise

Create one new Grade 8 problem involving Attendance change. Show the important steps, include units when needed, and explain how you checked the answer.

14.12 Price change

Price change is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find 10% of 80.

  1. Convert 10% to decimal 0.1.
  2. Multiply 0.1 × 80.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 2

Problem: Find 25% of 60.

  1. Convert 25% to decimal 0.25.
  2. Multiply 0.25 × 60.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 15

Worked Example 3

Problem: Find 15% of 120.

  1. Convert 15% to decimal 0.15.
  2. Multiply 0.15 × 120.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 18

Worked Example 4

Problem: Find 5% of 250.

  1. Convert 5% to decimal 0.05.
  2. Multiply 0.05 × 250.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 12.5

Worked Example 5

Problem: Find 13% of 75.

  1. Convert 13% to decimal 0.13.
  2. Multiply 0.13 × 75.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 9.75

Worked Example 6

Problem: Find 35% of 140.

  1. Convert 35% to decimal 0.35.
  2. Multiply 0.35 × 140.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 49

Worked Example 7

Problem: Find 8% of 500.

  1. Convert 8% to decimal 0.08.
  2. Multiply 0.08 × 500.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 40

Worked Example 8

Problem: Find 60% of 45.

  1. Convert 60% to decimal 0.6.
  2. Multiply 0.6 × 45.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 27

Worked Example 9

Problem: Find 2.5% of 320.

  1. Convert 2.5% to decimal 0.025.
  2. Multiply 0.025 × 320.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 10

Problem: Find 125% of 64.

  1. Convert 125% to decimal 1.25.
  2. Multiply 1.25 × 64.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 80

Practice exercise

Create one new Grade 8 problem involving Price change. Show the important steps, include units when needed, and explain how you checked the answer.

14.13 Multi-step percent problems

Percent means per hundred, so 35% means 35 out of 100. In this section, the focus is Multi-step percent problems.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find 10% of 80.

  1. Convert 10% to decimal 0.1.
  2. Multiply 0.1 × 80.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 2

Problem: Find 25% of 60.

  1. Convert 25% to decimal 0.25.
  2. Multiply 0.25 × 60.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 15

Worked Example 3

Problem: Find 15% of 120.

  1. Convert 15% to decimal 0.15.
  2. Multiply 0.15 × 120.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 18

Worked Example 4

Problem: Find 5% of 250.

  1. Convert 5% to decimal 0.05.
  2. Multiply 0.05 × 250.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 12.5

Worked Example 5

Problem: Find 13% of 75.

  1. Convert 13% to decimal 0.13.
  2. Multiply 0.13 × 75.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 9.75

Worked Example 6

Problem: Find 35% of 140.

  1. Convert 35% to decimal 0.35.
  2. Multiply 0.35 × 140.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 49

Worked Example 7

Problem: Find 8% of 500.

  1. Convert 8% to decimal 0.08.
  2. Multiply 0.08 × 500.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 40

Worked Example 8

Problem: Find 60% of 45.

  1. Convert 60% to decimal 0.6.
  2. Multiply 0.6 × 45.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 27

Worked Example 9

Problem: Find 2.5% of 320.

  1. Convert 2.5% to decimal 0.025.
  2. Multiply 0.025 × 320.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 8

Worked Example 10

Problem: Find 125% of 64.

  1. Convert 125% to decimal 1.25.
  2. Multiply 1.25 × 64.

Very beginner explanation: “Of” usually means multiply in a percent-of-a-number problem.

Answer: 80

Practice exercise

Create one new Grade 8 problem involving Multi-step percent problems. Show the important steps, include units when needed, and explain how you checked the answer.

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Chapter 14 Review Questions and Answers

Q1. What is important to remember about Original amount?

Answer: Original amount is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q2. What is important to remember about New amount?

Answer: New amount is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q3. What is important to remember about Amount of increase?

Answer: Amount of increase is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q4. What is important to remember about Amount of decrease?

Answer: Amount of decrease is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q5. What is important to remember about Percent increase?

Answer: Percent means per hundred, so 35% means 35 out of 100. In this section, the focus is Percent increase.

Q6. What is important to remember about Percent decrease?

Answer: Percent means per hundred, so 35% means 35 out of 100. In this section, the focus is Percent decrease.

Q7. What is important to remember about Finding final amount after increase?

Answer: Finding final amount after increase is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q8. What is important to remember about Finding final amount after decrease?

Answer: Finding final amount after decrease is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Reverse-percent problems?

Answer: Percent means per hundred, so 35% means 35 out of 100. In this section, the focus is Reverse-percent problems.

Q10. What is important to remember about Population change?

Answer: A population is the entire group being studied. In this section, the focus is Population change.

Q11. What is important to remember about Attendance change?

Answer: Attendance change is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q12. What is important to remember about Price change?

Answer: Price change is an important Grade 8 concept in Percent Increase, Decrease, and Change. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q13. What is important to remember about Multi-step percent problems?

Answer: Percent means per hundred, so 35% means 35 out of 100. In this section, the focus is Multi-step percent problems.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a calculated answer is reasonable.

Q16. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q17. When should you round?

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

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.

Q23. Why are tables useful?

Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.

Q24. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer was obtained.

Q25. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.

Q26. When is a calculator useful?

Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.

Q27. Why compare more than one strategy?

Answer: Different strategies may make a problem easier and provide a way to verify the result.

Q28. What is mathematical communication?

Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.

Q29. What is mathematical modelling?

Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.

Q30. Why should assumptions be stated?

Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.