Introduction

Percent Increase and Decrease is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.

In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with percent increase and decrease.

What Is Percent Increase and Decrease?

Percent Increase and Decrease means choosing a model, naming what each number means, and explaining the strategy.

The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.

Understanding Percent Increase and Decrease

Before solving, students should slow down and decide what each number, shape, unit, or label represents.

  • Read the question carefully and identify what is being asked.
  • Choose a model, equation, table, or diagram that matches the situation.
  • Solve one step at a time and keep units or labels attached.
  • Use the answer explanation to check that the result makes sense.

Visual Models

Visual Model 1

Question: A student made an error. She claimed that a \($200\) item with a \(50\%\) increase costs \($250\). What is her mistake?

Visual Model 1

  • A. She forgot to calculate \(50\%\) of the original price correctly.
  • B. The answer is actually correct.
  • C. She used the new price as the base for the percent, not the original.
  • D. She computed \(50\%\) of \($200\) as \($50\) instead of \($100\).

Why it works: Correct: increase \(= 50\% \times $200 = $100\); new price \(= $200 + $100 = $300\). She incorrectly calculated \(50\%\) of \($200\) as \($50\) and added that to \($200\) to get \($250\).

Answer: She computed \(50\%\) of \($200\) as \($50\) instead of \($100\).

Visual Model 2

Question: A bar graph shows that an item has been reduced. The shaded (coral) region represents \(75\%\) of the original price of \($80\). What is the percent decrease?

Visual Model 2

  • A. \(75\%\)
  • B. \(30\%\)
  • C. \(20\%\)
  • D. \(25\%\)

Why it works: If the new price is \(75\%\) of the original, the item was reduced by \(100\%-75\%=25\%\).

Answer: \(25\%\)

Worked Examples

Example 1

Question: A double number line shows a price increase from \($80\) to \($100\). What is the percent increase?

Example 1

  • A. \(100\%\)
  • B. \(20\%\)
  • C. \(80\%\)
  • D. \(25\%\)
  1. Change \(= $100 - $80 = $20\).
  2. Percent increase \(= \frac{20}{80}\times100\% = 25\%\).

Answer: \(25\%\)

Example 2

Question: A before-and-after bar diagram shows a quantity increasing from \($100\) to \($160\). What is the percent increase?

Example 2

  • A. \(40\%\)
  • B. \(62.5\%\)
  • C. \(37.5\%\)
  • D. \(60\%\)
  1. Change \(= $160 - $100 = $60\).
  2. Percent increase \(= \frac{60}{100}\times100\% = 60\%\).

Answer: \(60\%\)

Example 3

Question: A diagram shows an original price of \($250\) increased to \($312.50\). What is the percent increase?

Example 3

  • A. \(20\%\)
  • B. \(62.50\%\)
  • C. \(30\%\)
  • D. \(25\%\)
  1. Change \(= $312.50 - $250 = $62.50\).
  2. Percent increase \(= \frac{62.50}{250}\times100\% = 25\%\).

Answer: \(25\%\)

Real-World Word Problems

Problem 1

Question: A pair of jeans originally costs \($50\). The store raises the price to \($60\). What is the percent increase?

  • A. \(10\%\)
  • B. \(16.7\%\)
  • C. \(20\%\)
  • D. \(30\%\)

Why it works: Percent increase \(=\frac{\text{change}}{\text{original}}\times100\%=\frac{60-50}{50}\times100\%=20\%\).

Answer: \(20\%\)

Problem 2

Question: A tablet costs \($400\) and is discounted by \(25\%\). What is the new price?

  • A. \($100\)
  • B. \($375\)
  • C. \($325\)
  • D. \($300\)

Why it works: Discount amount \(= 25\% \times $400 = 0.25 \times $400 = $100\). New price \(= $400 - $100 = $300\).

Answer: \($300\)

Common Mistakes

  • Rushing before identifying what the numbers represent.
  • Choosing an operation that does not match the situation.
  • Dropping labels, units, or context from the answer.
  • Skipping the estimate or reasonableness check.

Strategy Tips

  • Underline the question being asked.
  • Use a model before jumping to computation.
  • Write an equation that matches the story or picture.
  • Explain the final answer in a sentence.

Practice Questions

Question 1

A restaurant bill was originally \($80\), and after a \(15\%\) increase, what is the new bill?

  • A. \($95\)
  • B. \($12\)
  • C. \($88\)
  • D. \($92\)

Question 2

The value of a car decreased from \($24\,000\) to \($18\,000\). What is the percent decrease?

  • A. \(33\%\)
  • B. \(20\%\)
  • C. \(16.7\%\)
  • D. \(25\%\)

Question 3

A student's test score improved from \(72\) to \(90\). What is the percent increase in the score?

  • A. \(18\%\)
  • B. \(20\%\)
  • C. \(25\%\)
  • D. \(80\%\)

Question 4

A store advertises "Save 30% on all winter coats!" If a coat originally costs \($120\), what is the sale price?

  • A. \($36\)
  • B. \($150\)
  • C. \($90\)
  • D. \($84\)

Question 5

The population of a town was \(5\,000\) and increased to \(6\,500\). What is the percent increase?

  • A. \(15\%\)
  • B. \(25\%\)
  • C. \(30\%\)
  • D. \(35\%\)

Question 6

An item originally marked at \($80\) is reduced to \($60\). What is the percent decrease?

  • A. \(20\%\)
  • B. \(33\%\)
  • C. \(30\%\)
  • D. \(25\%\)
Full Answer Explanations Click to show all answers and explanations

Question 1

Answer: \($92\)

Increase \(= 15\% \times $80 = 0.15 \times $80 = $12\). New bill \(= $80 + $12 = $92\).

Question 2

Answer: \(25\%\)

Percent decrease \(= \frac{24000-18000}{24000}\times100\% = \frac{6000}{24000}\times100\% = 25\%\).

Question 3

Answer: \(25\%\)

Percent increase \(= \frac{90-72}{72}\times100\% = \frac{18}{72}\times100\% = 25\%\).

Question 4

Answer: \($84\)

Savings \(= 30\% \times $120 = $36\). Sale price \(= $120 - $36 = $84\).

Question 5

Answer: \(30\%\)

Percent increase \(= \frac{6500-5000}{5000}\times100\% = \frac{1500}{5000}\times100\% = 30\%\).

Question 6

Answer: \(25\%\)

Percent decrease \(= \frac{80-60}{80}\times100\% = \frac{20}{80}\times100\% = 25\%\).

Timed practice quizzes

Related Quizzes

After studying Percent Increase and Decrease, open these two timed quizzes in a new tab for focused extra practice.

Connection to Standards

This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.

Summary

Percent Increase and Decrease becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.

GOLDEN RULE

Understand the model before choosing the operation.