Unit 2 · Topic 3

Percent Problems

Overview

Solve tax, tip, discount, markup, and percent-change problems.

Topic 3 of 3~59 min
Unit overview

The lesson

This lesson teaches Percent Problems. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.

Percent means 'per 100'

To find a percent of a number, change the percent to a decimal and multiply. 25% = 0.25, so 25% of 80 is 0.25 × 80 = 20.

Percent means "out of 100." 25% is 25 per hundred, or 25/100, or 0.25 depending on what form helps you calculate.

To find a percent of a number, convert the percent to a decimal and multiply. To find what percent one number is of another, divide and multiply by 100.

Tax, tip, discount, and markup

When you study tax, tip, discount, and markup, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

  1. 1Find the percent amount (the tax, tip, or discount).
  2. 2For tax, tip, or markup, add it to the original.
  3. 3For a discount, subtract it from the original.

Percent means "out of 100." 25% is 25 per hundred, or 25/100, or 0.25 depending on what form helps you calculate.

To find a percent of a number, convert the percent to a decimal and multiply. To find what percent one number is of another, divide and multiply by 100.

Worked example

A $40 shirt is 30% off. What is the sale price?

  1. 1Discount = 0.30 × 40 = 12.
  2. 2Sale price = 40 - 12 = 28.
  3. 3A shortcut: pay 70%, so 0.70 × 40 = 28.

Percent means "out of 100." 25% is 25 per hundred, or 25/100, or 0.25 depending on what form helps you calculate.

To find a percent of a number, convert the percent to a decimal and multiply. To find what percent one number is of another, divide and multiply by 100.

Why this matters

Percent Problems shows up constantly in solve tax, tip, discount, markup, and percent-change problems. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

Key ideas from this lesson

  1. Percent means 'per 100'
  2. Tax, tip, discount, and markup
  3. Find the percent amount (the tax, tip, or discount).
  4. For tax, tip, or markup, add it to the original.
  5. For a discount, subtract it from the original.

Video walkthrough

Math Antics

Finding a Percent of a Number

Two methods for finding a percent of any amount.

Watch on YouTube
Math Antics

Calculating Percent Change

The formula for percent increase and decrease.

Watch on YouTube

Practice

For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.

Exercise 1

Try it yourself

Find 18% of $250.

Step-by-step solution

  1. 118% = 0.18.
  2. 20.18 × 250 = 45.
  3. 318% of $250 is $45.

Exercise 2

Try it yourself

A $80 item is discounted 25%. What is the sale price?

Step-by-step solution

  1. 1Discount = 0.25 × 80 = 20.
  2. 2Sale price = 80 − 20 = 60.
  3. 3Shortcut: pay 75% → 0.75 × 80 = 60.

Exercise 3

Try it yourself

A meal costs $42. You leave a 15% tip. What is the total bill?

Step-by-step solution

  1. 1Tip = 0.15 × 42 = 6.30.
  2. 2Total = 42 + 6.30 = 48.30.

Exercise 4

Try it yourself

A price rises from $120 to $150. What is the percent increase?

Step-by-step solution

  1. 1Change = 150 − 120 = 30.
  2. 2Percent change = 30 ÷ 120 × 100 = 25%.

Exercise 5

Try it yourself

A $95 jacket has 8% sales tax. What is the total cost?

Step-by-step solution

  1. 1Tax = 0.08 × 95 = 7.60.
  2. 2Total = 95 + 7.60 = 102.60.

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Percent Problems

Question 1 of 5

Easy

A $60 jacket is marked up 20%. What is the new price?

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