Learn on PengiBig Ideas Math, Course 1Chapter 5: Ratios and Rates

Lesson 6: Solving Percent Problems

In this Grade 6 lesson from Big Ideas Math, Course 1, students learn how to find the percent of a number and find the whole when given a part and a percent. The lesson covers mental math strategies using 10% and 1% as benchmarks, writing percents as fractions to multiply or divide, and using ratio tables to solve percent problems. Real-world applications such as calculating sales tax, tips, and service charges help students connect these skills to everyday situations.

Section 1

Finding the Part by Multiplying by the Percent Fraction

Property

To find the percent of a number (the part), convert the percent to a fraction and multiply it by the whole number.

Part=Percent (as a fraction)×Whole \text{Part} = \text{Percent (as a fraction)} \times \text{Whole}

Examples

  • What is 25%25\% of 8080?
25100×80=14×80=20 \frac{25}{100} \times 80 = \frac{1}{4} \times 80 = 20
  • Find 60%60\% of 5050.
60100×50=35×50=30 \frac{60}{100} \times 50 = \frac{3}{5} \times 50 = 30
  • What is 150%150\% of 4040?
150100×40=32×40=60 \frac{150}{100} \times 40 = \frac{3}{2} \times 40 = 60

Explanation

This method helps you calculate the "part" when you know the "percent" and the "whole". First, you must convert the percentage into its equivalent fraction by placing it over 100 and simplifying if possible. Then, multiply this fraction by the whole number to find the answer. This is a direct application of the concept that "of" in mathematics often means multiplication.

Section 2

Finding the Whole by Dividing by the Percent Fraction

Property

To find the whole when the part and percent are known, you can divide the part by the percent expressed as a fraction. This is equivalent to multiplying the part by the reciprocal of the percent fraction.

Whole=PartPercent (as a fraction)=Part×Reciprocal of Percent Fraction \text{Whole} = \frac{\text{Part}}{\text{Percent (as a fraction)}} = \text{Part} \times \text{Reciprocal of Percent Fraction}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Finding the Part by Multiplying by the Percent Fraction

Property

To find the percent of a number (the part), convert the percent to a fraction and multiply it by the whole number.

Part=Percent (as a fraction)×Whole \text{Part} = \text{Percent (as a fraction)} \times \text{Whole}

Examples

  • What is 25%25\% of 8080?
25100×80=14×80=20 \frac{25}{100} \times 80 = \frac{1}{4} \times 80 = 20
  • Find 60%60\% of 5050.
60100×50=35×50=30 \frac{60}{100} \times 50 = \frac{3}{5} \times 50 = 30
  • What is 150%150\% of 4040?
150100×40=32×40=60 \frac{150}{100} \times 40 = \frac{3}{2} \times 40 = 60

Explanation

This method helps you calculate the "part" when you know the "percent" and the "whole". First, you must convert the percentage into its equivalent fraction by placing it over 100 and simplifying if possible. Then, multiply this fraction by the whole number to find the answer. This is a direct application of the concept that "of" in mathematics often means multiplication.

Section 2

Finding the Whole by Dividing by the Percent Fraction

Property

To find the whole when the part and percent are known, you can divide the part by the percent expressed as a fraction. This is equivalent to multiplying the part by the reciprocal of the percent fraction.

Whole=PartPercent (as a fraction)=Part×Reciprocal of Percent Fraction \text{Whole} = \frac{\text{Part}}{\text{Percent (as a fraction)}} = \text{Part} \times \text{Reciprocal of Percent Fraction}

Examples