Learn on PengiReveal Math, Course 1Module 2: Fractions, Decimals, and Percents

2-4 Find the Percent of a Number

In this Grade 6 lesson from Reveal Math, Course 1 (Module 2: Fractions, Decimals, and Percents), students learn how to find the percent of a number by reasoning about percent as a rate per 100. The lesson presents four methods — bar diagrams, ratio tables, equivalent ratios, and double number lines — to calculate values such as 20% of 50 or 30% of 240.

Section 1

Finding the part using the percent proportion

Property

To find the part when you know the percent and the whole, use the percent proportion:

partwhole=percent100\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}

Cross multiply and solve for the part:

part=percent×whole100\text{part} = \frac{\text{percent} \times \text{whole}}{100}

Section 2

Strategy: Ratio Tables for Percents

Property

A ratio table organizes equivalent ratios to find the percent of a number by scaling up or down. You start with 100%100\% representing the whole (ww), scale down to 1%1\% (or another friendly percent) by dividing, and then multiply to find the target percent (p%p\%).

Percent100%1%p%Valueww100p×w100 \begin{array}{|l|c|c|c|} \hline \text{Percent} & 100\% & 1\% & p\% \\ \hline \text{Value} & w & \frac{w}{100} & p \times \frac{w}{100} \\ \hline \end{array}

Section 3

Application: Percents Greater Than 100%

Property

When finding a percent of a number that is greater than 100%, the resulting part will be greater than the original whole. The relationship can be represented by the proportion:

partwhole=percent100\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}

Examples

  • Find 150%150\% of 6060.

Using the proportion x60=150100\frac{x}{60} = \frac{150}{100}, we can solve for xx.

100x=60⋅150100x = 60 \cdot 150
100x=9000100x = 9000
x=90x = 90
  • What is 225%225\% of 4040?

Using the decimal method, convert 225%225\% to 2.252.25.

2.25×40=902.25 \times 40 = 90

Explanation

A percent greater than 100% represents a quantity that is more than the original whole amount. To find a percent greater than 100% of a number, you can set up a proportion or convert the percent to a decimal and multiply. Since the percent is greater than 100, the resulting "part" will always be larger than the "whole". This concept is useful in contexts like calculating investment growth, price markups, or population increases over time.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Finding the part using the percent proportion

Property

To find the part when you know the percent and the whole, use the percent proportion:

partwhole=percent100\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}

Cross multiply and solve for the part:

part=percent×whole100\text{part} = \frac{\text{percent} \times \text{whole}}{100}

Section 2

Strategy: Ratio Tables for Percents

Property

A ratio table organizes equivalent ratios to find the percent of a number by scaling up or down. You start with 100%100\% representing the whole (ww), scale down to 1%1\% (or another friendly percent) by dividing, and then multiply to find the target percent (p%p\%).

Percent100%1%p%Valueww100p×w100 \begin{array}{|l|c|c|c|} \hline \text{Percent} & 100\% & 1\% & p\% \\ \hline \text{Value} & w & \frac{w}{100} & p \times \frac{w}{100} \\ \hline \end{array}

Section 3

Application: Percents Greater Than 100%

Property

When finding a percent of a number that is greater than 100%, the resulting part will be greater than the original whole. The relationship can be represented by the proportion:

partwhole=percent100\frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100}

Examples

  • Find 150%150\% of 6060.

Using the proportion x60=150100\frac{x}{60} = \frac{150}{100}, we can solve for xx.

100x=60⋅150100x = 60 \cdot 150
100x=9000100x = 9000
x=90x = 90
  • What is 225%225\% of 4040?

Using the decimal method, convert 225%225\% to 2.252.25.

2.25×40=902.25 \times 40 = 90

Explanation

A percent greater than 100% represents a quantity that is more than the original whole amount. To find a percent greater than 100% of a number, you can set up a proportion or convert the percent to a decimal and multiply. Since the percent is greater than 100, the resulting "part" will always be larger than the "whole". This concept is useful in contexts like calculating investment growth, price markups, or population increases over time.