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:

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

Cross multiply and solve for the part:

\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 $100\%$ representing the whole ( $w$ ), scale down to $1\%$ (or another friendly percent) by dividing, and then multiply to find the target percent ( $p\%$ ).

\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:

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

Examples

Find $150\%$ of $60$ .

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

100x = 60 \cdot 150

100x = 9000

x = 90

What is $225\%$ of $40$ ?

Using the decimal method, convert $225\%$ to $2.25$ .

2.25 \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.

Book overview

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Module 2: Fractions, Decimals, and Percents

Back to Reveal Math, Course 1

Lesson 1
2-1 Understand Percents
Learn Practice
Lesson 2
2-2 Percents Greater Than 100% and Less Than 1%
Learn Practice
Lesson 3
2-3 Relate Fractions, Decimals, and Percents
Learn Practice
Lesson 4Current
2-4 Find the Percent of a Number
Learn Practice
Lesson 5
2-5 Estimate the Percent of a Number
Learn Practice
Lesson 6
2-6 Find the Whole
Learn Practice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

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:

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

Cross multiply and solve for the part:

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

Section 2

Strategy: Ratio Tables for Percents

Property

\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:

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

Examples

Find $150\%$ of $60$ .

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

100x = 60 \cdot 150

100x = 9000

x = 90

What is $225\%$ of $40$ ?

Using the decimal method, convert $225\%$ to $2.25$ .

2.25 \times 40 = 90

Explanation

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Module 2: Fractions, Decimals, and Percents

Back to Reveal Math, Course 1

Lesson 1
2-1 Understand Percents
Learn Practice
Lesson 2
2-2 Percents Greater Than 100% and Less Than 1%
Learn Practice
Lesson 3
2-3 Relate Fractions, Decimals, and Percents
Learn Practice
Lesson 4Current
2-4 Find the Percent of a Number
Learn Practice
Lesson 5
2-5 Estimate the Percent of a Number
Learn Practice
Lesson 6
2-6 Find the Whole
Learn Practice

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

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:

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

Cross multiply and solve for the part:

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

Section 2

Strategy: Ratio Tables for Percents

Property

\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:

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

Examples

Find $150\%$ of $60$ .

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

100x = 60 \cdot 150

100x = 9000

x = 90

What is $225\%$ of $40$ ?

Using the decimal method, convert $225\%$ to $2.25$ .

2.25 \times 40 = 90

Explanation

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Module 2: Fractions, Decimals, and Percents

Back to Reveal Math, Course 1

Lesson 1
2-1 Understand Percents
Learn Practice
Lesson 2
2-2 Percents Greater Than 100% and Less Than 1%
Learn Practice
Lesson 3
2-3 Relate Fractions, Decimals, and Percents
Learn Practice
Lesson 4Current
2-4 Find the Percent of a Number
Learn Practice
Lesson 5
2-5 Estimate the Percent of a Number
Learn Practice
Lesson 6
2-6 Find the Whole
Learn Practice

2-4 Find the Percent of a Number

Property

Property

Property

Examples

Explanation

Module 2: Fractions, Decimals, and Percents

2-1 Understand Percents

2-2 Percents Greater Than 100% and Less Than 1%

2-3 Relate Fractions, Decimals, and Percents

2-4 Find the Percent of a Number

2-5 Estimate the Percent of a Number

2-6 Find the Whole

Lesson overview

Property

Property

Property

Examples

Explanation

Module 2: Fractions, Decimals, and Percents

2-1 Understand Percents

2-2 Percents Greater Than 100% and Less Than 1%

2-3 Relate Fractions, Decimals, and Percents

2-4 Find the Percent of a Number

2-5 Estimate the Percent of a Number

2-6 Find the Whole

2-1 Understand Percents

2-2 Percents Greater Than 100% and Less Than 1%

2-3 Relate Fractions, Decimals, and Percents

2-4 Find the Percent of a Number

2-5 Estimate the Percent of a Number

2-6 Find the Whole