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

Lesson 5: Percents

In this Grade 6 lesson from Big Ideas Math, Course 1 (Chapter 5: Ratios and Rates), students learn how percents relate to ratios and fractions by writing percents as fractions with a denominator of 100 and converting fractions to percents using equivalent fractions. The lesson covers key skills such as simplifying percent-based fractions, converting values like 35% to 7/20, and applying percent reasoning to real-world problems, aligned to standard 6.RP.3c.

Section 1

The Meaning of Percent

Property

A percent is a ratio that compares a number to 100.
The symbol % means "per hundred," so any percent can be written as a fraction with a denominator of 100.

p%=p100p\% = \frac{p}{100}

Section 2

Convert a percent to a fraction

Property

To convert a percent to a fraction:

Step 1. Write the percent as a ratio with the denominator 100.

Step 2. Simplify the fraction if possible.

Section 3

Convert Fractions to Percents

Property

To convert a fraction to a percent, you can create an equivalent fraction with a denominator of 100. The numerator of the new fraction is the percent value.

partwhole=x100=x%\frac{\text{part}}{\text{whole}} = \frac{x}{100} = x\%

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

The Meaning of Percent

Property

A percent is a ratio that compares a number to 100.
The symbol % means "per hundred," so any percent can be written as a fraction with a denominator of 100.

p%=p100p\% = \frac{p}{100}

Section 2

Convert a percent to a fraction

Property

To convert a percent to a fraction:

Step 1. Write the percent as a ratio with the denominator 100.

Step 2. Simplify the fraction if possible.

Section 3

Convert Fractions to Percents

Property

To convert a fraction to a percent, you can create an equivalent fraction with a denominator of 100. The numerator of the new fraction is the percent value.

partwhole=x100=x%\frac{\text{part}}{\text{whole}} = \frac{x}{100} = x\%