Learn on PengienVision, Mathematics, Grade 5Chapter 7: Use Equivalent Fractions to Add and Subtract Fractions

Lesson 1: Estimate Sums and Differences of Fractions

In this Grade 5 lesson from enVision Mathematics Chapter 7, students learn how to estimate sums and differences of fractions by replacing each fraction with a benchmark value of 0, one-half, or 1. Students use number lines to determine which benchmark a fraction is closest to, then apply that skill to estimate answers without calculating exact values. This lesson builds the number sense foundation needed for adding and subtracting fractions with unlike denominators.

Section 1

Rounding Fractions by Comparing Numerator and Denominator

Property

To compare a fraction $\frac{a}{b}$ to the benchmarks $0$ , $\frac{1}{2}$ , and $1$ :

If the numerator $a$ is very small compared to the denominator $b$ , the fraction is close to $0$ .
If the numerator $a$ is about half of the denominator $b$ (i.e., $a \approx \frac{b}{2}$ ), the fraction is close to $\frac{1}{2}$ .
If the numerator $a$ is very close to the denominator $b$ , the fraction is close to $1$ .

Examples

Section 2

Estimate Sums and Differences of Fractions

Property

To estimate the sum or difference of fractions, first round each fraction to the nearest benchmark ( $0$ , $\frac{1}{2}$ , or $1$ ).
Then, add or subtract the rounded numbers to find the estimate.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Rounding Fractions by Comparing Numerator and Denominator

Property

To compare a fraction $\frac{a}{b}$ to the benchmarks $0$ , $\frac{1}{2}$ , and $1$ :

If the numerator $a$ is very small compared to the denominator $b$ , the fraction is close to $0$ .
If the numerator $a$ is about half of the denominator $b$ (i.e., $a \approx \frac{b}{2}$ ), the fraction is close to $\frac{1}{2}$ .
If the numerator $a$ is very close to the denominator $b$ , the fraction is close to $1$ .

Examples

Section 2

Estimate Sums and Differences of Fractions

Property

To estimate the sum or difference of fractions, first round each fraction to the nearest benchmark ( $0$ , $\frac{1}{2}$ , or $1$ ).
Then, add or subtract the rounded numbers to find the estimate.

Examples

Overview

Lesson overview

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

Overview

Section 1

Rounding Fractions by Comparing Numerator and Denominator

Property

To compare a fraction $\frac{a}{b}$ to the benchmarks $0$ , $\frac{1}{2}$ , and $1$ :

If the numerator $a$ is very small compared to the denominator $b$ , the fraction is close to $0$ .
If the numerator $a$ is about half of the denominator $b$ (i.e., $a \approx \frac{b}{2}$ ), the fraction is close to $\frac{1}{2}$ .
If the numerator $a$ is very close to the denominator $b$ , the fraction is close to $1$ .

Examples

Section 2

Estimate Sums and Differences of Fractions

Property

To estimate the sum or difference of fractions, first round each fraction to the nearest benchmark ( $0$ , $\frac{1}{2}$ , or $1$ ).
Then, add or subtract the rounded numbers to find the estimate.