Learn on PengienVision, Mathematics, Grade 4Chapter 8: Extend Understanding of Fraction Equivalence and Ordering

Lesson 5: Use Benchmarks to Compare Fractions

Property.

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

Visualizing Benchmark Comparisons with Area Models

Property

To compare a fraction to a benchmark using an area model, shade the area representing the fraction and visually compare it to the area representing the benchmark (e.g., $\frac{1}{2}$ or $1$ ).

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

Visualizing Benchmark Comparisons with Area Models

Property

To compare a fraction to a benchmark using an area model, shade the area representing the fraction and visually compare it to the area representing the benchmark (e.g., $\frac{1}{2}$ or $1$ ).

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

Visualizing Benchmark Comparisons with Area Models

Property

To compare a fraction to a benchmark using an area model, shade the area representing the fraction and visually compare it to the area representing the benchmark (e.g., $\frac{1}{2}$ or $1$ ).