Section B: Practice Problems Equivalent Fractions

Section Summary

Details

In this section, we learned to identify and write equivalent fractions. We placed fractions on number lines and saw that two fractions that occupy the same spot on a number line are equivalent.

Number line. Scale 0 to 1. 13 evenly spaced tick marks. First tick mark, 0. Fifth tick mark, 1 third. Point at ninth tick mark, 2 thirds.

number line. Scale 0 to 1, by sixths. Point at 4 sixths.

We also looked at strategies for finding equivalent fractions and learned that multiplying or dividing the numerator and denominator by the same number will result in an equivalent fraction. Here are some examples:

$\frac{1 \times 2}{5 \times 2} = \frac{2}{10}$

$\frac{1 \times 4}{5 \times 4} = \frac{4}{20}$

$\frac{1}{5}$ is equivalent to $\frac{2}{10}$ and $\frac{4}{20}$ .

$\frac{8 \div 2}{12 \div 2} = \frac{4}{6}$

$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$

$\frac{8}{12}$ is equivalent to $\frac{4}{6}$ and $\frac{2}{3}$ .

Problem 1 (Lesson 7)

Name three fractions that are equivalent to $\frac{2}{5}$ . Explain or show your reasoning.

Problem 2 (Lesson 8)

Which of these could be the fraction that the point represents? Explain your reasoning.

$\frac{86}{100}$

$\frac{90}{100}$

$\frac{94}{100}$

$\frac{101}{100}$

Problem 3 (Lesson 9)

Explain why the fractions $\frac{10}{3}$ and $\frac{40}{12}$ are equivalent.

Problem 4 (Lesson 10)

Find two fractions equivalent to $\frac{10}{6}$ . Explain or show why they are equivalent to $\frac{10}{6}$ . Use the number line if you think it is helpful.

Number line. Scale 0 to 2. Evenly spaced by sixths.

Problem 5 (Lesson 11)

Jada says that $\frac{7}{5}$ is equivalent to $\frac{14}{10}$ because the numerator and denominator of $\frac{14}{10}$ are each 2 times the numerator and denominator of $\frac{7}{5}$ .

Explain why Jada’s reasoning is correct.
Use Jada’s method to find another fraction equivalent to $\frac{7}{5}$ .

Problem 6 (Exploration)

Jada is thinking of a fraction. She gives several clues to help you guess her fraction. Try to guess Jada’s fraction after each clue.

My fraction is equivalent to $\frac{2}{3}$ .
The numerator of my fraction is greater than 10.
8 is a factor of my numerator.
8 and 5 are a factor pair of my numerator.

Problem 7 (Exploration)

Think of a fraction:

Write several clues so a friend or family member can guess your fraction. Then, present the clues one at a time and ask them to make a guess after each one.

My fraction is equivalent to .
The numerator of my fraction is less than .
One multiple of my numerator is .
A factor pair of my denominator is and .

Problem 8 (Exploration)

Diego says he shaded $\frac{10}{20}$ of the diagram. Do you agree with Diego? Explain your reasoning.
Shade $\frac{18}{24}$ of the diagram. Explain how you know $\frac{18}{24}$ is shaded.