All the solutions provided inÂ **McGraw Hill My Math Grade 4 Answer Key PDF Chapter 8 Lesson 3 Model Equivalent Fractions **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 8 Lesson 3 Model Equivalent Fractions

The top number on a fraction is the numerator, The bottom number on a fraction is the denominator. Fractions that represent the same part of a number are equivalent fractions.

**Build it
**Generate two fractions that are equivalent to \(\frac{1}{3}\).

1. Model \(\frac{1}{3}\).

Place a \(\frac{1}{3}\) – tile.

2. Find a fraction equivalent to \(\frac{1}{3}\).

Place \(\frac{1}{6}\) – tiles below the \(\frac{1}{3}\) – tile to equal the length of the \(\frac{1}{3}\) – tile.

How many \(\frac{1}{6}\) – tiles did you place?

So, \(\frac{1}{3}\) and \(\frac{2}{6}\) are equivalent fractions.

3. Find another fraction equivalent to \(\frac{1}{3}\).

Place \(\frac{1}{12}\) – tiles below the \(\frac{1}{6}\) – tiles to equal the length of the \(\frac{1}{3}\) – tile.

How many \(\frac{1}{12}\) – tiles did you place?

So, \(\frac{1}{3}\) and \(\frac{4}{12}\) are equivalent fractions.

So, \(\frac{1}{3}\), are equivalent fractions.

Answer:

Equivalent fractions of \(\frac{1}{3}\) = \(\frac{4}{12}\) and \(\frac{2}{6}\).

Explanation:

Fraction given: \(\frac{1}{3}\)

\(\frac{1}{3}\) = \(\frac{1}{3}\) Ă— \(\frac{4}{4}\) = \(\frac{4}{12}\).

\(\frac{1}{3}\) = \(\frac{1}{3}\) Ă— \(\frac{2}{2}\) = \(\frac{2}{6}\)

**Try It
**Generate two fractions that are equivalent to \(\frac{1}{4}\).

1. The first number line is divided into fourths. Plot \(\frac{1}{4}\) on the number line.

2. The second number line is divided into eighths.

What fraction is at the same location as \(\frac{1}{4}\)?

Plot this fraction on the number line.

3. The third number line is divided into twelfths.

What fraction is at the same location as \(\frac{1}{4}\)?

Plot this fraction on the number line.

So, two fractions that are equivalent to \(\frac{1}{4}\) are and .

Answer:

Explanation:

Equivalent fraction:

\(\frac{1}{4}\) = \(\frac{1}{4}\) Ă— \(\frac{2}{2}\) = \(\frac{2}{8}\)

\(\frac{1}{4}\) = \(\frac{1}{4}\) Ă— \(\frac{3}{3}\) = \(\frac{3}{12}\)

**Talk About It
**Question 1.

**Mathematical PRACTICE**Look for a Pattern The table shows some equivalent fractions. Study the table. Describe the pattern, between the numerators and denominators of two equivalent fractions.

Answer:

The denominators are different and numerators are same in the both fractions \(\frac{2}{6}\) and \(\frac{2}{8}\).

The numerators are different and denominators are same in the both fractions \(\frac{4}{12}\) and \(\frac{3}{12}\)

Explanation:

Equivalent fractions: \(\frac{1}{3}\) = \(\frac{2}{6}\) and \(\frac{4}{12}\)

Equivalent fractions: \(\frac{1}{4}\) = \(\frac{2}{8}\) and \(\frac{3}{12}\)

Question 2.

**Mathematical PRACTICE** Draw a Conclusion, determine whether \(\frac{1}{2}\) and \(\frac{3}{6}\) are equivalent fractions. Explain.

Answer:

Both fractions \(\frac{1}{2}\) and \(\frac{3}{6}\) are equivalent fractions.

Explanation:

\(\frac{1}{2}\) = \(\frac{1}{2}\)

\(\frac{3}{6}\) = \(\frac{3}{6}\) Ă· \(\frac{3}{3}\) = \(\frac{1}{2}\)

**Practice It
**

**Recognize whether the fractions are equivalent. Write yes or no.**

Question 3.

\(\frac{2}{4}\) and \(\frac{6}{12}\)

Answer:

Yes, \(\frac{2}{4}\) and \(\frac{6}{12}\) both are equivalent fractions.

Explanation:

\(\frac{2}{4}\) = \(\frac{2}{4}\) Ă· \(\frac{2}{2}\) = \(\frac{1}{2}\)

\(\frac{6}{12}\) = \(\frac{6{12}\) Ă· \(\frac{6}{6}\) = \(\frac{1}{2}\)

Question 4.

\(\frac{6}{8}\) and \(\frac{5}{10}\)

Answer:

No, \(\frac{6}{8}\) and \(\frac{5}{10}\) both are not equivalent fractions.

Explanation:

\(\frac{6}{8}\) = \(\frac{6}{8}\) Ă· \(\frac{2}{2}\) = \(\frac{3}{4}\)

\(\frac{5}{10}\) = \(\frac{5}{10}\) Ă· \(\frac{5}{5}\) = \(\frac{1}{2}\)

Question 5.

\(\frac{2}{3}\) and \(\frac{3}{5}\)

Answer:

No, \(\frac{2}{3}\) and \(\frac{3}{5}\) both are not equivalent fractions.

Explanation:

\(\frac{2}{3}\) = \(\frac{2}{3}\)

\(\frac{3}{5}\) = \(\frac{2}{3}\)

Question 6.

\(\frac{9}{12}\) and \(\frac{3}{4}\)

Answer:

Yes, \(\frac{9}{12}\) and \(\frac{3}{4}\) both are equivalent fractions.

Explanation:

\(\frac{9}{12}\) = \(\frac{9}{12}\) Ă· \(\frac{3}{3}\) = \(\frac{3}{4}\)

\(\frac{3}{4}\) = \(\frac{3}{4}\)

Question 7.

\(\frac{4}{6}\) and \(\frac{8}{12}\)

Answer:

Yes, \(\frac{4}{6}\) and \(\frac{8}{12}\) both are equivalent fractions.

Explanation:

\(\frac{4}{6}\) = \(\frac{4}{6}\) Ă· \(\frac{2}{2}\)Â = \(\frac{2}{3}\)

\(\frac{8}{12}\) = \(\frac{8}{12}\) Ă· \(\frac{4}{4}\)Â = \(\frac{2}{3}\)

Question 8.

\(\frac{2}{3}\) and \(\frac{6}{10}\)

Answer:

No, \(\frac{2}{3}\) and \(\frac{6}{10}\) both are equivalent fractions.

Explanation:

\(\frac{2}{3}\) = \(\frac{2}{3}\)

\(\frac{6}{10}\) = \(\frac{6}{10}\)Â Ă· \(\frac{2}{2}\)Â = \(\frac{3}{5}\)

**Generate two equivalent fractions for each fraction.
**Question 9.

\(\frac{2}{4}\)

Answer:

Two equivalent fractions of \(\frac{2}{4}\) are \(\frac{4}{8}\) and \(\frac{12}{24}\)

Explanation:

\(\frac{2}{4}\) = \(\frac{2}{4}\) Ă— \(\frac{2}{2}\) = \(\frac{4}{8}\)

\(\frac{2}{4}\) = \(\frac{2}{4}\) Ă— \(\frac{6}{6}\) = \(\frac{12}{24}\)

Question 10.

\(\frac{2}{6}\)

Answer:

Two equivalent fractions of \(\frac{2}{6}\) are \(\frac{4}{12}\) and \(\frac{12}{36}\)

Explanation:

\(\frac{2}{6}\) = \(\frac{2}{6}\)Ă— \(\frac{2}{2}\) = \(\frac{4}{12}\)

\(\frac{2}{6}\) = \(\frac{2}{6}\) Ă— \(\frac{6}{6}\) = \(\frac{12}{36}\)

Question 11.

\(\frac{4}{8}\)

Answer:

Two equivalent fractions of \(\frac{4}{8}\) are \(\frac{16}{32}\) and \(\frac{32}{64}\)

Explanation:

\(\frac{4}{8}\) = \(\frac{4}{8}\) Ă— \(\frac{4}{4}\) = \(\frac{16}{32}\)

\(\frac{4}{8}\) = \(\frac{4}{8}\)Ă— \(\frac{8}{8}\) = \(\frac{32}{64}\)

Question 12.

\(\frac{5}{10}\)

Answer:

Two equivalent fractions of \(\frac{5}{10}\) are \(\frac{10}{20}\) and \(\frac{55}{110}\)

Explanation:

\(\frac{5}{10}\) = \(\frac{5}{10}\) Ă— \(\frac{2}{2}\) = \(\frac{10}{20}\)

\(\frac{5}{10}\) = \(\frac{5}{10}\) Ă— \(\frac{11}{11}\) = \(\frac{55}{110}\)

Question 13.

\(\frac{1}{3}\)

Answer:

Two equivalent fractions of \(\frac{1}{3}\) are \(\frac{5}{15}\) and \(\frac{3}{9}\)

Explanation:

\(\frac{1}{3}\) = \(\frac{1}{3}\)Ă— \(\frac{5}{5}\) = \(\frac{5}{15}\)

\(\frac{1}{3}\) = \(\frac{1}{3}\)Ă— \(\frac{3}{3}\) = \(\frac{3}{9}\)

Question 14.

\(\frac{2}{3}\)

Answer:

Two equivalent fractions of \(\frac{2}{3}\) are \(\frac{14}{21}\) and \(\frac{12}{18}\)

Explanation:

\(\frac{2}{3}\) = \(\frac{2}{3}\) Ă— \(\frac{7}{7}\) = \(\frac{14}{21}\)

\(\frac{2}{3}\) = \(\frac{2}{3}\) Ă— \(\frac{6}{6}\) = \(\frac{12}{18}\)

**Apply It
**Question 15.

**Mathematical PRACTICE**Model Math There were 10 baked goods in a basket. Four of them were sold. Write a fraction to show the part of the baked goods that were not sold. Then write an equivalent fraction to this number.

Answer:

Fraction to show the part of the baked goods that were not sold = \(\frac{2}{5}\)

Explanation:

Number of baked goods in a basket = 10.

Number of baked goods in a basket sold = 4.

Fraction to show the part of the baked goods that were not sold = Number of baked goods in a basket sold Ă· Number of baked goods in a basket

= 4 Ă· 10

= 2 Ă· 5 or \(\frac{2}{5}\)

Question 16.

Two-thirds of a jar of peanut butter has been used. Write an equivalent fraction.

Answer:

Equivalent fraction of \(\frac{2}{3}\) = \(\frac{10}{15}\)

Explanation:

Two-thirds of a jar of peanut butter has been used.

=> \(\frac{2}{3}\) = \(\frac{2}{3}\) Ă— \(\frac{5}{5}\) = \(\frac{10}{15}\)

Question 17.

A jar has marbles in it. Three-tenths of the marbles are red. Five-tenths of the marbles are blue. Two-tenths of the marbles are green. Which of these fractions is equivalent to four-eighths?

Answer:

Fractions is equivalent to four-eighths = Fraction of the marbles are blue = \(\frac{5}{10}\)

Explanation:

Fraction of the marbles are red = \(\frac{3}{10}\)

Fraction of the marbles are blue = \(\frac{5}{10}\)

Fraction of the marbles are green = \(\frac{2}{10}\)

Simplest form:

\(\frac{3}{10}\) = \(\frac{3}{10}\)

\(\frac{5}{10}\) = \(\frac{5}{10}\) Ă· \(\frac{5}{5}\) = \(\frac{1}{2}\)

\(\frac{2}{10}\) = \(\frac{2}{10}\) Ă· \(\frac{2}{2}\) = \(\frac{1}{5}\)

\(\frac{4}{8}\) = \(\frac{4}{8}\) Ă· \(\frac{4}{4}\)Â = \(\frac{1}{2}\)

Question 18.

**Mathematical PRACTICE** Use Number Sense Daria used fraction tiles to show that \(\frac{3}{5}\) is equivalent to \(\frac{6}{10}\). Compare the number and size of fraction tiles needed to model each fraction.

Answer:

\(\frac{3}{5}\) is equivalent to \(\frac{6}{10}\) both are size are same.

Explanation:

Given: \(\frac{3}{5}\) is equivalent to \(\frac{6}{10}\).

\(\frac{3}{5}\)

\(\frac{6}{10}\) = \(\frac{6}{10}\) Ă· \(\frac{2}{2}\) = \(\frac{3}{5}\)

Question 19.

**Mathematical PRACTICE** Make Sense of Problems

Complete the equation.

Answer:

Equation:Â

Explanation:

Equation:

\(\frac{2}{??}\) Ă— \(\frac{3}{3}\) = \(\frac{??}{6}\)

=> 6 Ă— 2 = 12.

\(\frac{2}{12}\) = \(\frac{1}{6}\)

**Write About It
**Question 20.

Write a real-world example of equivalent fractions.

Answer:

A real-world example of equivalent fractions is a piece of cake.

Explanation:

I have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake. If I cut a cake into eight equal pieces and eat four of them, I will still have eaten half the cake. These are equivalent fractions.

### McGraw Hill My Math Grade 4 Chapter 8 Lesson 3 My Homework Answer Key

**Practice
**

**Recognize whether the fractions are equivalent. Write yes or no.**

Question 1.

\(\frac{3}{5}\) and \(\frac{6}{8}\)

Answer:

Yes, \(\frac{3}{5}\) and \(\frac{6}{8}\) both are equivalent fractions.

Explanation:

\(\frac{3}{5}\) = \(\frac{3}{5}\)

\(\frac{6}{8}\) = \(\frac{6}{8}\)Â Ă· \(\frac{2}{2}\)Â = \(\frac{3}{5}\)

Question 2.

\(\frac{4}{5}\) and \(\frac{5}{6}\)

Answer:

No \(\frac{4}{5}\) and \(\frac{5}{6}\) both are not equivalent fractions.

Explanation:

\(\frac{4}{5}\) = \(\frac{4}{5}\)

\(\frac{5}{6}\) = \(\frac{5}{6}\)

Question 3.

\(\frac{2}{4}\) and \(\frac{6}{12}\)

Answer:

Yes \(\frac{2}{4}\) and \(\frac{6}{12}\) both are equivalent fractions.

Explanation:

\(\frac{2}{4}\) = \(\frac{2}{4}\) Ă· \(\frac{2}{2}\)Â = \(\frac{1}{2}\)

\(\frac{6}{12}\) = \(\frac{6}{12}\) Ă· \(\frac{6}{6}\)Â = \(\frac{1}{2}\)

Question 4.

\(\frac{2}{3}\) and \(\frac{4}{6}\)

Answer:

Yes \(\frac{2}{3}\) and \(\frac{4}{6}\) both are equivalent fractions.

Explanation:

\(\frac{2}{3}\) = \(\frac{2}{3}\)

\(\frac{4}{6}\) = \(\frac{4}{6}\) Ă· \(\frac{2}{2}\)Â = \(\frac{2}{3}\)

Question 5.

\(\frac{8}{12}\) and \(\frac{4}{6}\)

Answer:

Yes \(\frac{8}{12}\) and \(\frac{4}{6}\) both are equivalent fractions.

Explanation:

\(\frac{8}{12}\) = \(\frac{8}{12}\) Ă· \(\frac{4}{4}\)Â = \(\frac{2}{3}\)

\(\frac{4}{6}\) = \(\frac{4}{6}\) Ă· \(\frac{2}{2}\)Â = \(\frac{2}{3}\)

Question 6.

\(\frac{5}{6}\) and \(\frac{9}{10}\)

Answer:

No \(\frac{5}{6}\) and \(\frac{9}{10}\) both are not equivalent fractions.

Explanation:

\(\frac{5}{6}\) = \(\frac{5}{6}\)

\(\frac{9}{10}\) = \(\frac{9}{10}\)

**Generate two equivalent fractions for each fraction.
**Question 7.

\(\frac{1}{3}\)

Answer:

Two equivalent fractions of \(\frac{1}{3}\) are \(\frac{7}{21}\) and \(\frac{3}{9}\)

Explanation:

\(\frac{1}{3}\) = \(\frac{1}{3}\) Ă— \(\frac{7}{7}\) = \(\frac{7}{21}\)

\(\frac{1}{3}\) = \(\frac{1}{3}\) Ă— \(\frac{3}{3}\) = \(\frac{3}{9}\)

Question 8.

\(\frac{8}{12}\)

Answer:

Two equivalent fractions of \(\frac{8}{12}\) are \(\frac{16}{24}\) and \(\frac{24}{36}\)

Explanation:

\(\frac{8}{12}\) = \(\frac{8}{12}\) Ă— \(\frac{2}{2}\) = \(\frac{16}{24}\)

\(\frac{8}{12}\) = \(\frac{8}{12}\) Ă— \(\frac{3}{3}\) = \(\frac{24}{36}\)

Question 9.

\(\frac{3}{4}\)

Answer:

Two equivalent fractions of \(\frac{3}{4}\) are \(\frac{15}{20}\) and \(\frac{6}{8}\)

Explanation:

\(\frac{3}{4}\) = \(\frac{3}{4}\) Ă— \(\frac{5}{5}\) = \(\frac{15}{20}\)

\(\frac{3}{4}\) = \(\frac{3}{4}\) Ă— \(\frac{2}{2}\) = \(\frac{6}{8}\)

**Problem Solving
**Question 10.

**Mathematical PRACTICE**Justify Conclusions Francie lives \(\frac{1}{5}\) mile from the school. Jake lives \(\frac{2}{10}\) mile from the school. Do they live the same distance from the school? Explain.

Answer:

Yes, they live the same distance from the school because \(\frac{1}{5}\)Â is the simplest form of \(\frac{2}{10}\).

Explanation:

Number of miles Francie lives from the school = \(\frac{1}{5}\)

Number of miles Jake lives from the school = \(\frac{2}{10}\)

SimplestÂ form:

\(\frac{1}{5}\)Â = \(\frac{1}{5}\)

\(\frac{2}{10}\)Â = \(\frac{2}{10}\) Ă· \(\frac{2}{2}\)Â = \(\frac{1}{5}\)

**Vocabulary Check
**Draw a line to match the vocabulary term with its example.

Answer:

Explanation:

Numerator = the number above the line in a fraction showing how many of the parts indicated by the denominator are taken.

The denominator = The numeric value below the line of a fraction is called the denominator.

Equivalent fractions = They are fractions that represent the same value, even though they look different.