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

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## 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.
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 .

Explanation:
Equivalent fraction:
$$\frac{1}{4}$$ = $$\frac{1}{4}$$ Ă— $$\frac{2}{2}$$ = $$\frac{2}{8}$$
$$\frac{1}{4}$$ = $$\frac{1}{4}$$ Ă— $$\frac{3}{3}$$ = $$\frac{3}{12}$$

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.

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.
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 $$\frac{6}{12}$$
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 $$\frac{5}{10}$$
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 $$\frac{3}{5}$$
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 $$\frac{3}{4}$$
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 $$\frac{8}{12}$$
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 $$\frac{6}{10}$$
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.
$$\frac{2}{4}$$
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.
$$\frac{2}{6}$$
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.
$$\frac{4}{8}$$
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.
$$\frac{5}{10}$$
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.
$$\frac{1}{3}$$
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.
$$\frac{2}{3}$$
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.
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.
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?

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.
$$\frac{3}{5}$$ 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.
Equation:Â

Explanation:
Equation:
$$\frac{2}{??}$$ Ă— $$\frac{3}{3}$$ = $$\frac{??}{6}$$
=> 6 Ă— 2 = 12.
$$\frac{2}{12}$$ = $$\frac{1}{6}$$

Question 20.
Write a real-world example of equivalent fractions.
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 $$\frac{6}{8}$$
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 $$\frac{5}{6}$$
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 $$\frac{6}{12}$$
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 $$\frac{4}{6}$$
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 $$\frac{4}{6}$$
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 $$\frac{9}{10}$$
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.
$$\frac{1}{3}$$
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.
$$\frac{8}{12}$$
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.
$$\frac{3}{4}$$
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.
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.