This handy Spectrum Math Grade 4 Answer Key Chapter 6 Posttest provides detailed answers for the workbook questions.

Check What You Learned

Find the equivalent fraction.

Question 1.
a. $$\frac{3}{5}$$ = $$\frac{}{25}$$
$$\frac{15}{25}$$

Explanation:
Given,
$$\frac{3}{5}$$ = $$\frac{}{25}$$
Let the unknown number be x.
To find the unknown equivalent fraction,
cross multiply the numerator and denominator of the given fractions.
$$\frac{3 × 25}{x × 5}$$
x = $$\frac{75}{5}$$
x = 15
Therefore, $$\frac{3}{5}$$ = $$\frac{15}{25}$$

b. $$\frac{2}{6}$$ = $$\frac{}{18}$$
$$\frac{6}{18}$$

Explanation:
Given,
$$\frac{2}{6}$$ = $$\frac{}{18}$$
Let the unknown number be x.
To find the unknown equivalent fraction,
cross multiply the numerator and denominator of the given fractions.
$$\frac{2 × 18}{x × 6}$$
x = $$\frac{36}{16}$$
x = 6
Therefore, $$\frac{2}{6}$$ = $$\frac{6}{18}$$

c. $$\frac{1}{2}$$ = $$\frac{9}{}$$
$$\frac{9}{18}$$

Explanation:
Given,
$$\frac{1}{2}$$ = $$\frac{9}{}$$
Let the unknown number be x.
To find the unknown equivalent fraction,
cross multiply the numerator and denominator of the given fractions.
$$\frac{1 × x}{9 × 2}$$
x = 18
Therefore, $$\frac{1}{2}$$ = $$\frac{9}{18}$$

d. $$\frac{2}{8}$$ = $$\frac{10}{}$$
$$\frac{10}{40}$$

Explanation:
Given,
$$\frac{2}{8}$$ = $$\frac{10}{}$$
Let the unknown number be x.
To find the unknown equivalent fraction,
cross multiply the numerator and denominator of the given fractions.
$$\frac{2 × x}{8 × 10}$$ = $$\frac{2x}{80}$$
x = $$\frac{80}{2}$$
x = 40
Therefore, $$\frac{2}{8}$$ = $$\frac{10}{40}$$

Compare the fractions using <, >, or =.

Question 2.
a. $$\frac{1}{5}$$ $$\frac{2}{10}$$
$$\frac{1}{5}$$  = $$\frac{2}{10}$$

Explanation:
$$\frac{1}{5}$$  = $$\frac{2}{10}$$ b. $$\frac{3}{4}$$ $$\frac{1}{2}$$
$$\frac{3}{4}$$  > $$\frac{1}{2}$$

Explanation:
$$\frac{3}{4}$$  > $$\frac{1}{2}$$ c. $$\frac{7}{10}$$ $$\frac{3}{5}$$
$$\frac{7}{10}$$ > $$\frac{3}{5}$$

Explanation:
$$\frac{7}{10}$$ > $$\frac{3}{5}$$ Question 3.
a. $$\frac{1}{2}$$

Explanation:
When the denominators are same, then add the numerators.
$$\frac{1}{4}$$ + $$\frac{1}{4}$$ = $$\frac{1+1}{4}$$ = $$\frac{2}{4}$$
Reduce to the simplest form.
$$\frac{1}{2}$$
Write the sum over the common denominator.

b. $$\frac{7}{9}$$

Explanation:
When denominators are same, subtract the numerators.
$$\frac{8}{9}$$ – $$\frac{1}{9}$$ = $$\frac{8 – 1}{9}$$ = $$\frac{7}{9}$$
Write the difference over the common denominator.

c. $$\frac{2}{3}$$

Explanation:
When the denominators are same, then add the numerators.
$$\frac{5}{12}$$ + $$\frac{3}{12}$$ = $$\frac{5+3}{12}$$ = $$\frac{8}{12}$$
Reduce to the simplest form.
$$\frac{2}{3}$$

d. $$\frac{1}{5}$$

Explanation:
When denominators are same, subtract the numerators.
$$\frac{5}{10}$$ – $$\frac{3}{10}$$ = $$\frac{5 – 3}{10}$$
= $$\frac{2}{10}$$ or $$\frac{1}{5}$$

Decompose the fraction.

Question 4.
$$\frac{3}{5}$$ Explanation:
$$\frac{1}{5}$$ + $$\frac{1}{5}$$ + $$\frac{1}{5}$$ = $$\frac{3}{5}$$
OR
$$\frac{2}{5}$$ + $$\frac{1}{5}$$ = $$\frac{3}{5}$$

Write the decimal equivalent to the given fraction.

Question 5.
$$\frac{8}{100}$$ = _____________
0.08

Explanation:
To find the decimal equivalent of a fraction,
divide the numerator by the denominator.
Because the number in the numerator is smaller than the number in the denominator,
so place the decimal number over its place value.
Therefore, $$\frac{8}{100}$$  = 0.08

Question 6.
$$\frac{4}{10}$$ = _____________
0.4

Explanation:
To find the decimal equivalent of a fraction,
divide the numerator by the denominator.
Because the number in the numerator is smaller than the number in the denominator,
so place the decimal number over its place value.
Therefore, $$\frac{4}{10}$$  = 0.4

Question 7.
a. $$\frac{65}{100}$$

Explanation:
To find the equivalent fraction for the given,
$$\frac{6}{10}$$ = $$\frac{5}{100}$$
first multiple the numerator and denominator with same number to equalize the denominator. b. 4$$\frac{1}{7}$$

Explanation:
When denominators are same, subtract the fractions.
$$\frac{2}{7}$$ – $$\frac{1}{7}$$ = $$\frac{1}{7}$$
Subtract the whole numbers.
6 – 2 = 4
So, 4$$\frac{1}{7}$$

c. 7$$\frac{7}{11}$$

Explanation:
$$\frac{4}{11}$$ + $$\frac{3}{11}$$ = $$\frac{7}{11}$$
6 + 1 = 7
So, 7$$\frac{7}{11}$$

d. 3$$\frac{1}{9}$$

Explanation:
When denominators are same, subtract the fractions.
$$\frac{8}{9}$$ – $$\frac{7}{9}$$ = $$\frac{1}{9}$$
Subtract the whole numbers.
6 – 3 = 3
So, 3$$\frac{1}{9}$$

Question 8.
a. $$\frac{33}{100}$$

Explanation:
To find the equivalent fraction for the given,
$$\frac{3}{10}$$ = $$\frac{3}{100}$$
first multiple the numerator and denominator with same number to equalize the denominator. b. 3$$\frac{1}{3}$$

Explanation:
When denominators are same, subtract the fractions.
$$\frac{7}{9}$$ – $$\frac{4}{9}$$ = $$\frac{3}{9}$$
Subtract the whole numbers.
7 – 4 = 3
So, 3$$\frac{1}{3}$$

c. 1$$\frac{2}{5}$$

Explanation:
When denominators are same, subtract the fractions.
$$\frac{3}{5}$$ – $$\frac{1}{5}$$ = $$\frac{2}{5}$$
Subtract the whole numbers.
6 – 5 = 1
So, 1$$\frac{2}{5}$$

d. 9

Explanation:
$$\frac{4}{7}$$ + $$\frac{3}{7}$$ = $$\frac{7}{7}$$ = 1
3 + 5 = 8
So, 8 + 1 = 9

Multiply. Write answers in simplest form.

Question 9.
a. 8 × $$\frac{8}{9}$$ = ______________
7$$\frac{1}{9}$$

Explanation:
Given,
8 × $$\frac{8}{9}$$
= $$\frac{8}{1}$$ × $$\frac{8}{9}$$
= $$\frac{8 \times 1}{8 \times 9}$$
= $$\frac{64}{9}$$
Reduce to the simplest form.
7$$\frac{1}{9}$$

b. $$\frac{5}{12}$$ × 6 = ______________
2$$\frac{1}{2}$$

Explanation:
Given,
$$\frac{5}{12}$$ × 6
= $$\frac{5}{12}$$ × $$\frac{6}{1}$$
= $$\frac{5 \times 12}{6 \times 1}$$
= $$\frac{30}{12}$$
= 1$$\frac{5}{2}$$
Reduce to the simplest form.
2$$\frac{1}{2}$$

c. $$\frac{3}{8}$$ × 3 = ______________
1$$\frac{1}{8}$$

Explanation:
Given,
$$\frac{3}{8}$$ × 3
= $$\frac{3}{8}$$ × $$\frac{3}{1}$$
= $$\frac{3 \times 8}{3 \times 1}$$
= $$\frac{9}{8}$$
Reduce to the simplest form.
1$$\frac{1}{8}$$

d. 7 × $$\frac{4}{11}$$ = ______________
2$$\frac{6}{11}$$

Explanation:
Given,
7 × $$\frac{4}{11}$$
= $$\frac{7}{1}$$ × $$\frac{4}{11}$$
= $$\frac{7 \times 1}{4 \times 11}$$
= $$\frac{28}{11}$$
Reduce to the simplest form.
2$$\frac{6}{11}$$

Question 10.
a. $$\frac{1}{4}$$ × 3 = ________________
$$\frac{3}{4}$$

Explanation:
Given,
$$\frac{1}{4}$$ × 3
= $$\frac{1}{4}$$ × $$\frac{3}{1}$$
= $$\frac{1 \times 4}{3 \times 1}$$
= $$\frac{3}{4}$$

b. $$\frac{1}{2}$$ × 9 = ________________
4$$\frac{1}{2}$$

Explanation:
Given,
$$\frac{1}{2}$$ × 9
= $$\frac{1}{2}$$ × $$\frac{9}{1}$$
= $$\frac{1 \times 2}{9 \times 1}$$
= $$\frac{9}{2}$$
Reduce to the simplest form.
4$$\frac{1}{2}$$

c. 2 × $$\frac{3}{5}$$ = ________________
1$$\frac{1}{5}$$

Explanation:
Given,
2 × $$\frac{3}{5}$$
= $$\frac{2}{1}$$ × $$\frac{3}{5}$$
= $$\frac{2 \times 1}{3 \times 5}$$
= $$\frac{6}{5}$$
Reduce to the simplest form.
1$$\frac{1}{5}$$

d. 4 × $$\frac{7}{10}$$ = _________________
2$$\frac{4}{5}$$

Explanation:
Given,
4 × $$\frac{7}{10}$$
= $$\frac{4}{1}$$ × $$\frac{7}{10}$$
= $$\frac{4 \times 1}{7 \times 10}$$
= $$\frac{28}{10}$$
= $$\frac{14}{5}$$
Reduce to the simplest form.
2$$\frac{4}{5}$$

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