This handy Spectrum Math Grade 4 Answer Key Chapter 6 Posttest provides detailed answers for the workbook questions.
Spectrum Math Grade 4 Chapter 6 Posttest Answers Key
Check What You Learned
Find the equivalent fraction.
Question 1.
a. \(\frac{3}{5}\) = \(\frac{}{25}\)
Answer:
\(\frac{15}{25}\)
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. \(\frac{2}{6}\) = \(\frac{}{18}\)
Answer:
\(\frac{6}{18}\)
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. \(\frac{1}{2}\) = \(\frac{9}{}\)
Answer:
\(\frac{9}{18}\)
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. \(\frac{2}{8}\) = \(\frac{10}{}\)
Answer:
\(\frac{10}{40}\)
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. \(\frac{1}{5}\) 
\(\frac{2}{10}\)
Answer:
\(\frac{1}{5}\) = \(\frac{2}{10}\)
Explanation:
\(\frac{1}{5}\) = \(\frac{2}{10}\)
b. \(\frac{3}{4}\) \(\frac{1}{2}\)
Answer:
\(\frac{3}{4}\) > \(\frac{1}{2}\)
Explanation:
\(\frac{3}{4}\) > \(\frac{1}{2}\)
c. \(\frac{7}{10}\) \(\frac{3}{5}\)
Answer:
\(\frac{7}{10}\) > \(\frac{3}{5}\)
Explanation:
\(\frac{7}{10}\) > \(\frac{3}{5}\)
Add or subtract.
Question 3.
a.
Answer:
\(\frac{1}{2}\)
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.
Answer:
\(\frac{7}{9}\)
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.
Answer:
\(\frac{2}{3}\)
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.
Answer:
\(\frac{1}{5}\)
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.
\(\frac{3}{5}\)
Answer:
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.
\(\frac{8}{100}\) = _____________
Answer:
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.
\(\frac{4}{10}\) = _____________
Answer:
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
Add or Subtract.
Question 7.
a.
Answer:
\(\frac{65}{100}\)
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.
Answer:
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.
Answer:
7\(\frac{7}{11}\)
Explanation:
Add the fractions.
\(\frac{4}{11}\) + \(\frac{3}{11}\) = \(\frac{7}{11}\)
Add the whole numbers.
6 + 1 = 7
So, 7\(\frac{7}{11}\)
d.
Answer:
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.
Answer:
\(\frac{33}{100}\)
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.
Answer:
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.
Answer:
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.
Answer:
9
Explanation:
Add the fractions.
\(\frac{4}{7}\) + \(\frac{3}{7}\) = \(\frac{7}{7}\) = 1
Add the whole numbers.
3 + 5 = 8
So, 8 + 1 = 9
Multiply. Write answers in simplest form.
Question 9.
a. 8 × \(\frac{8}{9}\) = ______________
Answer:
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 = ______________
Answer:
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 = ______________
Answer:
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 × \(\frac{4}{11}\) = ______________
Answer:
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 = ________________
Answer:
\(\frac{3}{4}\)
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 = ________________
Answer:
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 × \(\frac{3}{5}\) = ________________
Answer:
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 × \(\frac{7}{10}\) = _________________
Answer:
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\(\frac{4}{5}\)