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

## Spectrum Math Grade 4 Chapter 6 Pretest Answers Key

**Check What You Know**

**To find an equivalent fraction, multiply the fraction by the number in the circle.**

Question 1.

a.

Answer:

\(\frac{12}{24}\)

Explanation:

Given,

\(\frac{3}{6}\)

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 4.

\(\frac{3 × 4}{6 × 4}\) = \(\frac{12}{24}\)

So, \(\frac{3}{6}\) and \(\frac{12}{24}\) are equivalent fractions.

b.

Answer:

\(\frac{10}{15}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 5.

\(\frac{2 × 5}{3 × 5}\) = \(\frac{10}{15}\)

So, \(\frac{2}{3}\) and \(\frac{10}{15}\) are equivalent fractions.

c.

Answer:

\(\frac{6}{36}\)

Explanation:

Given,

\(\frac{1}{6}\)

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 6.

\(\frac{1 × 6}{6 × 6}\) = \(\frac{6}{36}\)

So, \(\frac{1}{6}\) and \(\frac{6}{36}\) are equivalent fractions.

d.

Answer:

\(\frac{9}{27}\)

Explanation:

Given,

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

To find an equivalent fraction,

multiply both the numerator and denominator by the given number 9.

\(\frac{1 × 9}{3 × 9}\) = \(\frac{9}{27}\)

So, \(\frac{1}{3}\) and \(\frac{9}{27}\) are equivalent fractions.

**Draw a picture to compare the fractions. Then, write >, <, or =.**

Question 2.

Answer:

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

Explanation:

**Add.**

Question 3.

Answer:

\(\frac{10}{10}\) or 1

Explanation:

When the denominators are same, then add the numerators.

\(\frac{7}{10}\) + \(\frac{3}{10}\) = \(\frac{7+3}{10}\) = \(\frac{10}{10}\) or 1.

Write the sum over the common denominator as shown above.

Question 4.

Answer:

\(\frac{7}{8}\)

Explanation:

When the denominators are same, then add the numerators.

\(\frac{3}{8}\) + \(\frac{4}{8}\) = \(\frac{3+4}{8}\) = \(\frac{7}{8}\)

Write the sum over the common denominator as shown above.

**Subtract.**

Question 5.

Answer:

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

Explanation:

When denominators are same, subtract the numerators.

\(\frac{4}{5}\) – \(\frac{2}{5}\) = \(\frac{4 – 2}{5}\) = \(\frac{2}{5}\)

Write the difference over the common denominator as shown above.

Question 6.

\(\frac{11}{12}\) – \(\frac{8}{12}\) = _____________

Answer:

\(\frac{3}{12}\) or \(\frac{1}{4}\)

Explanation:

When denominators are same, subtract the numerators.

\(\frac{11}{12}\) – \(\frac{8}{12}\) = \(\frac{11 – 8}{12}\)

= \(\frac{3}{12}\) or \(\frac{1}{4}\)

Write the difference over the common denominator as shown above.

**Decompose the fraction.**

Question 7.

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

Answer:

Explanation:

\(\frac{1}{4}\) + \(\frac{1}{4}\) = \(\frac{2}{4}\)

Reduce to the simplest form.

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

**Write the decimal and fraction for each model.**

Question 8.

__________ or ___________

Answer:

\(\frac{5}{10}\) or 0.5

Explanation:

The given model is divided into 10 parts.

Number of shaded parts = \(\frac{5}{10}\)

So, \(\frac{5}{10}\) is written as 0.5.

Question 9.

__________ or ___________

Answer:

\(\frac{44}{100}\) or 0.44

Explanation:

The given model is divided into 10 rows and columns.

Each unit in the model represent as 1.

Number of shaded parts = \(\frac{44}{100}\)

So, \(\frac{44}{100}\) is written as 0.44.

Question 10.

__________ or ___________

Answer:

\(\frac{1}{10}\) or 0.1

Explanation:

The given model is divided into 10 parts.

Number of shaded parts = \(\frac{1}{10}\)

So, \(\frac{1}{10}\) is written as 0.1.

**Add or subtract.**

Question 11.

a.

Answer:

\(\frac{48}{100}\)

Explanation:

To find the equivalent fraction for the given,

\(\frac{4}{10}\) = \(\frac{8}{100}\)

first multiple the numerator and denominator with same number to equalize the denominator.

b.

Answer:

10\(\frac{2}{6}\) or 10\(\frac{1}{3}\)

Explanation:

Add the fractions.

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

Add the whole numbers.

7 + 3 = 10

Reduce to simplest form.

\(\frac{2}{6} \div \frac{2}{2}\) = \(\frac{1}{3}\)

Hence, 10\(\frac{1}{3}\)

c.

Answer:

13\(\frac{6}{8}\) or 13\(\frac{3}{4}\)

Explanation:

Add the fractions.

\(\frac{3}{8}\) + \(\frac{3}{8}\) = \(\frac{6}{8}\)

Add the whole numbers.

5 + 8 = 13

So, 13\(\frac{6}{8}\)

Reduce to simplest form.

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

Hence, 13\(\frac{3}{4}\)

d.

Answer:

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

Explanation:

Add the fractions.

\(\frac{3}{5}\) + \(\frac{1}{5}\) = \(\frac{4}{5}\)

Add the whole numbers.

8 + 8 = 16

So, 16\(\frac{4}{5}\)

Question 12.

a.

Answer:

3\(\frac{3}{9}\) or 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\(\frac{3}{9}\)

Reduce to simplest form.

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

b.

Answer:

\(\frac{22}{100}\)

Explanation:

To find the equivalent fraction for the given,

\(\frac{2}{10}\) = \(\frac{2}{100}\)

first multiple the numerator and denominator with same number to equalize the denominator.

c.

Answer:

11\(\frac{12}{10}\)

or

12\(\frac{2}{10}\)

or

12\(\frac{1}{5}\)

Explanation:

Add the fractions.

\(\frac{3}{10}\) + \(\frac{9}{10}\) = \(\frac{12}{10}\)

Add the whole numbers.

9 + 2 = 11

So, 11\(\frac{12}{10}\)

Reduce to simplest form.

12\(\frac{2}{10}\) = 12\(\frac{1}{5}\)

d.

Answer:

3\(\frac{3}{7}\)

Explanation:

Subtract the numerators when denominators are same.

\(\frac{5}{7}\) – \(\frac{2}{7}\) = \(\frac{3}{7}\)

Then subtract the whole numbers.

4 – 1 = 3

So, 3\(\frac{3}{7}\)

**Multiply.**

Question 13.

a. \(\frac{8}{9}\) × 4 = _____________

Answer:

\(\frac{32}{9}\) or 3\(\frac{5}{9}\)

Explanation:

Given,

\(\frac{8}{9}\) × 4

= \(\frac{8}{9}\) × \(\frac{4}{1}\)

= \(\frac{8 \times 4}{9 \times 1}\)

= \(\frac{32}{7}\)

Reduce to the simplest form.

3\(\frac{5}{9}\)

b. 3 × \(\frac{1}{8}\) = ______________

Answer:

\(\frac{3}{8}\)

Explanation:

Given,

3 × \(\frac{1}{8}\)

= \(\frac{3}{1}\) × \(\frac{1}{8}\)

= \(\frac{3 \times 1}{1 \times 8}\)

= \(\frac{3}{8}\)

c. \(\frac{4}{7}\) × 2 = ______________

Answer:

\(\frac{8}{7}\) or 1\(\frac{1}{7}\)

Explanation:

Given,

\(\frac{4}{7}\) × 2

= \(\frac{4}{7}\) × \(\frac{2}{1}\)

= \(\frac{4 \times 2}{7 \times 1}\)

= \(\frac{8}{7}\)

Reduce to the simplest form.

1\(\frac{1}{7}\)

d. \(\frac{5}{7}\) × 8 = ______________

Answer:

\(\frac{40}{7}\) or 5\(\frac{5}{7}\)

Explanation:

Given,

\(\frac{5}{7}\) × 8

= \(\frac{5}{7}\) × \(\frac{8}{1}\)

= \(\frac{5 \times 8}{7 \times 1}\)

= \(\frac{40}{7}\)

Reduce to the simplest form.

5\(\frac{35}{7}\)

Question 14.

a. 5 × \(\frac{3}{10}\) = _______________

Answer:

\(\frac{15}{10}\) or \(\frac{3}{2}\)

Explanation:

Given,

5 × \(\frac{3}{10}\)

= \(\frac{5}{1}\) × \(\frac{3}{10}\)

= \(\frac{5 \times 1}{3 \times 10}\)

= \(\frac{15}{10}\)

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

b. 2 × \(\frac{7}{12}\) = ________________

Answer:

\(\frac{14}{12}\) or 1\(\frac{1}{7}\)

Explanation:

Given,

2 × \(\frac{7}{12}\)

= \(\frac{2}{1}\) × \(\frac{7}{12}\)

= \(\frac{2 \times 1}{7 \times 12}\)

= \(\frac{14}{12}\)

Reduce to the simplest form.

1 \(\frac{1}{7}\)

c. \(\frac{6}{11}\) × 7 = ________________

Answer:

\(\frac{42}{11}\) or 3\(\frac{9}{11}\)

Explanation:

Given,

\(\frac{6}{11}\) × 7

= \(\frac{6}{11}\) × \(\frac{7}{1}\)

= \(\frac{6 \times 7}{11 \times 1}\)

= \(\frac{42}{11}\)

Reduce to the simplest form.

3\(\frac{9}{11}\)

d. \(\frac{2}{9}\) × 8 = ________________

Answer:

\(\frac{16}{9}\) or 1\(\frac{7}{9}\)

Explanation:

Given,

\(\frac{2}{9}\) × 8

= \(\frac{2}{9}\) × \(\frac{8}{1}\)

= \(\frac{2 \times 8}{9 \times 1}\)

= \(\frac{16}{9}\)

Reduce to the simplest form.

1\(\frac{7}{9}\)