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

Check What You Know

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

Question 1.
a. $$\frac{12}{24}$$

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. $$\frac{10}{15}$$

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. $$\frac{6}{36}$$

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. $$\frac{9}{27}$$

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

Explanation: Question 3. $$\frac{10}{10}$$ 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. $$\frac{7}{8}$$

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

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.
$$\frac{11}{12}$$ – $$\frac{8}{12}$$ = _____________
$$\frac{3}{12}$$ 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.
$$\frac{2}{4}$$ 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 ___________
$$\frac{5}{10}$$ 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 ___________
$$\frac{44}{100}$$ 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 ___________
$$\frac{1}{10}$$ 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.

Question 11.
a. $$\frac{48}{100}$$

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. 10$$\frac{2}{6}$$ or 10$$\frac{1}{3}$$

Explanation:
$$\frac{1}{6}$$ + $$\frac{1}{6}$$ = $$\frac{2}{6}$$
7 + 3 = 10
Reduce to simplest form.
$$\frac{2}{6} \div \frac{2}{2}$$ = $$\frac{1}{3}$$
Hence, 10$$\frac{1}{3}$$

c. 13$$\frac{6}{8}$$ or 13$$\frac{3}{4}$$

Explanation:
$$\frac{3}{8}$$ + $$\frac{3}{8}$$ = $$\frac{6}{8}$$
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. 16$$\frac{4}{5}$$

Explanation:
$$\frac{3}{5}$$ + $$\frac{1}{5}$$ = $$\frac{4}{5}$$
8 + 8 = 16
So, 16$$\frac{4}{5}$$

Question 12.
a. 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. $$\frac{22}{100}$$

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. 11$$\frac{12}{10}$$
or
12$$\frac{2}{10}$$
or
12$$\frac{1}{5}$$

Explanation:
$$\frac{3}{10}$$ + $$\frac{9}{10}$$ = $$\frac{12}{10}$$
9 + 2 = 11
So, 11$$\frac{12}{10}$$
Reduce to simplest form.
12$$\frac{2}{10}$$ = 12$$\frac{1}{5}$$

d. 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 = _____________
$$\frac{32}{9}$$ 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 × $$\frac{1}{8}$$ = ______________
$$\frac{3}{8}$$

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 = ______________
$$\frac{8}{7}$$ 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 = ______________
$$\frac{40}{7}$$ 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 × $$\frac{3}{10}$$ = _______________
$$\frac{15}{10}$$ 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 × $$\frac{7}{12}$$ = ________________
$$\frac{14}{12}$$ 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 = ________________
$$\frac{42}{11}$$ 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 = ________________
$$\frac{16}{9}$$ or 1$$\frac{7}{9}$$
$$\frac{2}{9}$$ × 8
= $$\frac{2}{9}$$ × $$\frac{8}{1}$$
= $$\frac{2 \times 8}{9 \times 1}$$
= $$\frac{16}{9}$$
1$$\frac{7}{9}$$