Practice with the help of **Spectrum Math Grade 5 Answer Key Chapter 4 Lesson 4.3 Changing Mixed Numbers to Improper Fractions** regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 4 Lesson 4.3 Changing Mixed Numbers to Improper Fractions Answers Key

To change a mixed number to a fraction, multiply the denominator by the whole number. Then, add the numerator to the product to get the new numerator. Keep the denominator the same.

4\(\frac{3}{5}\) = \(\frac{(5 \times 4)+3}{5}\) = \(\frac{20+3}{5}\) = \(\frac{23}{5}\)

2\(\frac{3}{4}\) = \(\frac{(4 \times 2)+3}{4}\) = \(\frac{8+3}{4}\) = \(\frac{11}{4}\)

**Change each mixed number to an improper fraction.**

Question 1.

a. 2\(\frac{5}{8}\) _______

Answer:

Improper fraction of 2\(\frac{5}{8}\) is 21 ÷ 8 or \(\frac{21}{8}\).

Explanation:

2\(\frac{5}{8}\) = {[(2 × 8) + 5] ÷ 8}

= [(16 + 5) ÷ 8]

= 21 ÷ 8 or \(\frac{21}{8}\)

b. 3\(\frac{1}{4}\) _______

Answer:

Improper fraction of 3\(\frac{1}{4}\) is 13 ÷ 4 or \(\frac{13}{4}\).

Explanation:

3\(\frac{1}{4}\) = {[(3 × 4) + 1] ÷ 4}

= [(12 + 1) ÷ 4]

= 13 ÷ 4 or \(\frac{13}{4}\)

c. 2\(\frac{3}{7}\) _______

Answer:

Improper fraction of 2\(\frac{3}{7}\) is 17 ÷ 7 or \(\frac{17}{7}\).

Explanation:

2\(\frac{3}{7}\) = {[(2 × 7) + 3] ÷ 7}

= [(14 + 3) ÷ 7]

= 17 ÷ 7 or \(\frac{17}{7}\)

d. 4\(\frac{1}{1}\) _______

Answer:

Improper fraction of 4\(\frac{1}{1}\) is 5 ÷ 1 or \(\frac{5}{1}\).

Explanation:

4\(\frac{1}{1}\) = {[(4 × 1) + 1] ÷ 1}

= [(4 + 1) ÷ 1]

= 5 ÷ 1 or \(\frac{5}{1}\)

Question 2.

a. 3\(\frac{3}{4}\) _______

Answer:

Improper fraction of 3\(\frac{3}{4}\) is 15 ÷ 4 or \(\frac{15}{4}\).

Explanation:

3\(\frac{3}{4}\) = {[(3 × 4) + 3] ÷ 4}

= [(12 + 3) ÷ 4]

= 15 ÷ 4 or \(\frac{15}{4}\)

b. 2\(\frac{5}{12}\) _______

Answer:

Improper fraction of 2\(\frac{5}{12}\) is 29 ÷ 12 or \(\frac{29}{12}\).

Explanation:

2\(\frac{5}{12}\) = {[(2 × 12) + 5] ÷ 12}

= [(24 + 5) ÷ 12]

= 29 ÷ 12 or \(\frac{29}{12}\)

c. 4\(\frac{1}{6}\) _______

Answer:

Improper fraction of 4\(\frac{1}{6}\) is 25 ÷ 6 or \(\frac{25}{6}\).

Explanation:

4\(\frac{1}{6}\) = {[(4 × 6) + 1] ÷ 6}

= [(24 + 1) ÷ 6]

= 25 ÷ 6 or \(\frac{25}{6}\)

d. 5\(\frac{2}{3}\) _______

Answer:

Improper fraction of 5\(\frac{2}{3}\) is 17 ÷ 3 or \(\frac{17}{3}\).

Explanation:

5\(\frac{2}{3}\) = {[(5 × 3) + 2] ÷ 3}

= [(15 + 2) ÷ 3]

= 17 ÷ 3 or \(\frac{17}{3}\)

Question 3.

a. 2\(\frac{7}{16}\) _______

Answer:

Improper fraction of 2\(\frac{7}{16}\) is 39 ÷ 16 or \(\frac{39}{16}\).

Explanation:

2\(\frac{7}{16}\) = {[(2 × 16) + 7] ÷ 16}

= [(32 + 7) ÷ 16]

= 39 ÷ 16 or \(\frac{39}{16}\)

b. 3\(\frac{1}{2}\) _______

Answer:

Improper fraction of 3\(\frac{1}{2}\) is 7 ÷ 2 or \(\frac{7}{2}\).

Explanation:

3\(\frac{1}{2}\) = {[(3 × 2) + 1] ÷ 2}

= [(6 + 1) ÷ 2]

= 7 ÷ 2 or \(\frac{7}{2}\)

c. 1\(\frac{7}{16}\) _______

Answer:

Improper fraction of 1\(\frac{7}{16}\) is 23 ÷ 16 or \(\frac{23}{16}\).

Explanation:

1\(\frac{7}{16}\) = {[(1 × 16) + 7] ÷ 16}

= [(16 + 7) ÷ 16]

= 23 ÷ 16 or \(\frac{23}{16}\)

d. 2\(\frac{5}{8}\) _______

Answer:

Improper fraction of 2\(\frac{5}{8}\) is 21 ÷ 8 or \(\frac{21}{8}\).

Explanation:

2\(\frac{5}{8}\) = {[(2 × 8) + 5] ÷ 8}

= [(16 + 5) ÷ 8]

= 21 ÷ 8 or \(\frac{21}{8}\)

Question 4.

a. 3\(\frac{1}{3}\) _______

Answer:

Improper fraction of 3\(\frac{1}{3}\) is 10 ÷ 3 or \(\frac{10}{3}\).

Explanation:

3\(\frac{1}{3}\) = {[(3 × 3) + 1] ÷ 3}

= [(9 + 1) ÷ 3]

= 10 ÷ 3 or \(\frac{10}{3}\)

b. 4\(\frac{2}{5}\) _______

Answer:

Improper fraction of 4\(\frac{2}{5}\) is 22 ÷ 5 or \(\frac{22}{5}\).

Explanation:

4\(\frac{2}{5}\) = {[(4 × 5) + 2] ÷ 5}

= [(20 + 2) ÷ 5]

= 22 ÷ 5 or \(\frac{22}{5}\)

c. 3\(\frac{1}{8}\) _______

Answer:

Improper fraction of 3\(\frac{1}{8}\) is 25 ÷ 8 or \(\frac{25}{8}\).

Explanation:

3\(\frac{1}{8}\) = {[(3 × 8) + 1] ÷ 8}

= [(24 + 1) ÷ 8]

= 25 ÷ 8 or \(\frac{25}{8}\)

d. 7\(\frac{1}{3}\) _______

Answer:

Improper fraction of 7\(\frac{1}{3}\) is 22 ÷ 3 or \(\frac{22}{3}\).

Explanation:

7\(\frac{1}{3}\) = {[(7 × 3) + 1] ÷ 3}

= [(21 + 1) ÷ 3]

= 22 ÷ 3 or \(\frac{22}{3}\).

Question 5.

a. 8\(\frac{2}{3}\) _______

Answer:

Improper fraction of 8\(\frac{2}{3}\) is 26 ÷ 3 or \(\frac{26}{3}\).

Explanation:

8\(\frac{2}{3}\) = {[(8 × 3) + 2] ÷ 3}

= [(24 + 2) ÷ 3]

= 26 ÷ 3 or \(\frac{26}{3}\)

b. 1\(\frac{2}{5}\) _______

Answer:

Improper fraction of 1\(\frac{2}{5}\) is 7 ÷ 5 or \(\frac{7}{5}\).

Explanation:

1\(\frac{2}{5}\) = {[(1 × 5) + 2] ÷ 5}

= [(5 + 2) ÷ 5]

= 7 ÷ 5 or \(\frac{7}{5}\)

c. 2\(\frac{3}{7}\) _______

Answer:

Improper fraction of 2\(\frac{3}{7}\) is 17 ÷ 7 or \(\frac{17}{7}\).

Explanation:

2\(\frac{3}{7}\) = {[(2 × 7) + 3] ÷ 7}

= [(14 + 3) ÷ 7]

= 17 ÷ 7 or \(\frac{17}{7}\)

d. 3\(\frac{8}{9}\) _______

Answer:

Improper fraction of 3\(\frac{8}{9}\) is 35 ÷ 9 or \(\frac{35}{9}\).

Explanation:

3\(\frac{8}{9}\) = {[(3 × 9) + 8] ÷ 9}

= [(27 + 8) ÷ 9]

= 35 ÷ 9 or \(\frac{35}{9}\)

Question 6.

a. 4\(\frac{2}{5}\) _______

Answer:

Improper fraction of 4\(\frac{2}{5}\) is 22 ÷ 5 or \(\frac{22}{5}\).

Explanation:

4\(\frac{2}{5}\) = {[(4 × 5) + 2] ÷ 5}

= [(20 + 2) ÷ 5]

= 22 ÷ 5 or \(\frac{22}{5}\)

b. 3\(\frac{5}{6}\) _______

Answer:

Improper fraction of 3\(\frac{5}{6}\) is 23 ÷ 6 or \(\frac{23}{6}\).

Explanation:

3\(\frac{5}{6}\) = {[(3 × 6) + 5] ÷ 6}

= [(18 + 5) ÷ 6]

= 23 ÷ 6 or \(\frac{23}{6}\)

c. 2\(\frac{4}{9}\) _______

Answer:

Improper fraction of 2\(\frac{4}{9}\) is 22 ÷ 9 or \(\frac{22}{9}\).

Explanation:

2\(\frac{4}{9}\) = {[(2 × 9) + 4] ÷ 9}

= [(18 + 4) ÷ 9]

= 22 ÷ 9 or \(\frac{22}{9}\)

d. 4\(\frac{5}{12}\) _______

Answer:

Improper fraction of 4\(\frac{5}{12}\) is 53 ÷ 12 or latex]\frac{53}{12}[/latex].

Explanation:

4\(\frac{5}{12}\) = {[(4 × 12) + 5] ÷ 12}

= [(48 + 5) ÷ 12]

= 53 ÷ 12 or latex]\frac{53}{12}[/latex]