Spectrum Math Grade 5 Chapter 4 Lesson 8 Answer Key Simplifying Mixed Numbers

Practice with the help of Spectrum Math Grade 5 Answer Key Chapter 4 Lesson 4.8 Simplifying Mixed Numbers regularly and improve your accuracy in solving questions.

Spectrum Math Grade 5 Chapter 4 Lesson 4.8 Simplifying Mixed Numbers Answers Key

A mixed number is in simplest form if its fraction is in simplest form and names a number less than 1.
The greatest common factor of 8 and 12 is 4.
3\(\frac{8}{12}\)
3 + \(\frac{8 \div 4}{12 \div 4}\) = \(\frac{2}{3}\)
3\(\frac{8}{12}\) = 3\(\frac{2}{3}\)
Spectrum Math Grade 5 Chapter 4 Lesson 8 Answer Key Simplifying Mixed Numbers 1

Reduce each mixed number to simplest form.

Question 1.
a. 3\(\frac{6}{8}\) ______
Answer:
Simplest form of 3\(\frac{6}{8}\) is 3\(\frac{3}{4}\).

Explanation:
3\(\frac{6}{8}\)
= {[(3 × 8) + 6] ÷ 8}
= [(24 + 6) ÷ 8]
= (30 ÷ 8)
= 15 ÷ 4
= 3\(\frac{3}{4}\)

b. 2\(\frac{12}{15}\) ______
Answer:
Simplest form of 2\(\frac{12}{15}\) is 2\(\frac{3}{5}\).

Explanation:
2\(\frac{12}{15}\)
= {[(2 × 15) + 12] ÷ 15}
= [(30 + 12) ÷ 15]
= (42 ÷ 15)
= 13 ÷ 5
= 2\(\frac{3}{5}\)

c. 1\(\frac{9}{12}\) ______
Answer:
Simplest form of 1\(\frac{9}{12}\) is 1\(\frac{3}{4}\).

Explanation:
1\(\frac{9}{12}\)
= {[(1 × 12) + 9] ÷ 12}
= [(12 + 9) ÷ 12]
= (21 ÷ 12)
= 7 ÷ 4
= 1\(\frac{3}{4}\)

d. 4\(\frac{10}{15}\) ______
Answer:
Simplest form of 4\(\frac{10}{15}\) is 4\(\frac{2}{3}\).

Explanation:
4\(\frac{10}{15}\)
= {[(4 × 15) + 10] ÷ 15}
= [(60 + 10) ÷ 15]
= (70 ÷ 15)
= 14 ÷ 3
= 4\(\frac{2}{3}\)

Question 2.
a. 2\(\frac{8}{5}\) ______
Answer:
Simplest form of 2\(\frac{8}{5}\) is 1\(\frac{1}{5}\).

Explanation:
2\(\frac{8}{5}\)
= {[(2 × 5) + 8] ÷ 5}
= [(10 + 8) ÷ 5]
= (18 ÷ 15)
= 6 ÷ 5
= 1\(\frac{1}{5}\)

b. 3\(\frac{15}{4}\) ______
Answer:
Simplest form of 3\(\frac{15}{4}\) is 6\(\frac{3}{4}\).

Explanation:
3\(\frac{15}{4}\)
{[(3 × 4) + 15] ÷ 4}
= [(12 + 15) ÷ 4]
= (27 ÷ 4)
= 6\(\frac{3}{4}\)

c. 1\(\frac{7}{3}\) ______
Answer:
Simplest form of 1\(\frac{7}{3}\) is 3\(\frac{1}{3}\).

Explanation:
1\(\frac{7}{3}\)
{[(1 × 3) + 7] ÷ 3}
= [(3 + 7) ÷ 3]
= (10 ÷ 3)
= 3\(\frac{1}{3}\)

d. 2\(\frac{5}{2}\) ______
Answer:
Simplest form of 2\(\frac{5}{2}\) is 4\(\frac{1}{2}\).

Explanation:
2\(\frac{5}{2}\)
{[(2 × 2) + 5] ÷ 2}
= [(4 + 5) ÷ 2]
= (9 ÷ 2)
= 4\(\frac{1}{2}\)

Question 3.
a. 4\(\frac{4}{8}\) ______
Answer:
Simplest form of 4\(\frac{4}{8}\) is 4\(\frac{1}{2}\).

Explanation:
4\(\frac{4}{8}\)
{[(4 × 8) + 4] ÷ 8}
= [(32 + 4) ÷ 8]
= (36 ÷ 8)
= 9 ÷ 2
= 4\(\frac{1}{2}\)

b. 5\(\frac{6}{9}\) ______
Answer:
Simplest form of 5\(\frac{6}{9}\) is 5\(\frac{2}{3}\).

Explanation:
5\(\frac{6}{9}\)
{[(5 × 9) + 6] ÷ 9}
= [(45 + 6) ÷ 9]
= (51 ÷ 9)
= 17 ÷ 3
= 5\(\frac{2}{3}\)

c. 8\(\frac{12}{20}\) ______
Answer:
Simplest form of 8\(\frac{12}{20}\) is 8\(\frac{3}{5}\).

Explanation:
8\(\frac{12}{20}\)
{[(8 × 20) + 12] ÷ 20}
= [(160 + 12) ÷ 20]
= (172 ÷ 20)
= 43 ÷ 5
= 8\(\frac{3}{5}\)

d. 7\(\frac{4}{16}\) ______
Answer:
Simplest form of 7\(\frac{4}{16}\) is 7\(\frac{1}{4}\).

Explanation:
7\(\frac{4}{16}\)
{[(7 × 16) + 4] ÷ 16}
= [(112 + 4) ÷ 16]
= (116 ÷ 16)
= 29 ÷ 4
= 7\(\frac{1}{4}\)

Question 4.
a. 2\(\frac{10}{4}\) ______
Answer:
Simplest form of 2\(\frac{10}{4}\) is 4\(\frac{1}{2}\).

Explanation:
2\(\frac{10}{4}\)
{[(2 × 4) + 10] ÷ 4}
= [(8 + 10) ÷ 4]
= (18 ÷ 4)
= 9 ÷ 2
= 4\(\frac{1}{2}\)

b. 3\(\frac{3}{2}\) ______
Answer:
Simplest form of 3\(\frac{3}{2}\) is 4\(\frac{1}{2}\).

Explanation:
3\(\frac{3}{2}\)
{[(3 × 2) + 3] ÷ 2}
= [(6 + 3) ÷ 2]
= (9 ÷ 2)
= 4\(\frac{1}{2}\)

c. 7\(\frac{8}{12}\) ______
Answer:
Simplest form of 7\(\frac{8}{12}\) is 7\(\frac{2}{3}\).

Explanation:
7\(\frac{8}{12}\)
{[(7 × 12) + 8] ÷ 12}
= [(84 + 8) ÷ 12]
= (92 ÷ 12)
= 23 ÷ 3
= 7\(\frac{2}{3}\)

d. 5\(\frac{3}{9}\) ______
Answer:
Simplest form of 5\(\frac{3}{9}\) is 5\(\frac{1}{3}\).

Explanation:
5\(\frac{3}{9}\)
{[(5 × 9) + 3] ÷ 9}
= [(45 + 3) ÷ 9]
= (48 ÷ 9)
= 16 ÷ 3
= 5\(\frac{1}{3}\)

Question 5.
a. 2\(\frac{10}{3}\) ______
Answer:
Simplest form of 2\(\frac{10}{3}\) is 5\(\frac{1}{3}\).

Explanation:
2\(\frac{10}{3}\)
{[(2 × 3) + 10] ÷ 3}
= [(6 + 10) ÷ 3]
= (16 ÷ 3)
= 5\(\frac{1}{3}\)

b. 4\(\frac{6}{5}\) ______
Answer:
Simplest form of 4\(\frac{6}{5}\) is 5\(\frac{1}{5}\).

Explanation:
4\(\frac{6}{5}\)
{[(4 × 5) + 6] ÷ 5}
= [(20 + 6) ÷ 5]
= (26 ÷ 5)
= 5\(\frac{1}{5}\)

c. 3\(\frac{15}{7}\) ______
Answer:
Simplest form of 3\(\frac{15}{7}\) is 5\(\frac{1}{7}\).

Explanation:
3\(\frac{15}{7}\)
{[(3 × 7) + 15] ÷ 7}
= [(21 + 15) ÷ 7]
= (36 ÷ 7)
= 5\(\frac{1}{7}\)

d. 2\(\frac{20}{9}\) ______
Answer:
Simplest form of 2\(\frac{20}{9}\) is 4\(\frac{4}{9}\).

Explanation:
2\(\frac{20}{9}\)
{[(2 × 9) + 20] ÷ 9}
= [(18 + 20) ÷ 9]
= (38 ÷ 9)
= 4\(\frac{4}{9}\)

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