Practice the questions of **McGraw Hill Math Grade 8 Answer Key**** PDF** **Lesson 3.2 Changing Mixed Numbers to Improper Fractions** to secure good marks & knowledge in the exams.

## McGraw-Hill Math Grade 8 Answer Key Lesson 3.2 Changing Mixed Numbers to Improper Fractions

**Exercises Convert to an Improper Fraction**

Question 1.

5\(\frac{3}{4}\)

Answer:

\(\frac{23}{4}\),

Explanation:

Given 5\(\frac{3}{4}\) to convert to an improper fraction

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{5 X 4 + 3}{4}\) = \(\frac{20 + 3}{4}\) = \(\frac{23}{4}\).

Question 2.

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

Answer:

\(\frac{54}{7}\),

Explanation:

Given 7\(\frac{5}{7}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{7 X 7 + 5}{7}\) = \(\frac{49 + 5}{7}\)

= \(\frac{54}{7}\).

Question 3.

25\(\frac{7}{11}\)

Answer:

\(\frac{282}{11}\),

Explanation:

Given 25\(\frac{7}{11}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{25 X 11 + 7}{11}\) = \(\frac{275 + 7}{11}\) = \(\frac{282}{11}\).

Question 4.

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

Answer:

\(\frac{124}{5}\),

Explanation:

Given 24\(\frac{4}{5}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{24 X 5 + 4}{5}\) = \(\frac{120 + 4}{5}\) = \(\frac{124}{5}\).

Question 5.

16\(\frac{5}{13}\)

Answer:

\(\frac{213}{13}\),

Explanation:

Given 16\(\frac{5}{13}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{16 X 13 + 5}{13}\) = \(\frac{208 + 5}{13}\) = \(\frac{213}{13}\).

Question 6.

14\(\frac{9}{14}\)

Answer:

\(\frac{205}{14}\),

Explanation:

Given 14\(\frac{9}{14}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{14 X 14 + 9}{14}\) = \(\frac{196 + 9}{14}\) = \(\frac{205}{14}\).

Question 7.

53\(\frac{4}{9}\)

Answer:

\(\frac{481}{9}\),

Explanation:

Given 53\(\frac{4}{9}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{53 X 9 + 4}{9}\) = \(\frac{477 + 4}{9}\) = \(\frac{481}{9}\).

Question 8.

17\(\frac{3}{4}\)

Answer:

\(\frac{71}{4}\),

Explanation:

Given 17\(\frac{3}{4}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{17 X 4 + 3}{4}\) = \(\frac{68 + 3}{4}\) = \(\frac{71}{4}\).

Question 9.

3\(\frac{6}{17}\)

Answer:

\(\frac{57}{17}\),

Explanation:

Given 3\(\frac{6}{17}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{3 X 17 + 6}{17}\) = \(\frac{51 + 6}{17}\) = \(\frac{57}{17}\).

Question 10.

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

Answer:

\(\frac{437}{7}\),

Explanation:

Given 62\(\frac{3}{7}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{62 X 7 + 3}{7}\) = \(\frac{434 + 3}{7}\) = \(\frac{437}{7}\).

Question 11.

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

Answer:

\(\frac{45}{2}\),

Explanation:

Given 22\(\frac{1}{2}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{22 X 2 + 1}{2}\) = \(\frac{44 + 1}{2}\) = \(\frac{45}{2}\).

Question 12.

32\(\frac{11}{29}\)

Answer:

\(\frac{939}{29}\),

Explanation:

Given 32\(\frac{11}{29}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{32 X 29 + 11}{29}\) = \(\frac{928 + 11}{29}\) = \(\frac{939}{29}\).

Question 13.

27\(\frac{5}{8}\)

Answer:

\(\frac{221}{8}\),

Explanation:

Given 27\(\frac{5}{8}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{27 X 8 + 5}{8}\) = \(\frac{216 + 5}{8}\) = \(\frac{221}{8}\).

Question 14.

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

Answer:

\(\frac{76}{3}\),

Explanation:

Given 25\(\frac{1}{3}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{25 X 3 + 1}{3}\) = \(\frac{75 + 1}{3}\) = \(\frac{76}{3}\).

Question 15.

41\(\frac{9}{14}\)

Answer:

\(\frac{583}{14}\),

Explanation:

Given 41\(\frac{9}{14}\) to convert to an improper fraction,

1. Multiply the whole number by the denominator.

2. Add the answer from Step 1 to the numerator.

3. Write answer from Step 2 over the denominator.

So it is \(\frac{41 X 14 + 9}{14}\) = \(\frac{574 + 9}{14}\) = \(\frac{583}{14}\).

Question 16.

Gene’s bucket holds \(\frac{1}{3}\) of a pound of soil. Gene ñeeds to move 10\(\frac{2}{3}\) pounds of topsoil to his grandmother’s garden. How many times will he need to fill his bucket if he wants to move the entire pile of topsoil to the garden?

Answer:

32 times

Explanation:

Given Gene’s bucket holds \(\frac{1}{3}\) of a pound of soil.

Gene ñeeds to move 10\(\frac{2}{3}\) pounds of topsoil to his grandmother’s garden. So many times will he need to fill his bucket if he wants to move the entire pile of topsoil to the garden is as

10\(\frac{2}{3}\) pounds ÷ \(\frac{1}{3}\) pound =

\(\frac{10 X 3 + 2}{3}\) pounds ÷ \(\frac{1}{3}\) pound= \(\frac{32}{3}\) pounds X 3 pound = 32 times.

Question 17.

Kayla wants to give a third of a pie to each of her 25 relatives. She has already baked 6 pies. How many more pies will she need to bake so that each relative can have a third?

Answer:

Kayla needs 3 pies,

Explanation:

Given Kayla wants to give a third of a pie to each of her 25 relatives.

She has already baked 6 pies. So many more pies will she need to bake so that each relative can have a third is first we’d have to find out how many thirds of pies she has already, so,

6 x 3 = 18 slices of pie and she needs 25 slices of pie,

so 25 – 18 = 7 slices of pie turn the 7 slices into pies

7 ÷ 3 = 2.33, Kayla needs 2.33 more pies and so if rounded up 2.33 pies = 3 pies.