Practice questions available in **McGraw Hill Math Grade 6 Answer Key PDF Lesson 8.4 Dividing Mixed Numbers** will engage students and is a great way of informal assessment.

## McGraw-Hill Math Grade 6 Answer Key Lesson 8.4 Dividing Mixed Numbers

**Exercises Divide**

Question 1.

1\(\frac{1}{2}\) ÷ 2\(\frac{1}{2}\)

Answer:

Dividing 1\(\frac{1}{2}\) by 2\(\frac{1}{2}\),we get the quotient \(\frac{3}{5}\)

Explanation:

1\(\frac{1}{2}\) ÷ 2\(\frac{1}{2}\)

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

= [(2 + 1) ÷ 2] ÷ [(4 + 1) ÷ 2]

=(3 ÷ 2) ÷ (5 ÷ 2)

= \(\frac{3}{2}\) × \(\frac{2}{5}\)

= \(\frac{3}{1}\) × \(\frac{1}{5}\)

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

Question 2.

3\(\frac{3}{5}\) ÷ 1\(\frac{1}{8}\)

Answer:

Dividing 3\(\frac{3}{5}\) by 1\(\frac{1}{8}\),we get the quotient \(\frac{72}{25}\)

Explanation:

3\(\frac{3}{5}\) ÷ 1\(\frac{1}{8}\)

= {[(3 × 5) + 3] ÷ 5} ÷ {[(1 × 8) + 1] ÷ 8}

= [(15 + 3) ÷ 5] ÷ [(9 + 1) ÷ 8]

=(18 ÷ 5) ÷ (10 ÷ 8)

= \(\frac{18}{5}\) × \(\frac{8}{10}\)

= \(\frac{9}{5}\) × \(\frac{8}{5}\)

= \(\frac{72}{25}\)

Question 3.

7\(\frac{1}{7}\) ÷ 3\(\frac{1}{3}\)

Answer:

Dividing 7\(\frac{1}{7}\) by 3\(\frac{1}{3}\),we get the quotient \(\frac{15}{7}\)

Explanation:

7\(\frac{1}{7}\) ÷ 3\(\frac{1}{3}\)

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

= [(49 + 1) ÷ 7] ÷ [(9 + 1) ÷ 3]

= (50 ÷ 7) ÷ (10 ÷ 3)

= \(\frac{50}{7}\) ÷ \(\frac{10}{3}\)

= \(\frac{50}{7}\) × \(\frac{3}{10}\)

= \(\frac{5}{7}\) × \(\frac{3}{1}\)

= \(\frac{15}{7}\)

Question 4.

3\(\frac{4}{7}\) ÷ 2\(\frac{2}{5}\)

Answer:

Dividing 3\(\frac{4}{7}\) by 2\(\frac{2}{5}\),we get the quotient \(\frac{125}{84}\)

Explanation:

3\(\frac{4}{7}\) ÷ 2\(\frac{2}{5}\)

= {[(3 × 7) + 4] ÷ 7} ÷ {[(2 × 5) + 2] ÷ 5}

= [(21 + 4) ÷ 7] ÷ [(10 + 2) ÷ 5]

=(25 ÷ 7) ÷ (12 ÷ 5)

= \(\frac{25}{7}\) ÷ \(\frac{12}{5}\)

= \(\frac{25}{7}\) × \(\frac{5}{12}\)

= \(\frac{125}{84}\)

Question 5.

6\(\frac{4}{5}\) ÷ 3\(\frac{2}{5}\)

Answer:

Dividing 6\(\frac{4}{5}\) by 3\(\frac{2}{5}\),we get the quotient 2.

Explanation:

6\(\frac{4}{5}\) ÷ 3\(\frac{2}{5}\)

= {[(6 × 5) + 4] ÷ 5} ÷ {[(3 × 5) + 2] ÷ 5}

= [(30 + 4) ÷ 5] ÷ [(15 + 2) ÷ 5]

= (34 ÷ 5) ÷ (17 ÷ 5)

= \(\frac{34}{5}\) ÷ \(\frac{17}{5}\)

= \(\frac{34}{5}\) × \(\frac{5}{17}\)

= \(\frac{34}{1}\) × \(\frac{1}{17}\)

= \(\frac{2}{1}\) × \(\frac{1}{1}\)

= \(\frac{2}{1}\) or 2.

Question 6.

5\(\frac{1}{2}\) ÷ 3\(\frac{3}{4}\)

Answer:

Dividing 5\(\frac{1}{2}\) by 3\(\frac{3}{4}\),we get the quotient \(\frac{22}{15}\)

Explanation:

5\(\frac{1}{2}\) ÷ 3\(\frac{3}{4}\)

= {[(5 × 2) + 1] ÷ 2} ÷ {[(3 × 4) + 3] ÷ 4}

= [(10 + 1) ÷ 2] ÷ [(12 + 3) ÷ 4]

=(11 ÷ 2) ÷ (15 ÷ 4)

= \(\frac{11}{2}\) ÷ \(\frac{15}{4}\)

= \(\frac{11}{2}\) × \(\frac{4}{15}\)

= \(\frac{11}{1}\) × \(\frac{2}{15}\)

= \(\frac{22}{15}\)

Question 7.

4\(\frac{2}{9}\) ÷ 2\(\frac{4}{9}\)

Answer:

Dividing 4\(\frac{2}{9}\) by 2\(\frac{4}{9}\),we get the quotient \(\frac{19}{11}\)

Explanation:

4\(\frac{2}{9}\) ÷ 2\(\frac{4}{9}\)

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

= [(36 + 2) ÷ 9] ÷ [(18 + 4) ÷ 9]

=(38 ÷ 9) ÷ (22 ÷ 9)

= \(\frac{38}{9}\) ÷ \(\frac{22}{9}\)

= \(\frac{38}{9}\) × \(\frac{9}{22}\)

= \(\frac{38}{1}\) × \(\frac{1}{22}\)

= \(\frac{19}{1}\) × \(\frac{1}{11}\)

= \(\frac{19}{11}\)

Question 8.

9\(\frac{2}{7}\) ÷ 2\(\frac{1}{2}\)

Answer:

Dividing 9\(\frac{2}{7}\) by 2\(\frac{1}{2}\),we get the quotient \(\frac{26}{7}\)

Explanation:

9\(\frac{2}{7}\) ÷ 2\(\frac{1}{2}\)

= {[(9 × 7) + 2] ÷ 7} ÷ {[(2 × 2) + 1] ÷ 2}

= [(63 + 2) ÷ 7] ÷ [(4 + 1) ÷ 2]

= (65 ÷ 7) ÷ (5 ÷ 2)

= \(\frac{65}{7}\) ÷ \(\frac{5}{2}\)

= \(\frac{65}{7}\) × \(\frac{2}{5}\)

= \(\frac{13}{7}\) × \(\frac{2}{1}\)

= \(\frac{26}{7}\)

Question 9.

Frankie was making batches of cookies to bring to the school activities meeting. The recipe called for 1\(\frac{3}{4}\) cups of flour per batch. He had 5\(\frac{1}{4}\) cups of flour left in a bag. How many batches of cookies can Frankie bake?

Answer:

Number of batches of cookies can Frankie bake = 3.

Explanation:

Number of cups of flour per batch recipe called for = 1\(\frac{3}{4}\)

Number of cups of flour left in a bag = 5\(\frac{1}{4}\)

Number of batches of cookies can Frankie bake = Number of cups of flour left in a bag ÷ Number of cups of flour per batch recipe called for

= 5\(\frac{1}{4}\) ÷ 1\(\frac{3}{4}\)

= {[(5 × 4) + 1] ÷ 4} ÷ {[(1 × 4) + 3] ÷ 4}

= [(20 + 1) ÷ 4] ÷ [(4 + 3) ÷ 4]

= (21 ÷ 4) ÷ (7 ÷ 4)

= \(\frac{21}{4}\) × \(\frac{4}{7}\)

= \(\frac{3}{4}\) × \(\frac{4}{1}\)

= \(\frac{3}{1}\) × \(\frac{1}{1}\)

= \(\frac{3}{1}\) or 3.

Question 10.

Jonas was making balloon decorations for the school dance. Each balloon needs 3\(\frac{2}{3}\) feet of ribbon to tie it down to the refreshment table. He has 51\(\frac{1}{3}\) feet of ribbon. How many balloons can he secure to the table?

Answer:

Number of balloons he can secure to the table = 14.

Explanation:

Number of feet of balloons each balloon needs = 3\(\frac{2}{3}\)

Number of feet of balloons he has = 51\(\frac{1}{3}\)

Number of balloons he can secure to the table = Number of feet of balloons he has ÷ Number of feet of balloons each balloon needs

= 51\(\frac{1}{3}\) ÷ 3\(\frac{2}{3}\)

= {[(51 × 3) + 1] ÷ 3} ÷ {[(3 × 3) + 2] ÷ 3}

= [(153 + 1) ÷ 3] ÷ [(9 + 2) ÷ 3]

= (154 ÷ 3) ÷ (11 ÷ 3)

= \(\frac{154}{3}\) × \(\frac{3}{11}\)

= \(\frac{154}{1}\) × \(\frac{1}{11}\)

= \(\frac{14}{1}\) × \(\frac{1}{1}\)

= 14.