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

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$$\frac{1}{2}$$
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$$\frac{1}{8}$$
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$$\frac{1}{3}$$
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$$\frac{2}{5}$$
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$$\frac{2}{5}$$
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$$\frac{3}{4}$$
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$$\frac{4}{9}$$
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$$\frac{1}{2}$$
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?
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?
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.