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.