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2.04 Multiplying and dividing mixed numbers

Worksheet
Mixed numbers
1

What is a mixed number?

2

Write the following improper fractions as simplified mixed numbers:

a

\dfrac{125}{60}

b

\dfrac{85}{25}

c

\dfrac{15}{7}

d

\dfrac{21}{9}

e

\dfrac{40}{32}

f

\dfrac{125}{60}

g

\dfrac{44}{3}

h

\dfrac{215}{65}

3

Complete the table below:

Mixed numberImproper fractionEquivalent fraction
2 \dfrac{1}{6}
3 \dfrac{4}{5}
4 \dfrac{2}{7}
1 \dfrac{2}{5}
6 \dfrac{1}{8}
2 \dfrac{3}{8}
3 \dfrac{3}{7}
4 \dfrac{2}{9}
5 \dfrac{1}{4}
Multiplication of mixed numbers
4

Simplify each expression, giving your answer as a mixed number:

a
4 \times 2\dfrac{2}{3}
b
1\dfrac{1}{10} \times 6
c
3 \times 3\dfrac{1}{2}
d
9 \times 5\dfrac{1}{2}
e
8 \times 2\dfrac{1}{5}
f
1\dfrac{2}{9} \times 6
g
1\dfrac{1}{6} \times 4
h
7\dfrac{5}{6} \times 10
5

Simplify each expression, giving your answer as a mixed number:

a
2\dfrac{3}{4} \times \dfrac{5}{7}
b
\dfrac{3}{4} \times 2\dfrac{4}{5}
c
\dfrac{6}{5} \times 1\dfrac{3}{5}
d
1\dfrac{5}{6} \times \dfrac{8}{3}
e
1\dfrac{3}{4} \times \dfrac{4}{9}
f
\dfrac{3}{4} \times 1\dfrac{3}{7}
g
\dfrac{1}{4} \times 4\dfrac{2}{5}
h
3\dfrac{1}{3} \times \dfrac{4}{7}
6

Simplify each expression, giving your answer as a mixed number:

a
2\dfrac{2}{5} \times 1\dfrac{3}{5}
b
3\dfrac{1}{3} \times 1\dfrac{5}{6}
c
1\dfrac{1}{7} \times 2\dfrac{2}{5}
d
3\dfrac{1}{3} \times 1\dfrac{3}{4}
e
4\dfrac{1}{2} \times 1\dfrac{5}{6}
f
2\dfrac{2}{3} \times 1\dfrac{1}{7}
g
2\dfrac{1}{2} \times 1\dfrac{2}{3}
h
2\dfrac{1}{4} \times 4\dfrac{5}{6}
Division of mixed numbers
7

Simplify each expression, giving your answer as a mixed number:

a
8 \div 2\dfrac{3}{4}
b
1\dfrac{1}{5} \div 12
c
8 \div 2\dfrac{1}{4}
d
5 \div 3\dfrac{2}{3}
e
3\dfrac{1}{9} \div 4
f
4\dfrac{1}{2} \div 3
g
1\dfrac{1}{5} \div 12
h
5\dfrac{2}{7} \div 3
8

Simplify each expression, giving your answer as a mixed number:

a
1\dfrac{1}{6} \div \dfrac{1}{8}
b
1\dfrac{1}{7} \div \dfrac{2}{5}
c
2\dfrac{3}{4} \div \dfrac{5}{3}
d
\dfrac{1}{4} \div 1\dfrac{2}{7}
e
\dfrac{7}{8} \div 2\dfrac{2}{5}
f
1\dfrac{2}{7} \div \dfrac{1}{7}
g
\dfrac{4}{9} \div 1\dfrac{2}{9}
h
\dfrac{25}{4} \div 1\dfrac{2}{3}
9

Simplify each expression, giving your answer as a mixed number:

a
8\dfrac{3}{4} \div 8\dfrac{3}{4}
b
3\dfrac{2}{3} \div 2\dfrac{1}{4}
c
5\dfrac{1}{7} \div 4\dfrac{4}{7}
d
3\dfrac{3}{7} \div 1\dfrac{3}{5}
e
2\dfrac{2}{5} \div 1\dfrac{2}{3}
f
1\dfrac{4}{5} \div 2\dfrac{7}{10}
g
10\dfrac{1}{2} \div 6\dfrac{6}{7}
h
8\dfrac{1}{2} \div 1\dfrac{5}{6}
10

Simplify each expression, giving your answer as a mixed number:

a
1\dfrac{1}{5} \times 3\dfrac{1}{4} \times 1\dfrac{1}{2}
b
3\dfrac{1}{8} \times 4\dfrac{2}{5} \times 5\dfrac{1}{3}
c
2\dfrac{3}{4} \times 2\dfrac{4}{7} \times 2\dfrac{1}{3}
d
5\dfrac{2}{5} \times 1\dfrac{2}{3} \times 6\dfrac{1}{4}
e
6\dfrac{1}{2} \div 1\dfrac{4}{5} \div 1\dfrac{1}{4}
f
5\dfrac{1}{2} \div 1\dfrac{1}{3} \div 2\dfrac{1}{4}
g
4\dfrac{3}{4} \div 2\dfrac{2}{5} \div 1\dfrac{2}{3}
h
4\dfrac{4}{5} \div 2\dfrac{1}{4} \div 1\dfrac{3}{10}
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Outcomes

MA.6.NSO.2.2

Extend previous understanding of multiplication and division to compute products and quotients of positive fractions by positive fractions, including mixed numbers, with procedural fluency.

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