Multiplication and Division of Fractions

Multiplying and Dividing Fractions

Multiplying Fractions

​The diagrams help you understand how to manipulate fractions and add or subtract fractions. You will explore area diagrams to multiply fractions, which show a portion of a portion.

Multiplying the numerators gets the number of shaded pieces. Multiplying the denominators gets the size of the pieces..

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Multiply the numerators together and the denominators together.

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Multiplying Without a Diagram

​Unlike adding and subtracting fractions, you do not need common denominators to multiply and divide fractions.

Multiple Choice

$$\frac{4}{9}\cdot\frac{5}{7}$$

• 20/63

• 3/20

• 16/9

Multiple Choice

$$\frac{3}{8}\cdot\frac{2}{5}$$

• $$\frac{20}{63}$$

• $$\frac{3}{20}$$

• $$\frac{16}{9}$$

Multiple Choice

$$\frac{8}{3}\cdot\frac{2}{3}$$

• $$\frac{20}{63}$$

• $$\frac{16}{9}$$

• $$\frac{3}{20}$$

Multiplying fractions with a whole number

Desmos

Handheld

Lets Look at Calculators for multiplying and dividing fractions

​Calculator.net

Multiple Choice

$$2\frac{1}{2}\cdot1\frac{3}{5}$$

• 3
• 5
• 4

Multiple Choice

$$3\cdot\frac{15}{6}$$

• $$7\frac{1}{2}$$

• 10
• 5

Multiple Choice

$$\frac{7}{4}\cdot\frac{5}{8}$$

• $$10\ \frac{1}{2}$$

• $$\frac{75}{11}$$

• $$\frac{35}{32}$$

Dividing Fractions

Draw a Diagram

Multiple Choice

$$8\div\frac{2}{7}$$

• 28
• 21
• 14

Multiple Choice

$$8\div\frac{4}{10}$$

• 20
• 15
• 10

When multiplying or dividing with mixed numbers, always convert them to an improper fraction first.

Dividing with Mixed numbers

Multiple Choice

$$\frac{2}{9}\div4$$

•  $$9\frac{1}{3}$$

• 2
• $$\frac{1}{18}$$

Multiple Choice

$$4\frac{1}{3}\div\frac{2}{9}$$

• $$19\ \frac{1}{2}$$

• $$12\ \frac{1}{4}$$

• $$8\ \frac{1}{3}$$

Multiple Choice

Dividing by a fraction is the same as which statement below?

• adding the reciprocal

• multiplying by the reciprocal

• dividing by the reciprocal