 Content description

Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)

Elaboration

• investigating multiplication of fractions and decimals, using strategies including patterning and multiplication as repeated addition, with both concrete materials and digital technologies, and identifying the processes for division as the inverse of multiplication

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

Mixed numerals

When multiplying and dividing mixed numerals, convert to improper fractions and then proceed as you have already learned.

Example 1

1. $$5\dfrac{1}{2}×6\dfrac{1}{4}$$
2. $$7\dfrac{1}{4}÷1\dfrac{1}{5}$$

Solution

1. \begin{align}5\dfrac{1}{2}×6\dfrac{1}{4}&=\dfrac{11}{2}×\dfrac{25}{4}\\\\ &=\dfrac{275}{8}\\\\ &=34\dfrac{3}{8}\end{align}
2. \begin{align}7\dfrac{1}{4}÷1\dfrac{1}{5}&=\dfrac{29}{4}÷\dfrac{6}{5}\\\\ &=\dfrac{29}{4}×\dfrac{5}{6}\\\\ &=\dfrac{145}{24}\\\\ &=6\dfrac{1}{24}\end{align}   