Quick Notes

 Multiply proper fractions with proper fractions

• Multiply the numerator with the numerator.
• Multiply the denominator with the denominator.
• Give the answer in the simplest form.

 Multiply proper fractions with mixed numbers

• Convert the mixed numbers to improper fractions.
• Give the answer in the simplest form.

• The diagram for the larger fraction is drawn first.

 Situation 1

Mr Leong has \(3\dfrac{1}{2}\) packets of fertilizer. He wants to use \(\dfrac{2}{5}\)of the fertilizer to fertilize his hibiscus plant. How many packets of the fertilizer will he use to fertilize the hibiscus plant?

\(\dfrac{2}{5}\times3\dfrac{1}{2}=\dfrac{2}{5}\times\dfrac{7}{2}\\ \quad\quad\quad\quad=\dfrac{14}{10}\\ \quad\quad\quad\quad=1\dfrac{4\div2}{10\div2}\\ \quad\quad\quad\quad=1\dfrac{2}{5} \)                                                        

 Multiply mixed numbers with mixed numbers 

• A fraction multiplied by the inverse of the fraction will give the answer 1.

 Situation 1

\(1\dfrac{1}{3}\times1\dfrac{1}{2}= \)

\(1\dfrac{1}{3}\times1\dfrac{1}{2}=(1\times1\dfrac{1}{2})+(\dfrac{1}{3}\times1\dfrac{1}{2})\\ \quad\quad\quad\quad=1\dfrac{1}{2}+(\dfrac{1}{3}\times\dfrac{3}{2})\\ \quad\quad\quad\quad=1\dfrac{1}{2}+\dfrac{3\div3}{6\div3}\\ \quad\quad\quad\quad=1\dfrac{1}{2}+\dfrac{1}{2}\\ \quad\quad\quad\quad=2 \)                             

 Divide proper fractions by whole numbers

 Situation 1

\(\begin {array} {rr}\\ \dfrac{4}{5}\div8=\dfrac{4}{5}\div\dfrac{8}{1}\quad\quad\quad\quad\quad\\ \quad\small{\color{red}1}\quad\quad\quad\quad\quad\quad\quad\quad\\ =\dfrac{\cancel4}{5}\times\dfrac{1}{\cancel8}\quad\quad\quad\quad\quad\\ \quad\quad\quad\small{\color{red}2}\quad\quad\quad\quad\quad\\ \quad=\dfrac{1}{5}\times\dfrac{1}{2}\quad\quad\quad\quad\quad\\ \quad=\dfrac{1}{10}\quad\quad\quad\quad\quad\quad \end {array} \)                                  

 Divide proper fractions by proper fractions

• Change division to multiplication.
• Inverse the divisor.
• Simplify the numerator and the denominator by cancellation (if any).

 Situation 1

This is only \(\dfrac{3}{4}\)m. Cut the wood into a few pieces, each measuring \(\dfrac{1}{8}\)m. How many pieces of wood measuring \(\dfrac{1}{8}\)m were cut by Paramjit's father? 

\(\dfrac{3}{4} m\div\dfrac{1}{8}m=\)                             

\(\quad\quad\quad\quad\quad\quad\small{\color{red}2}\\ \dfrac{3}{4}\div\dfrac{1}{8}=\dfrac{3}{\cancel4}\times\dfrac{\cancel8}{1}\\ \quad\quad\quad\quad\quad\small{\color{red}1}\\ \quad\quad\quad=6\)                               

 Divide mixed numbers by whole numbers

 Situation 1

\(1\dfrac{7}{9}\div4=\\ 1\dfrac{7}{9}\div4=1\dfrac{7}{9}\div\dfrac{4}{1}\\ \quad\quad\quad\quad\small{\color{red}4}\\ \quad\quad\quad=\dfrac{\cancel{16}}{9}\times\dfrac{1}{\cancel4}\\ \quad\quad\quad\quad\quad\quad\quad\small{\color{red}1}\\ \quad\quad\quad=\dfrac{4}{9} \)                                                              

 Situation 2

\(6\dfrac{2}{7}\div22=\\ 6\dfrac{2}{7}\div22=6\dfrac{2}{7}\div\dfrac{22}{1}\\ \quad\quad\quad\quad\small{\color{red}2}\\ \quad\quad\quad=\dfrac{\cancel{44}}{7}\times\dfrac{1}{\cancel{22}}\\ \quad\quad\quad\quad\quad\quad\quad\small{\color{red}1}\\ \quad\quad\quad=\dfrac{2}{7} \)                                                    

 Divide mixed numbers by proper fractions

  Situation 1

How many \(\dfrac{1}{5}\)are there in \(1\dfrac{1}{2}\)?

\(1\dfrac{1}{2}\div\dfrac{1}{5}=\dfrac{3}{2}\times\dfrac{5}{1}\\ \quad\quad\quad=\dfrac{15}{2}\\ \quad\quad\quad=7\dfrac{1}{2} \)                             

 Situation 1

The recipe to make chocolate chip muffins is as shown. \(\dfrac{3}{4}\)cup of chocolate chips is needed to produce 12 muffins. Zara tried the recipe and used only half of the flour. How chocolate chips did Zara use?

Solution

\(\dfrac{1}{2}\times\dfrac{3}{4}=\dfrac{1\times3}{2\times4}\\ \quad\quad\quad=\dfrac{3}{8}\)

 Situation 2

Damia has \(1\dfrac{1}{2} m\)  of ribbon. She uses \(\dfrac{1}{3}\)of the ribbon to decorate her mother's gift box. What is the length of the ribbon that she uses?          

Solution

\(\quad\quad\quad\quad\quad\quad\small{\color{red}1}\\ \dfrac{1}{3}\times1\dfrac{1}{2}=\dfrac{1}{\cancel3}\times\dfrac{\cancel3}{2}\\ \quad\quad\quad\quad\quad\small{\color{red}1}\\ \quad\quad\quad\quad=\dfrac{1}{1}\times\dfrac{1}{2}\\ \quad\quad\quad\quad=\dfrac{1}{2}\)