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Fractions, SM-Bank 070

Write reciprocals for the following.

  1. `4/5`  (1 mark)

  2. `3`  (1 mark)

  3. `1 3/4`  (2 marks)

Show Answers Only

a.    `5/4`

b.    `1/3`

c.    `4/7`

Show Worked Solution
a.    `5/4`
 `=> 4/5\ \ \ \ text{(Swap the numerator and denominator)}`

 

b.    `3` `= 3/1\ \ \ \ text{(Write whole numbers as fractions with a denominator of 1)}`  
  `=> 1/3\ \ \ \ text{(Then swap the numerator and denominator)}`  

 

c.    `1 3/4`
 `= 7/4 \ \ \ \ text{(Change mixed numbers to improper fractions)}`
  `=> 4/7 \ \ \ \ text{(Then swap the numerator and denominator)}`

Fractions, SM-Bank 061

Transmission Oils import engine oil.

They sell one brand of engine oil at `2 1/4` times the wholesale price.

If the wholesale price is $12 per litre, what is the selling price per litre?  (2 marks)

Show Answers Only

`$27\ text(per litre)`

Show Worked Solution

`text(Wholesale price) = $12\ text(per litre)`

`text(Sale price)` `= 2 1/4 xx 12`
  `= 9/4 xx 12`
  `= 9 xx 3`
  `=27`

 
`:.\ text(The selling price per litre)\ = $27`

Fractions, SM-Bank 059

Find:

  1. `1/4` of 20 apples.  (1 mark)

  2. `4/5` of 60 years.  (1 mark)

  3. `3/11` of 110 kilometres.  (1 mark)

Show Answers Only

a.    `5\ text(apples)`

b.    `48\ text(years)`

c.    `30\ text(kilometres)`

Show Worked Solution

a.    `1/4 xx 20 =1/4 xx 20/1= 5\ text(apples)`
 

b.    `4/5 xx 60`
`=4/5 xx 60/1`  
  `=4 xx 12`  
  `= 48\ text(years)`  

   

c.    `3/11 xx 110`
`=3/11 xx 110/1`
  `=3 xx 10`
  `= 30\ text(kilometres)`

 

Fractions, SM-Bank 056

Sally makes bird feeders to hang in her garden.

The table below shows the fraction of the bird feeder eaten each day by the birds. 

\begin{array} {|l|c|c|}
\hline \textbf{Day} & \textbf{Fraction Eaten} \\
\hline \text{Monday}  &  3/10\\
\hline \text{Tuesday} & 1/5  \\
\hline \text{Wednesday} &  1/4  \\
\hline \text{Thursday} & ?   \\
\hline \end{array}

  1. If the whole feeder was consumed in four days, what fraction did the birds eat on Thursday?  (2 marks)

  2. The bird feeder weighs 5 kilograms. How many kilograms were consumed on Monday?  (2 marks)

Show Answers Only

a.    `1/4`

b.    `1 1/2\ text(kilograms)`

Show Worked Solution
a.    `text(Eaten Thursday)` `= 1-(3/10+1/5+1/4)`
  `= 1-(6/20+4/20+5/20)`
  `= 1-15/20`
  `=5/20=1/4`

 

b.    `text(Monday Kilograms)` `= 3/10 xx 5`
  `= 15/10`
  `= 1 1/2\ text(kilograms)`

Fractions, SM-Bank 047

Mike is downloading a complete hard drive onto his new computer.

It should take 24 minutes to download the full hard drive.

Mike loses his internet connection when  `5/6`  of the hard drive is downloaded.

How many more minutes are needed for Mike to complete the download?  (2 marks)

Show Answers Only

`text(4 minutes)`

Show Worked Solution

`5/6 xx 24 =\ text(20 minutes)`

`:.\ text(Minutes needed)` `= 24-20`
  `= 4\ text(minutes)`

Fractions, SM-Bank 036

Jaime and Jordan ordered 2 extra large pizzas for dinner.

Jaime ate `2/5` of an extra large pizza.

  1. If Jordan ate 3 times as much pizza as Jaime, how much pizza did Jordan eat? Give your answer as a mixed number.  (1 mark)

  2. What fraction of pizza is left over?  (2 marks)

Show Answers Only

a.    `1 1/5\ text(pizzas)`

b.    `2/5\ text(of a pizza)`

Show Worked Solution

a.    `text(Jordan’s Pizza)`

`= 3 xx 2/5`

`= 6/5`

 `= 1 1/5\ text(pizzas)`
  

b.    `text(Leftover pizza)`

`= 2-(2/5 + 1 1/5)`

`= 2-1 3/5`

`= 2/5\ text(of a pizza)`