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Fractions, SM-Bank 018

  1. List all factors of 20 and 36.  (2 marks)

  2. What is the highest common factor (HCF) of 20 and 36?  (1 mark)

  3. Use the HCF of 20 and 36 to simplify `20/36`.  (1 mark)

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a.    `text(Factors of)\ 20: 1, 2, 4, 5, 10, 20`

`text(Factors of)\ 36: 1, 2, 3, 4, 6, 9, 12, 16, 36`

b.    `text(HCF) = 4`

c.    `20/36 = (20 ÷ 4)/(36 ÷ 4) = 5/9`

Show Worked Solution

a.    `text(Factors of)\ 20: 1, 2, 4, 5, 10, 20`

`text(Factors of)\ 36: 1, 2, 3, 4, 6, 9, 12, 16, 36`
  

b.   `text(Common Factors:)\ 1, 2, 4`

`text(HCF) = 4`
  

c.    `text(To simplify, divide the numerator and denominator by HCF.)`

`20/36 = (20 ÷ 4)/(36 ÷ 4) = 5/9`

Fractions, SM-Bank 017

State whether the following pairs of fractions are equivalent by using the `=` or `≠` symbol in the box between the fractions.  (3 marks)

a.    

  
b.    

  
c.    

  
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a.    `4/5 = 36/45`

b.    `56/63 ≠ 7/9`

c.    `5/8 ≠ 3/5`

Show Worked Solution
a.    `4/5` `= (4 xx 9)/(5 xx 9) = 36/45`

 
`:.\ 4/5 = 36/45`

 

b.    `56/63` `= (56 ÷ 7)/(63 ÷ 7) = 8/9`

 
`:.\ 56/63 ≠ 7/9`
 

c.    `text(Lowest common multiple of)\ 8\ text(and)\ 5 = 40`

`:.\ 5/8` `= (5 xx 5)/(8 xx 5) = 25/40`

 
`text(and)`

`:.\ 3/5` `= (3 xx 8)/(5 xx 8) = 24/40`

 
`:.\ 5/8 ≠ 3/5`

 

Fractions, SM-Bank 016

A bowl has 16 pieces of fruit in it.

12 of the pieces of fruit are oranges.

What fraction of the pieces of fruit are oranges?  Give your answer in simplest form.  (1 mark)

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`3/4`

Show Worked Solution
`text(Fraction of oranges)` `= text(number of oranges)/ text(total number of fruit pieces)`
  `=12/16`
  `= (12 ÷ 4)/(16 ÷ 4)`
  `=3/4 `

Fractions, SM-Bank 015

  1. The shape below has some triangles shaded.
    Shade some extra triangles so that `1/3` of the the shape is shaded.  (1 mark)
      
  2. Using the shape in (a.) above, or otherwise, write two more fractions that are equivalent to `1/3`.  (2 marks)

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a.    `5\ text(additional triangles need to be shaded (8 in total))`

`text(One possible solution.`

b.    `8/24 = 4/12 = 2/6 = 1/3`

`text(Note: Many other fractions equivalent to)\ 1/3\ text(are possible.)`

Show Worked Solution

a.   `text(There are 24 triangles altogether.)`

`text(Number of triangles)\ = 1/3 xx 24 = 8`

`:.\ 5\ text(additional triangles need to be shaded (8 in total))`

`text(One possible solution.`

b.   `text(Using diagram)`

`8/24 = 4/12 = 2/6 = 1/3`

`text(Note: Many other fractions equivalent to)\ 1/3\ text(are possible.)`

Fractions, SM-Bank 012

Shade  `4/7`  of the image below. (1 mark)

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`text(8 triangles must be shaded.)`

`text(Note: Many options are possible.)`

Show Worked Solution

`text(There are 14 triangles)`

`4/7 xx 14 = 8`

`:.\ text(Any 8 triangles shaded is acceptable.)`