Initial Diagnostic Audit - Foundation Course - Unit 9: Fraction Calculations
For each question that has a fraction as its answer, always give the fraction in its lowest terms
Section 9.1 - Addition and Subtraction of Fractions
1. Calculate:

(a)   
3
5
  + 
1
5
  = 
  
(b)   
4
7
  + 
2
7
  = 
  
(c)   
2
9
  + 
5
9
  = 
  
(d)   
9
10
  − 
3
10
  = 
  
(e)   
4
5
  − 
2
5
  = 
  
(f)    
7
9
  − 
2
9
  = 
  

2. Calculate:

(a)   
1
2
  + 
1
4
  = 
  
(b)   
3
10
  + 
2
5
  = 
  
(c)   
3
4
  + 
1
8
  = 
  
(d)   
1
3
  − 
1
7
  = 
  
(e)   
5
6
  − 
1
2
  = 
  
(f)    
5
8
  − 
1
4
  = 
  

3. Work out the mixed number calculations below giving your answer as an improper fraction where necessary:

(a)   
1
1
2
  + 
3
4
  = 
  
(b)   
2
1
3
  + 
1
1
2
  = 
  
(c)   
1
1
4
  − 
2
3
  = 
  
(d)   
3
1
2
  − 
1
1
4
  = 
  
(e)   
5
1
2
  − 
3
2
3
  = 
  
(f)    
1
1
4
  − 
2
5
  = 
  


4.
Laura eats 
1
5
  of a cake. Her sister eats 
1
4
  of the cake.
What fraction of the cake is left?   
  
Section 9.2 - Multiplying Fractions
5. Calculate:

(a)   
1
2
   × 18 =
(b)   
1
4
   × 24 =
(c)   
1
6
   × 30 =
(d)   
2
3
   × 60 =
(e)   
3
4
   × 20 =
(f)    
4
5
   × 30 =

6. Calculate:

(a)   
1
4
   ×  
1
5
   =  
  
(b)   
1
2
   ×  
2
3
   =  
  
(c)   
3
4
   ×  
4
5
   =  
  
(d)   
1
7
   ×  
3
5
   =  
  
(e)   
2
3
   ×  
2
5
   =  
  
(f)   
3
8
   ×  
4
5
   =  
  

7. Work out the mixed number calculations below giving your answer as an improper fraction where necessary:

(a)   
1
1
2
   ×  
1
2
   =  
  
(b)   
1
3
4
   ×  
2
3
   =  
  
(c)   
4
1
2
   ×  
1
5
   =  
  
(d)   
3
1
8
   ×  
3
5
   =  
  

8. Write down the area of each of these rectangles:

(a)       cm2

(b)      
  cm2

Section 9.3 - Dividing Fractions

The questions in this section have answers that may be a whole number or a fraction. You need to select either 'Whole Number' or 'Fraction' to display the appropriate input box(es) to enter your answer. If you need to switch the type of box from the one you originally chose, click on 'switch' and you will be able to choose again. Any answers that could be given as a mixed number should be given as an improper fraction.
9. Calculate:

(a)  3 ÷  
1
2
   =     
(b)  8 ÷  
1
4
   =     
(c)  9 ÷  
1
5
   =     
(d)   
1
4
   ÷ 2 =     
(e)   
3
5
   ÷ 6 =     
(f)    
5
8
   ÷ 5 =     

10. Calculate:

(a)   
1
6
   ÷  
1
3
   =     
(b)   
4
5
   ÷  
1
8
   =     
(c)   
5
9
   ÷  
7
9
   =     
(d)   
3
4
   ÷  
1
8
   =     
(e)   
1
7
   ÷  
4
5
   =     
(f)    
2
9
   ÷  
1
8
   =     

11. Calculate:

(a)   
1
1
2
   ÷  
3
4
   =     
(b)   
2
1
2
   ÷  
5
7
   =     
(c)   
6
1
4
   ÷  
1
1
2
   =     
(d)   
3
1
2
   ÷  
1
2
3
   =     


12.
A sports car uses 
3
25
  litres of fuel for every kilometre it travels.
How far does it travel if it uses:

(a)  3 litres of fuel?     
(b)   
2
1
2
   litres of fuel?     

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Produced by Russell Geach for CIMT - November 2017