Solutions and Explanations to Grade 4 Questions on Fractions

Solutions and detailed explanations to Grade 4 maths questions on fractions are presented. Problems are also included.

Questions and their Solutions

1. Use fractions to write the part of the whole shape that is shaded?
   

   .

   
   
   Solution
   The whole shape has 8 parts but only 3 parts are shaded. The shaded part of the whole shape is written as
   

   3

   ____

   8

   
   
2. Which figure is shaded to show a fraction equal to 2/5 of its whole?
   

   .

   
   
   Solution
   Figure C shows a fraction equal to
   

   4

   ____

   10

   
   Divide numeraor and denominator by 2 to obtain an equivalent fraction equal to
   

   2

   ____

   5

   
   
3. Which two fractions are equivalent?
   
   1. 1/2 and 1/3
   2. 1/2 and 2/4
   3. 1/4 and 1/6
   4. 2/3 and 1/3
   
   
   Solution
   1/2 and 2/4 are equivalent because if you multiply the numerator and denominator of the fraction 1/2 by 2, you obtain 2/4
   
4. The figures below show that
   

   

   
   
   1. 1/5 = 1/4
   2. 2/5 = 2/4
   3. 2/5 > 2/4
   4. 2/5 < 2/4
   
   
   Solution
   The whole parts of both figures have the same lengths. The shaded part in the top figure is smaller than the shaded part in the lower fraction. Hence 2/5 < 2/4
   
5. Half of half is the same as the fraction .
   
   Solution
   Half of half is calculated as follows
   

   1		1		1
   ___	×	___	=	___
   2		2		4

   
   
   
6. If the fractions N/6 and 2/3 are equivalent, what is the value of N? .
   
   Solution
   The denominator of 2/3 is 3 and the denominator of N/6 is 6. We need to multiply 3 by 2 in order to obtain 6. Therefore we need to multiply the numerator 2 in 2/3 by 2 to obtain N and N = 2 × 2 = 4
   
7. Which two figures have shaded parts that represent equivalent fractions?
   

   

   
   
   Solution
   Examining all figures, the only two figures that have equivalent shaded fractions are those in D. In fact each figure has a shaded part equal to 1/2.
   
8. Order from greatest to least the fractions 1/3 , 1/6 , 1/2 , 1/7.
   
   Solution
   Each of the above fractions is represented by 1 part of a whole and it is clear from the figure that 1/2 is the greatest, then 1/3, then 1/6 and 1/7 is the smallest.

   

   
   
9. What value of the number N given below makes N/3 < 1/2?
   
   1. N = 3
   2. N = 2
   3. N = 1
   4. N = 4
   
   
   Solution
   For N = 3 the fraction N/3 = 3/3 = 1 and is greater than 1/2. For N = 2, N/3 = 2/3 is also greater than 1/2. For N = 1, N/3 = 1/3 and is smaller than 1/2. So for N = 1, N/3 < 1/2.
   
10. John, Sarah, Tom and Joane bought 2 pizzas of the same size. John ate 2/4 of a pizza. Tom, Sarah and Joane ate 1/4 of a pizza each. How much pizza was left?
    
    Solution
    There are 4 quarters (4/4) of a pizza in one pizza and 8 quarters (8/4) of one pizza in 2 pizzas. John, Tom, Sarah and Joane ate
    2/4 + 1/4 + 1/4 + 1/4 = 5/4
    The pizza left is equal to
    8/4 - 5/4 = 3/4 , 3 quarters of a pizza are left.
    

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