Question 9 - Fractions

• A group of boys played only two types of sports during recess. 1/4 of them played badminton and 2/3 of them played football. 1/6 of the boys played both sports and 90 boys did not play any sports at all. How many boys were there?

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Question 9 - Answer

Both = 1/6 = 2/12

Badminton = 1/4 = 3/12              3/12 -2/12 = 1/12 ( Badminton only)

Football = 2/3 = 8/12                  8/12 - 2/12 = 6/12 ( Football only)

1- 1/12 -6/12 - 2/12 = 3/12         3/12 = 90 ( did not play any sport)

90/3 = 30/unit                              30 x 12 = 360

There were 360 boys.

Question 3 - Fraction

• Shawn and Michael had different number of stamps at first. After Shawn gave Michael 1/4 of his stamps. Michael had more stamps than him. Michael then gave Shawn 1/4 of his new number of stamps and they had 126 stamps each at the end. How many stamps did Shawn have at first?

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Question 3 - Answer

This question we have to work backward.


Step 1 : Michael : 126 = 3 units 42 = 1 unit (give Shawn)

                            126 + 42 = 168

Step 2 : Shawn : 126 – 42 = 84 = 3 units 28 = 1 unit ( give Michael)

                          84 + 28 = 112 ( initial stamps)

Step 3 : Michael : 168 – 28 = 140 ( initial stamps)

Shawn had 112 stamps at first.