Equalising Units Concept (Equal Portions)

1) 1/2 of boys is equal to 1/3 of girls. What is the ratio of boys to girls?

2) 1/2 of boys is equal to 2/3 of girls. What is the ratio of boys to girls?

3) John has $28 more than Peter. 1/3 of John's money is equal to 4/5 of Peter money. Find John money?

4) 2/5 of James’ pencils is equal to 1/3 of Kelvin’s pencils. If Kelvin has 4 more pencils than James, how many pencils does James have?

5) There are 836 students in a school. 7/10 of the boys and 7/8 of the girls take the bus to school. The number of boys who do not take the bus is twice the number of girls who do not take bus. How many girls do not take bus?


Equal Portions and Excess

First
There were a total of 410 boys and girls in a school. After 3/4 of the boys and 3/5 of the girls left the school, there were 60 more girls than boys that remained. How many boys were at the school at first?

(After)
Boys = 1 - 3/4 = 1/4 = 2/8
Girls = 1 - 3/5 = 2/5

Boys = 2u
Girls = 2u + 60

(Before)
Boys = 8u
Girls = 5u + 150 (Distribution Concept)

8u + 5u = 13u
13u =  = 410 - 150 = 260 (Total - Excess Concept)
Boys = 8u =160