Solving problem sums involving quantity, fractions and changes to the quantity

An example from our high quality Primary Mathematics Tuition

How To Identify Such Problems

Such problems will typically have all of the following:

1. Involves 2 items

2. Expresses the quantity of one item as a fraction of another item

3. An action increases or decreases one or both of the items.

4. The new fraction after the action is given

5. Need to solve for the quantity of a specific item

*Don’t worry if you don’t fully understand above at this point. Use the following example to help you with your understanding. Come back here again after you have gone through the rest of the tip.

An Example Problem

In a class, there are 2/3 as many boys as there are girls. After 15 boys left the class, the number of boys is only 1/9 that of the girls. What is the total number of students in the class at first?

Breaking Down the Example Problem

• The persons/objects involved: 

  • Boys (A)

  • Girls (G)

• The starting info: 

  • B = (2/3) x G

• Change that happened: 15 boys left

• The ending info:

  • B = (1/9) x G

• Problem to solve: Total number of students initially = ? 

General Technique To Use

You can follow the following steps to solve such problems:

1. Express the fractions as ratio

2. Apply the “Problem Sum: Ratio of Quantity of 2 Items that Changed (Before-After)” technique to solve it!

Solving the Example Problem (Step-By-Step Guide)

Change the fractions into ratio: 

•  There are 2/3 as many boys as there are girls => The ratio of Girls to Boys is 3 : 2

• The number of boys is 1/9 that of the girls => The ratio of Girls to Boys is 9 : 1

More Similar Problems

1. In a class, there are 2/3 as many boys as there are girls. After 9 boys joined the class, there are equal number of boys and girls. What is the total number of students in the class at the beginning? (Hint: This is a slight variation from the example problem) 

   Ans: Total of 45 students initially

2. Alicia had 2/5 as many sweets as Betty. After Betty gave Alicia 18 sweets, Alicia had as many sweets as Betty. How many sweets did Alicia have initially? (Hint: The total is unchanged)

   Ans: Alicia had 24 sweets initially

3. The number of sweets Charles had was 3/4 that of David. Elias decided to give both Charles and David 12 sweets each. After receiving the sweets from Elias, Charles had 9/11 as many sweets as David. How many sweets did David have initially? (Hint: The difference in the number of sweets between Charles and David is unchanged)

   Ans: David had 32 sweets initially