Expressing One Quality as a Fraction of Another

Quantities as fractions of another

  1. Often when we compare things we want to compare quantities as fractions of something.
  2. Fractions compare things against wholes.

Let’s go through some examples:

Example 1

You have a class, where there are 23 girls and 17 boys in total we have 40 students.

This means the whole class = 40 students

Therefore if we want to express the fraction of girls in the class, we would put 23/40, the fraction of boys in the class would be 17/40. Both of these fractions are out of 40 because 40 is the number of students in total, the whole.

Example 2

The whole here is £80, which means £80 will be our denominator, and we have £5 of that £80, so £5 will be our numerator.

Therefore we can write this as 1/16 here I have simplified the fraction by dividing the top and bottom by 5.

1. Kate buys some drinks, she buys 4 coffees , 3 cans of coke and 1 frappe. What fraction of drinks does she have that are coffees?
Your answer should include: 4/8 / 1/2
In an exam hall Mr Peterson collects mobile phones from the students. There are 23 iphones, 17 Samsung’s and 10 other makes. What fraction of the phones are other makes?
Your answer should include: 10/50 / 1/5
In a biscuit tin 6 biscuits are custard creams, 8 are bourbons and 3 are jammy dodgers. What fraction are jammy dodgers?