Solving problems with percentages

# Solving problems with percentages

## Expressing one quantity as a percentage of another

#### Question

There were only 14 students in Rina's class on Wednesday. The other 11 were absent.
What percentage of Rina's class was absent?

#### Solution

The number of students present in the class = 14.
The number of students absent from the class = 11.
Total number of students in the class = 25.
Fraction of students absent from the class = $$\dfrac{11}{25}$$.
There are two approaches to this.

##### Method 1

$$\dfrac{11}{25}$$ = $$\dfrac{11 \times 4}{25 \times 4}$$ = $$\dfrac{44}{100}$$.

Hence, $$\dfrac{11}{25}$$ = 44%. You can do this easily in your head as 25 divides exactly into 100.

##### Method 2

The other method is to multiply by $$\dfrac{100}{1}$$. This method always works.

$$\dfrac{11}{25}$$ = $$\dfrac{11}{25}$$ × $$\dfrac{100}{1}$$% = $$\dfrac{11 \times 4}{1 \times 1}$$% = 44%.

It is good to include part of the question in your answer. In this case: 44% of the students were absent from the course.