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.

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