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AQA GCSE · Question 09 · Ratio Proportion and Rates of Change
In a house, the floor area of the living room is 26 m² and the floor area of the kitchen is 16.4 m².
Express the area of the living room as a fraction of the area of the kitchen. Give your answer in its simplest form.
In a house, the floor area of the living room is 26 m² and the floor area of the kitchen is 16.4 m².
Express the area of the living room as a fraction of the area of the kitchen. Give your answer in its simplest form.
How to approach this question
1. Write the relationship as a fraction: (Area of living room) / (Area of kitchen).
2. You will have a decimal in the denominator. To get rid of it, multiply both the top and bottom of the fraction by 10.
3. Now you have a fraction with two integers. Simplify this fraction by finding common factors and dividing both the numerator and denominator by them until it can't be simplified any further.
Full Answer
The question asks to express the area of the living room (26 m²) as a fraction of the area of the kitchen (16.4 m²).
This means we need to calculate the fraction:
Fraction = (Area of living room) / (Area of kitchen) = 26 / 16.4
To work with this, we should remove the decimal. We can do this by multiplying the numerator and the denominator by 10:
Fraction = (26 × 10) / (16.4 × 10) = 260 / 164
Now we need to simplify this fraction. Both numbers are even, so we can divide by 2:
260 ÷ 2 = 130
164 ÷ 2 = 82
So, the fraction is 130 / 82.
Both are still even, so we divide by 2 again:
130 ÷ 2 = 65
82 ÷ 2 = 41
So, the fraction is 65 / 41.
41 is a prime number. We check if 65 is divisible by 41. It is not. Therefore, the fraction is in its simplest form.
The answer is 65/41.
Common mistakes
✗ Writing the fraction the wrong way around (16.4 / 26).
✗ Making errors when multiplying by 10 (e.g., 26 / 164).
✗ Not simplifying the fraction fully. For example, leaving it as 130/82.
✗ Trying to convert to a mixed number when an improper fraction is simpler and correct.
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