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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
Step 1: Write the areas as a fraction.
Living Room / Kitchen = 26 / 16.4
Step 2: Eliminate the decimal by multiplying the numerator and denominator by 10.
(26 × 10) / (16.4 × 10) = 260 / 164
Step 3: Simplify the fraction. Both numbers are even, so divide by 2.
260 / 2 = 130
164 / 2 = 82
Fraction is 130 / 82.
Step 4: Divide by 2 again.
130 / 2 = 65
82 / 2 = 41
Fraction is 65 / 41.
41 is a prime number, and 65 is not a multiple of 41. So the fraction is in its simplest form.
Answer: 65/41
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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