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Write each of the following ratios in their simplest form - OCR - GCSE Maths - Question 9 - 2020 - Paper 1
Question 9
Write each of the following ratios in their simplest form. (a) 12 : 15 (b) 600g : 1.8kg
Worked Solution & Example Answer:Write each of the following ratios in their simplest form - OCR - GCSE Maths - Question 9 - 2020 - Paper 1
Step 1
(a) 12 : 15
Answer
To simplify the ratio 12 : 15, we need to find the greatest common divisor (GCD) of both numbers.
- The factors of 12 are: 1, 2, 3, 4, 6, 12.
- The factors of 15 are: 1, 3, 5, 15.
- The GCD of 12 and 15 is 3.
Now, divide both terms of the ratio by the GCD:
- For 12: 12 ÷ 3 = 4
- For 15: 15 ÷ 3 = 5
Thus, the simplified ratio is:
4 : 5
Step 2
(b) 600g : 1.8kg
Answer
First, convert 1.8 kg to grams for easier comparison:
1.8 kg = 1.8 × 1000 g = 1800 g
Now the ratio becomes 600 g : 1800 g.
Next, find the GCD of 600 and 1800:
- The factors of 600 include: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600.
- The factors of 1800 include: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 60, 75, 90, 100, 150, 180, 300, 900, 1800.
- The GCD of 600 and 1800 is 600.
Now, divide both parts of the ratio by 600:
- For 600: 600 ÷ 600 = 1
- For 1800: 1800 ÷ 600 = 3
Thus, the simplified ratio is:
1 : 3