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6. (a) The ratio is given as 2 : 6 : 3 - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 1
Question 6
6. (a) The ratio is given as 2 : 6 : 3. (b) The ratio is given as 1 : 10.
Worked Solution & Example Answer:6. (a) The ratio is given as 2 : 6 : 3 - Edexcel - GCSE Maths - Question 6 - 2022 - Paper 1
Step 1
2 : 6 : 3 - For process to compare ratios
Answer
To compare the ratios 2 : 6 : 3, we need to express each part in terms of a common ratio. We can start with the values given:
Let the common ratio be represented as a, b, and c such that:
- Let the first part be 2x, the second part be 6x, and the third part be 3x.
This gives us:
rac{2x}{2x + 6x + 3x} = rac{2x}{11x} = rac{2}{11}
This means the ratio of the first part to the total is ( \frac{2}{11} ), the second part is ( \frac{6}{11} ), and the third part is ( \frac{3}{11} ).
Step 2
For process to find fractions
Answer
We express each number from the ratio in fraction form. From the ratio 2 : 6 : 3, we can write:
- First part: ( \frac{2}{11} )
- Second part: ( \frac{6}{11} )
- Third part: ( \frac{3}{11} )
These fractions show the proportion of each number in relation to the total.
Step 3
1 : 10 - For process to express all numbers in terms of one number
Answer
To express all numbers in the ratio 1 : 10 in terms of one number, we can define the first part as ( x ). Hence, the second part becomes ( 10x ):
The total ratio is represented as ( x : 10x ).
This allows us to express any calculations based on a single variable.
Step 4
For assigning values in the ratio given
Answer
Given the ratio 1 : 10, we can assign values directly. For example:
- If ( x = 1 ), then the values are 1 and 10.
- Alternatively, if we let ( x = 2 ), the respective values become 2 and 20.
Thus, the ratio may be expressed as:
- 1 : 10, 2 : 20, 3 : 30, etc.