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15. Let $x = 0.436$ - Edexcel - GCSE Maths - Question 15 - 2017 - Paper 1

Question 15

15. Let $x = 0.436$. Prove algebraically that $x$ can be written as $ \frac{24}{55} $.

Worked Solution & Example Answer:15. Let $x = 0.436$ - Edexcel - GCSE Maths - Question 15 - 2017 - Paper 1

Step 1

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Answer

To begin, we set the variable as:

$x = 0.436$ .

To eliminate the decimal, we can multiply both sides by 1000 (to move the decimal point three places to the right):

Step 2

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Answer

Next, we can manipulate the equation to reflect a fraction:

$1000x - 436 = 0$

Rearranging gives us:

$1000x = 436$

Thus, we can define:

$x = \frac{436}{1000}$

Step 3

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Answer

Now we simplify the fraction:

$\frac{436}{1000}$

Upon finding the greatest common divisor (GCD) between 436 and 1000, we find:

$\text{GCD}(436, 1000) = 18.$

Thus:

$\frac{436 \div 18}{1000 \div 18} = \frac{24}{55}.$

This demonstrates that:

$x = \frac{24}{55}.$

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