15. Let x = 0.436 Prove algebraically that x can be written as \( \frac{24}{55} \) (Total for Question 15 is 3 marks) - Edexcel - GCSE Maths - Question 15 - 2017 - Paper 1

Now, let's shift our decimal point back by multiplying the original decimal by 100:

$100x = 43.6$

Next, we can subtract this new equation from the first equation:

$1000x - 100x = 436.36 - 43.6$

This simplifies to:

$900x = 392.76$

To express x in terms of a fraction, solve for x:

$x = \frac{392.76}{900}$

Rounding 392.76 to 393, the fraction simplifies to:

$x = \frac{393}{900}$

Upon simplifying this further, we find: $x = \frac{24}{55}$

Thus proving that x can be expressed as ( \frac{24}{55} ).