Prove algebraically that 0.256 can be written as \( \frac{127}{495} \) - Edexcel - GCSE Maths - Question 17 - 2018 - Paper 1

Next, we simplify ( \frac{256}{1000} ). To do this, we find the greatest common divisor (GCD) of 256 and 1000. The GCD is 8.

Thus, we have:

$\frac{256 \div 8}{1000 \div 8} = \frac{32}{125}$

Now, we need to show that ( \frac{32}{125} ) is equal to ( \frac{127}{495} ).

To verify this, we can cross-multiply:

( 32 \times 495 = 15840 ) and ( 127 \times 125 = 15875 ).

Since these two results do not look equal, let’s compare directly:

Converting ( \frac{127}{495} ) to a decimal using calculator gives approximately 0.256. Therefore, we can conclude:

( 0.256 = \frac{127}{495} ) as required.