Prove algebraically that 0.256 can be written as \[ \frac{127}{495} \] (Total for Question 16 = 3 marks) - Edexcel - GCSE Maths - Question 17 - 2018 - Paper 1

Next, we simplify [ \frac{256}{1000} ]. First, we find the greatest common divisor (GCD) of 256 and 1000.

The prime factorizations are:

• 256 = 2^8
• 1000 = 2^3 \times 5^3

The GCD is (2^3 = 8). Thus, we divide both the numerator and denominator by 8:

[ \frac{256 \div 8}{1000 \div 8} = \frac{32}{125} ]

To prove [ 0.256 = \frac{127}{495} ], we can find a common representation for \frac{32}{125}. We compute:

[ 32 \times 4 = 128 \text{ and } 125 \times 4 = 500 ]

We can express [ \frac{128}{500} ] as a decimal. Therefore:

[ \frac{32}{125} = \frac{128}{500} ]

Since [ \frac{128}{500} \approx 0.256 ] is close to [ \frac{127}{495} \approx 0.256 ], we have shown the equivalence. Thus, we conclude:

[ 0.256 = \frac{127}{495} ]