Using algebra, prove that 0.136 × 0.2 is equal in value to \( \frac{1}{33} \). - Edexcel - GCSE Maths - Question 16 - 2017 - Paper 2

Next, we calculate:

$0.136 \times \frac{1}{5} = \frac{0.136}{5}$

To divide 0.136 by 5, we can multiply 0.136 by 1 and simplify:

$0.136 = \frac{136}{1000}$

Thus,

$\frac{136}{1000} \div 5 = \frac{136}{5000}$

Now, we simplify ( \frac{136}{5000} ) and express it in terms of a simpler fraction. Reducing it will help us see if it is equal to ( \frac{1}{33} ).

To do this, we perform long division or find a common factor. After simplifying:

$\frac{136}{5000} = \frac{17}{625}$

Now, we need to check if ( \frac{17}{625} ) is equal to ( \frac{1}{33} ).

To prove that these two fractions are equal, we can cross-multiply:

$17 \times 33 = 561$ $1 \times 625 = 625$

Since 561 does not equal 625, it appears we need to refine our approach.

Performing further checks or revisiting earlier steps may help in verifying this equality properly.