Work out. $$\frac{33}{35} \div \frac{4}{7}$$ Give your answer as a fraction in its simplest form. - OCR - GCSE Maths - Question 1 - 2023 - Paper 5

First, multiply the numerators and then multiply the denominators:

Numerators: $33 \times 7 = 231$

Denominators: $35 \times 4 = 140$

So we have:

$\frac{231}{140}$

To simplify $\frac{231}{140}$, find the greatest common divisor (GCD) of 231 and 140. After finding the GCD, you can reduce the fraction:

• The prime factors of 231 are $3 \times 7 \times 11$.
• The prime factors of 140 are $2 \times 2 \times 5 \times 7$.

The GCD is 7, so divide both the numerator and the denominator by 7:

$\frac{231 \div 7}{140 \div 7} = \frac{33}{20}$

Thus, the final answer in its simplest form is $\frac{33}{20}$.