14 (a) Write each of the following ratios in their simplest form - OCR - GCSE Maths - Question 14 - 2019 - Paper 1

First, convert 2.1 litres to millilitres:

$2.1 \text{ litres} = 2.1 \times 1000 = 2100 \text{ ml}$

Now we have the ratio 300 ml : 2100 ml. To simplify, we find the GCD of 300 and 2100, which is 300.

Dividing both terms by 300:

$\frac{300}{300} : \frac{2100}{300} = 1 : 7$

Thus, the simplified form is 1 : 7.

To find the value of n in the ratio sin 30° : tan 45°, we first calculate each trigonometric function:

• $\sin 30° = \frac{1}{2}$
• $\tan 45° = 1$

The ratio is:

$\frac{\sin 30°}{\tan 45°} = \frac{\frac{1}{2}}{1} = \frac{1}{2}$

This can be written in the form 1 : n:

$1 : n = 1 : 2$

Therefore, n = 2.