Exercise solution 5, page 185 - GCSE Mathematics for OCR Higher Student Book

⭐ What you need to know:

A) To express one quantity as a fraction of another, both quantities must be written in the same unit first. Then you form the fraction

\[ \text{fraction}=\frac{\text{first quantity}}{\text{second quantity}} \]

For example, to express \(300\text{ g}\) as a fraction of \(2\text{ kg}\), first change \(2\text{ kg}\) into grams:

\[ 2\text{ kg}=2000\text{ g} \]

Then write

\[ \frac{300}{2000} \]

and simplify if possible.

B) You need to know how to convert between kilograms and grams. The key fact is:

\[ 1\text{ kg}=1000\text{ g} \]

So:

To change kilograms into grams, multiply by \(1000\).
To change grams into kilograms, divide by \(1000\).

Example:

\[ 7\text{ kg}=7000\text{ g} \]

and

\[ 8500\text{ g}=8.5\text{ kg} \]

C) A mixed number must often be turned into an improper fraction before using it in calculations. For instance, if you have \(3\frac{1}{4}\), convert it like this:

\[ 3\frac{1}{4}=\frac{3\times 4+1}{4}=\frac{13}{4} \]

This is useful when the quantity you are comparing with is written as a whole number and a fraction together.

D) After writing the fraction, always simplify it by dividing the numerator and denominator by the same number. Example:

\[ \frac{360}{2400}=\frac{3}{20} \]

Simplifying gives a clearer final answer and is usually expected unless the question says otherwise.

E) If several steps are needed, work in a clear order: convert units, write the fraction, then simplify. For example, to express \(450\text{ g}\) as a fraction of \(1.5\text{ kg}\):

\[ \begin{aligned} 1.5\text{ kg} &= 1500\text{ g} \\ \text{fraction} &= \frac{450}{1500} \\ &= \frac{3}{10} \end{aligned} \]

This method helps avoid mistakes and makes your reasoning easy to follow.