Exercise solution 7, page 185 - GCSE Mathematics for OCR Higher Student Book

⭐ What you need to know:

A) To find how many equal plots can be made, you need to divide the total area by the area of one plot. In this type of question, the key idea is:

\[ \text{number of plots}=\frac{\text{total area}}{\text{area of one plot}} \]

This works because division tells us how many times one quantity fits into another.

B) When dividing by a fraction, remember that dividing by a fraction is the same as multiplying by its reciprocal. For example, dividing by \(\frac{1}{4}\) means multiplying by \(4\):

\[ a \div \frac{1}{4}=a \times 4 \]

A similar example is:

\[\begin{aligned} 8 \div \frac{1}{4} &= 8 \times 4 \\ &= 32 \end{aligned}\]

This means that there are \(32\) quarters in \(8\).

C) Make sure the units are the same before dividing. Here, both areas are measured in \(\text{km}^2\), so the division can be done directly. After dividing, the \(\text{km}^2\) units cancel out, leaving just the number of plots.

For instance, if a field has area \(12\text{ m}^2\) and each section is \(3\text{ m}^2\), then:

\[ 12\text{ m}^2 \div 3\text{ m}^2 = 4 \]

The answer is a number of sections, not an area.

D) It can help to think of a fraction such as \(\frac{1}{2}\) as meaning half of one whole unit. So if each plot is \(\frac{1}{2}\text{ km}^2\), then two such plots make \(1\text{ km}^2\). This means the number of half-size plots will be twice the number of whole square kilometres.

For example, in \(9\text{ km}^2\), the number of plots of size \(\frac{1}{2}\text{ km}^2\) would be:

\[ 9 \times 2 = 18 \]

E) A quick check is useful at the end. If each plot is smaller than \(1\text{ km}^2\), then the number of plots should be greater than the number of square kilometres in the total area. This helps you decide whether your answer is sensible.

For example, if each plot was \(\frac{1}{2}\text{ km}^2\) and the total area was \(6\text{ km}^2\), an answer such as \(3\) would not make sense, because using smaller plots should produce more plots, not fewer.