1.7.1 Ratios

Ratio:

A ratio is a comparison between two quantities.

There are few different ways to describe the ratio

e.g.

There are \( 4 \) bananas and \( 3 \) oranges

The ratio of bananas to oranges can be described as

• There are \( 4 \) bananas for every \( 3 \) oranges

• The ratio of bananas to oranges is \( 4 \):\( 3 \)

• The ratio of bananas to oranges is \( 4 \) to \( 3 \)

Order in ratio matters a lot.

As \( 4 \):\( 3\neq 4 \): \( 4 \)

• The ratio can also be expressed as a fraction.

• If \(a\):\(b\) is a ratio, its fraction form is \( \frac{a}{b} \).

To simplify a ratio

• Divide both sides by the same number

Equivalent ratios:

Equivalent ratios are those that are the same when compared. Two or more ratios can be compared to determine whether they are equivalent.

To find equivalent ratios,

• Convert the given ratio to fraction form

• Multiply the numerator and denominator by the same number

• The resulting fraction can then be written as an equivalent ratio

Tip:

When finding equivalent ratios, make a note of what you’re doing on both sides; this will come in handy when it comes time to check your work.

Worked example:

The fares for a train journey are shown in the table below.

For the standard fare, write the ratio \( adult \ fare \) : \( \ child \ fare \) in its simplest form.

The prices for an adult and child standard fare are \( $ \ 84 \) and \( $ \ 60\) respectively

\(84\):\(60\)

Divide both sides by \( 12 \) as it’s a highest common factor

\( (84 \div 12) \):\( (60 \div 12) \)

\( 7 \):\( 5 \)

\( 7 \):\( 5 \)

Tip:

Enter the given ratio in your calculator as a fraction, it will give you a simplified form of fraction, write this fraction as a simplified ratio.