Concepts – Ratios, Solving proportions

• A ratio is a comparison of two quantities by division.

• Ratios describe a part-to-part comparison or a part-to-whole comparison. 

• The order of the values in a ratio relates directly to the order of the quantities described.

• A proportion is a statement that two ratios are equal. It can be written in two ways: as two equal fractions, ab = cd ; or using a colon, a:b = c:d.

Rules

To solve equivalent ratios:

• State the ratios as fractions

• Set the two fractions equal to each other

• Write equivalent fractions.

Example

The ratio of grams of peanuts to grams of almonds in a trail mix is 5:2. If there is 20 grams of almonds in a mixture, how many grams of peanuts are there?

Solution

1. Write the ratios as fractions. 

 Amount of peanuts(in grams)Amount of almonds(in grams)

2. Set up a proportion and solve using equivalent fractions to find the missing quantity. 

Part ratio of peanutsPart ratio of almonds=x g peanuts20g almonds

52 = x20

5 × 102 × 10 = 5020

50 grams of peanuts

Pre-requisite Skills

Understand Ratios (6.6.1)

Solving Proportions (6.6.9)

Equivalent Fractions (5.10.5)

Simplifying fractions (5.10.6)