☰ Year plan · Mathematics

Proportion

Week 1 · Proportion: equal ratios, cross multiplication and solving for the unknown · 3 lessons
1

Ratios in simplest form and what a proportion is

Mathematics Prep 1 Term 1, Unit 1, Lesson 1
GoalWrite a ratio in simplest form, make equal ratios, and say what a proportion is.
New words
ratio · compares two quantities of the same kindproportion · two ratios that are equalextremes · the first and last terms of a proportionmeans · the two middle terms of a proportion
Explanation

A ratio such as 6 : 9 compares two quantities. To write it in simplest form, divide both terms by the same number, here 3, and you get 2 : 3. Dividing or multiplying both terms by the same number gives an equal ratio, so 2 : 3, 4 : 6 and 6 : 9 are all the same ratio. A proportion is the statement that two ratios are equal: a : b = c : d. The outer terms a and d are the extremes, and the two middle terms b and c are the means. Before you write a ratio, make sure both quantities are in the same unit.

ƒFormula
a : b = c : d
Extremes: a and d. Means: b and c.
Worked examples
Red1212Blue121212
Mariam has 24 red beads and 36 blue beads. The ratio red : blue is 24 : 36. Both numbers divide by 12, so the simplest form is 2 : 3. The picture shows it: red is 2 groups of 12 and blue is 3 groups of 12.
RatioMultiply both terms byEqual ratio
2 : 524 : 10
2 : 536 : 15
2 : 5510 : 25
Equal ratios come from multiplying both terms by the same number. Start with 2 : 5. Multiply by 2 to get 4 : 10, by 3 to get 6 : 15, by 5 to get 10 : 25. So 2 : 5 = 4 : 10 = 6 : 15 = 10 : 25.
Find the ratio of 50 cm to 2 m. The units differ, so change 2 m to 200 cm first. The ratio is 50 : 200. Divide both terms by 50 and you get 1 : 4.
Class activity

Ratio cards. Write six ratios on small cards, such as 2 : 3, 4 : 6, 3 : 5, 6 : 10, 5 : 7 and 8 : 12. Turn them face down. Turn over two cards: if they are equal ratios, keep the pair. How many pairs can you find?

Practice
1
Write 18 : 27 in simplest form.
2
Write 45 : 60 in simplest form.
3
Find the missing number: 5 : 8 = 15 : ?
4
In the proportion 3 : 5 = 9 : 15, name the extremes and the means.
5
Karim says 2 : 3 = 5 : 6 because he added 3 to each term. Is he right?