Week 18 · What a ratio is, how to show it, and equivalent ratios · 3 lessons
1
What a ratio is: comparing two quantities
Discover Mathematics P6: Term 2, Unit 9, Lessons 1–3
GoalDescribe how two quantities compare with a ratio in words, with a colon and as a fraction, and keep the order right.
New words
ratio · a comparison of two quantitiespart-to-part · a ratio that compares one group with another grouppart-to-whole · a ratio that compares one group with everythingfor every · words that tell how many of one thing go with another
Explanation
A ratio compares two quantities. A fruit tray holds 3 apples and 5 oranges. Comparing the apples with the oranges gives the ratio 3 to 5. We can write it three ways: with words (3 to 5), with a colon (3 : 5) and as a fraction (3/5). The order matters: the ratio of oranges to apples is 5 : 3, which is different. When we compare one group with another group it is a part-to-part ratio. When we compare a group with the whole, it is a part-to-whole ratio: there are 3 + 5 = 8 fruits, so the ratio of apples to all the fruit is 3 : 8. We also say it with rate language: “for every 3 apples there are 5 oranges”.
★Remember
Ratio of A to B is written A to B, A : B or A/B. The order matters. Part-to-part compares two groups; part-to-whole compares a group with all.
Worked examples
A tray has 3 apples and 5 oranges. Apples to oranges is 3 : 5. Oranges to apples is 5 : 3. Apples to all the fruit is 3 : 8, and as a fraction 3/8 of the fruit are apples.
Ratio
Kind
Written
girls to boys
part-to-part
12 : 18
boys to girls
part-to-part
18 : 12
girls to all pupils
part-to-whole
12 : 30
In a class there are 12 girls and 18 boys. Girls to boys is 12 : 18. Boys to girls is 18 : 12. There are 12 + 18 = 30 pupils, so girls to the whole class is 12 : 30.
Rate language. A recipe uses 2 cups of rice for every 3 cups of water, so rice to water is 2 : 3. A bus travels 60 km for every hour; that is also a ratio of two quantities, 60 km to 1 hour.
Class activity
Ratio hunt. Look in the kitchen or the room and find two groups of things (for example spoons and forks, or books and pencils). Count both and say the ratio in three ways. Then say the ratio of the other order and the ratio of one group to everything.
Practice
1
A garden has 4 roses and 7 tulips. Write the ratios of roses to tulips, tulips to roses and roses to all flowers.
Roses to tulips 4 : 7. Tulips to roses 7 : 4. Roses to all flowers 4 : 11.
2
Write the ratio of cats to birds in the picture, in two orders.
Cats to birds 2 : 6. Birds to cats 6 : 2.
3
A recipe uses 1 cup of sugar for every 4 cups of flour. Write sugar to flour and flour to sugar.
Sugar to flour 1 : 4. Flour to sugar 4 : 1.
4
Karim says the ratio of 5 red pens to 3 blue pens is 3 : 5. What did he do wrong?
He wrote the blue pens first. Red to blue is 5 : 3; 3 : 5 is blue to red.
5
Of 20 pupils, 8 walk to school and the others come by bus. Write the ratio of walkers to bus riders and of walkers to all pupils.
12 pupils come by bus. Walkers to bus riders 8 : 12. Walkers to all pupils 8 : 20.
