Showing a ratio with pictures, tables and the colon
Discover Mathematics P6: Term 2, Unit 9, Lessons 1–3
GoalShow one ratio in different ways and write several true statements about it.
New words
ratio table · a table whose columns show the same ratio again and againtape diagram · bars of equal units for two quantitiesstatement · a sentence that tells what a ratio says
Explanation
The same ratio can be shown in many ways. A picture shows the two groups. A tape diagram uses bars made of equal units, one bar for each quantity. A ratio table lists how many of each there are in 1 group, 2 groups, 3 groups and so on: the ratio stays the same in every column. Words can say it in more than one way: “for every 2 hats there are 3 scarves”, “the ratio of hats to scarves is 2 to 3”, “scarves are 3 out of every 5 items”. When you look at a picture of two groups you can write at least four statements: part to part in both orders and each part to the whole.
★Remember
Picture, tape diagram, ratio table, words: all show the same ratio. In a ratio table every column has the same ratio.
Worked examples
A salad has 4 tomatoes and 6 cucumbers. Tomatoes to cucumbers is 4 : 6; cucumbers to tomatoes is 6 : 4; tomatoes to all vegetables is 4 : 10; cucumbers to all is 6 : 10. In words: for every 2 tomatoes there are 3 cucumbers.
Trays
1
2
3
4
Cupcakes
3
6
9
12
Muffins
2
4
6
8
A bakery packs each tray with 3 cupcakes and 2 muffins. The ratio table shows 1, 2, 3 and 4 trays. The ratio of cupcakes to muffins is 3 : 2 in every column: 6 : 4, 9 : 6 and 12 : 8 are the same ratio.
A tape diagram for boys to girls 3 : 5. Each small box is one unit. Boys have 3 units and girls have 5 units. The whole class has 3 + 5 = 8 units. So boys to the whole class is 3 : 8.
Class activity
Many ways. Choose a ratio from your home (for example 2 pillows to 3 chairs). Show it with a drawing, a short ratio table with 4 columns, a tape diagram and two sentences in words. Explain to a family member how they are connected.
Practice
1
Write four true statements about the lemons and pears in the picture.
Lemons to pears 5 : 3. Pears to lemons 3 : 5. Lemons to all fruit 5 : 8. Pears to all fruit 3 : 8.
2
Each box has 2 pencils and 5 pens. How many pens are in 4 boxes? How many pencils?
4 boxes have 4 × 5 = 20 pens and 4 × 2 = 8 pencils.
3
A drink is made from 2 parts syrup and 5 parts water. Draw a tape diagram and write syrup to water and syrup to the whole drink.
The tape for syrup has 2 equal units and the tape for water has 5. Syrup to water is 2 : 5. The whole drink has 2 + 5 = 7 units, so syrup to the whole drink is 2 : 7.
4
Say the ratio of cars to buses 7 : 2 in words with “for every”.
For every 7 cars there are 2 buses.
5
Which of these say the same as “3 to 8”: 3 : 8, 8 : 3, 3/8?
3 : 8 and 3/8. The ratio 8 : 3 has the opposite order.
