Week 19 · Ratios with tape diagrams, number lines and comparing · 3 lessons
1
Tape diagrams for ratio problems
Discover Mathematics P6: Term 2, Unit 9, Lessons 4–6
GoalDraw a tape diagram for a ratio, find the value of one part and solve problems where the total or one part is known.
New words
part · one equal unit of a tape diagramtotal · all the parts togethervalue of one part · what one equal unit of the tape stands for
Explanation
A tape diagram helps with ratio problems. Draw one bar for each quantity, made of as many equal parts as its ratio number. All the parts must be the same size, because they stand for the same amount. If the total is known, add the parts, then divide the total by the number of parts to find the value of one part. If the value of one quantity is known, divide it by its number of parts to find the value of one part. Once you know one part, multiply to find the other quantity, and check that the answers fit the story.
★Remember
Equal parts. Total known: total ÷ all parts = one part. One quantity known: quantity ÷ its parts = one part. Then multiply.
Worked examples
The total is known. A farm has hens and ducks in the ratio 5 : 2, and 28 birds altogether. There are 5 + 2 = 7 parts, so one part is 28 ÷ 7 = 4 birds. Hens: 5 × 4 = 20. Ducks: 2 × 4 = 8. Check: 20 + 8 = 28.
One quantity is known. The ratio of pupils who walk to pupils who ride a bike is 3 : 4, and 12 pupils ride a bike. Four parts are 12, so one part is 12 ÷ 4 = 3. Walkers: 3 × 3 = 9 pupils.
The value of the larger quantity is known. Red and blue cars are in the ratio 2 : 7, and there are 21 blue cars. Seven parts are 21, so one part is 3. Red cars: 2 × 3 = 6. Together there are 6 + 21 = 27 cars.
Class activity
Draw it. A grown-up gives you a ratio and a total, for example 3 : 5 and 40 sweets. Draw the tape diagram with equal boxes on squared paper, write the value of one part in each box and give the two amounts. Swap roles for a new problem.
Practice
1
The ratio of apples to pears is 3 : 5 and there are 24 fruits. How many apples and pears?
8 parts, one part is 24 ÷ 8 = 3. Apples 9, pears 15. Check: 9 + 15 = 24.
2
The ratio of teachers to pupils is 1 : 12. There are 36 pupils. How many teachers?
12 parts are 36, so one part is 3. There are 3 teachers.
3
Blue to green beads are in the ratio 4 : 3 and there are 20 blue beads. How many green beads?
4 parts are 20, so one part is 5. Green beads: 3 × 5 = 15.
4
Cats and dogs are in the ratio 2 : 5, and there are 35 animals in all. How many of each?
7 parts, one part is 35 ÷ 7 = 5. Cats 10, dogs 25. Check: 10 + 25 = 35.
5
Marwan says that boys and girls in the ratio 3 : 2 with 15 children are 3 boys and 2 girls. What went wrong?
He used the ratio numbers as the amounts. There are 5 parts, so one part is 15 ÷ 5 = 3. Boys: 9. Girls: 6.
