3
Tape diagrams for fraction division stories
Discover Mathematics P6: Term 2, Unit 8, Lessons 1–2
GoalChoose the right division for a story, draw a tape diagram, solve and check by multiplying.
New words
tape diagram · a bar drawing that shows the parts of a storyoperation · the calculation we choose: +, −, × or ÷check · to test an answer, for example by multiplying
Explanation
A division story is one of two kinds. In a sharing story we cut an amount into equal shares: 3/5 of a bag of rice shared by 3 jars. In a how-many-fit story we ask how many pieces of a given size we can make: 5 m of ribbon cut into 1/2 m bows. To solve, read the story, decide which kind it is, draw a tape diagram, write the division sentence, find the quotient from the diagram, and check by multiplying the quotient by the divisor. The check must give back the number you started with.
★Remember
Sharing: amount ÷ number of shares. How many fit: amount ÷ piece size. Check: quotient × divisor = amount.
Worked examples
Sharing. 3/5 of a bag of rice is shared equally by 3 jars. The tape has 5 equal parts and 3 are shaded; each jar gets one of the shaded parts, so 3/5 ÷ 3 = 1/5 of the bag. Check: 1/5 × 3 = 3/5.
How many fit. Mina has 5 m of ribbon and every bow needs 1/2 m. Each metre gives 2 bows, so 5 ÷ 1/2 = 5 × 2 = 10 bows. Check: 10 × 1/2 = 5 m.
A fraction divided by a fraction. A rope of 3/4 m is cut into pieces of 1/8 m. Rename 3/4 as 6/8, so there are 6 pieces. 3/4 ÷ 1/8 = 6. Check: 6 × 1/8 = 6/8 = 3/4.
Class activity
Story makers. Write one sharing story and one how-many-fit story using fractions of a metre or a litre, with numbers you can draw. Swap with a family member who draws the tape diagram and solves both.
Practice
1
Write the division sentence and the answer: (a) a 4 m cloth is cut into pieces of 1/4 m, (b) 1/4 kg of nuts is shared equally among 4 children.
(a) 4 ÷ 1/4 = 16 pieces. (b) 1/4 ÷ 4 = 1/16 kg each.
2
2/3 of a field is planted equally with 4 crops. What fraction of the field does each crop get?
2/3 ÷ 4 = 4/6 ÷ 4 = 1/6 of the field.
3
Find 6 ÷ 2/3 and check it.
6 wholes are 18 thirds. 18 ÷ 2 = 9. Check: 9 × 2/3 = 18/3 = 6.
4
How many pieces of 1/12 m can be cut from 5/6 m?
5/6 = 10/12, so 5/6 ÷ 1/12 = 10 pieces.
5
Rana says 1/2 ÷ 4 = 2. Check her answer by multiplying and correct it.
2 × 4 = 8, not 1/2, so it is wrong. Half shared by 4 gives 1/8, and 1/8 × 4 = 1/2.