Discover Mathematics P5: Term 2, Unit 9, Lessons 5–8
GoalSolve story problems that multiply fractions and mixed numbers, and check that the answer makes sense.
New words
of · in a story, “a fraction of an amount” means multiplyarea · the number of square units that cover a flat shapereasonable · close to what you expected
Explanation
In a story problem, first decide what you are asked to find. “A fraction of an amount” means multiply. The area of a rectangle is length × width, even when the sides are mixed numbers. Follow five steps: read the story, estimate with easy numbers, multiply, simplify, and check that the answer and its unit make sense. For example, a garden bed is 3 1/2 m long and 2 1/4 m wide. Estimate: about 4 × 2 = 8. Exactly: 7/2 × 9/4 = 63/8 = 7 7/8 square metres. That is close to 8, so it is reasonable. If a story has two steps, do one step at a time and write what each answer means.
Read→Estimate→Multiply→Simplify→Check
Worked examples
A garden bed is 3 1/2 m long and 2 1/4 m wide. Its area is 7/2 × 9/4 = 63/8 = 7 7/8 square metres. The estimate was about 8, so the answer is reasonable.
Marwan buys 3 1/2 kg of guavas at 18 LE a kilogram. 3 1/2 × 18 = 7/2 × 18 = 126/2 = 63 LE. Check: 3 kg cost 54 LE and half a kilogram costs 9 LE, and 54 + 9 = 63.
Salma runs 3/4 of a track that is 2 1/2 km long, and she does this twice. One run: 3/4 × 5/2 = 15/8 = 1 7/8 km. Two runs: 2 × 15/8 = 30/8 = 15/4 = 3 3/4 km.
Class activity
Our own story. Each player writes a story with a rectangle (a rug, a field, a balcony) whose sides are mixed numbers, for example 1 1/2 m and 2 1/4 m. Swap stories, estimate, calculate the area, and check with the author. Then write a second story that starts with “2/3 of …”.
Practice
1
A rug is 2 1/2 m long and 1 1/4 m wide. Find its area.
5/2 × 5/4 = 25/8 = 3 1/8 square metres.
2
Dates cost 40 LE a kilogram. How much do 2 1/2 kg cost?
2 1/2 × 40 = 5/2 × 40 = 100 LE.
3
Farida has 5 1/3 m of cloth and uses 3/4 of it for a curtain. How much does she use?
3/4 × 16/3 = 48/12 = 4 m.
4
One batch of dough needs 1 1/3 cups of flour. How much flour for 2 1/2 batches?
4/3 × 5/2 = 20/6 = 10/3 = 3 1/3 cups.
5
A tank holds 120 L. It is 5/8 full. Then 1/3 of the water in it is used. How many litres are left?
5/8 × 120 = 75 L. 1/3 × 75 = 25 L is used. 75 − 25 = 50 L left.
