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Rounding & Compensation in Multiplication

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Rounding & Compensation in Multiplication

A hospital ward needs supplies packed quickly. Use rounding to make multiplication easier, then compensate to find the exact total. When you round a factor up, subtract the extra groups; when you round it down, add the missing groups.

Get ready to estimate

Round to the nearest ten. Use the number lines to help you decide which ten each number is closest to.

1.The ward has 36 boxes of gloves. Round 36 to the nearest ten to make a quick estimate.

2.A trolley holds 43 rolls of bandage. Round 43 to the nearest ten. Write the rounded number.

Make it tidy, then compensate

Follow the example: 29 × 5 = 30 × 5 − 1 × 5 = 150 − 5 = 145. The tidy multiplication gives an estimate; compensation fixes the difference.

3.Harrison is packing 6 trays with 19 cups on each tray. Complete the compensation equation: 20 × 6 − 1 × 6 = .

4.The ward needs 4 packs of 32 face masks. Hugo rounds 32 down to 30. What amount must he add back after calculating 30 × 4? Find the exact total.

5.Tui calculates 7 × 48 by doing 7 × 50, then subtracting 7 × 2. Is the compensation correct? Write the exact answer and explain briefly.

6.Match each multiplication to its useful compensation step.

6 × 29
3 × 42
5 × 58

40 × 3 + 2 × 3
30 × 6 − 1 × 6
60 × 5 − 2 × 5

Solve the supply problems

Show how you round and compensate. Remember to include the correct unit in each answer.

7.There are 8 shelves with 39 rolls of tape on each shelf. Estimate by rounding 39 to 40, then compensate to find the exact number of rolls.

8.A delivery brings 6 cartons with 52 disposable aprons in each carton. Round 52 to 50 for an estimate, then compensate to find the exact total.

9.The ward uses 9 packs of 27 gauze pads. Complete the working and find the exact total: 9 × 27 = 9 × 30 − 9 × = − = pads.

10.A ward orders 7 boxes containing 61 pairs of gloves each. Choose a nearby ten, write a compensation equation, and calculate the exact number of pairs.

11.Which estimate is closer to the exact answer for 4 × 73: 4 × 70 or 4 × 80? Calculate both estimates, then explain your choice.