Discover Mathematics P5: Term 1, Unit 4, Lessons 1–7
GoalCheck a division by multiplying, decide what to do with a remainder, and solve multistep stories.
New words
check · to test a result with the opposite operationround up · to use the next whole number because a leftover still needs a group
Explanation
Division is checked with multiplication: quotient × divisor + remainder = dividend. For 1,000 ÷ 36 = 27 remainder 28, check 27 × 36 + 28 = 972 + 28 = 1,000. A remainder must be understood in the story. Sometimes it is left out: 1,000 notebooks in boxes of 24 make 41 full boxes (remainder 16 notebooks). Sometimes it is rounded up: 250 children need seats in buses of 45, so 250 ÷ 45 = 5 remainder 25 means 6 buses, because the last children still need a bus. Sometimes it is shared into smaller parts. In multistep stories do one operation at a time and write what each answer means.
★Remember
quotient × divisor + remainder = dividend
Worked examples
Check 1,000 ÷ 36 = 27 remainder 28. 27 × 36 = 972, and 972 + 28 = 1,000. This equals the dividend, so the division is correct.
250 children go on a trip. A bus has 45 seats. 250 ÷ 45 = 5 remainder 25, because 45 × 5 = 225 and 250 − 225 = 25. Five buses carry 225 children, and 25 children still need a seat. So the school needs 6 buses.
A baker bakes 14 trays with 36 rolls on each tray. Step 1: 14 × 36 = 504 rolls. Step 2: the rolls are packed in bags of 12: 504 ÷ 12 = 42 bags. Step 3: each bag sells for 8 LE: 42 × 8 = 336 LE. The baker gets 336 LE.
Class activity
Remainder stories. Use the same division, 100 ÷ 8 = 12 remainder 4, for three stories: one where the remainder is ignored, one where it is rounded up and one where it is shared. Write each story and its answer: 12, 13 or 12 and a half (or 4 left over).
Practice
1
Check 3,654 ÷ 42 = 87 by multiplying.
87 × 42 = 3,654. It is correct.
2
Check 2,000 ÷ 48 = 41 remainder 32.
41 × 48 = 1,968 and 1,968 + 32 = 2,000. It is correct.
3
310 pupils go on a trip in microbuses with 14 seats. How many microbuses are needed?
310 ÷ 14 = 22 remainder 2 (14 × 22 = 308). The 2 pupils left need a seat, so 23 microbuses.
4
A rope 500 cm long is cut into pieces of 35 cm. How many pieces are there, and how much rope is left?
500 ÷ 35 = 14 remainder 10 (35 × 14 = 490). 14 pieces and 10 cm left.
5
18 boxes hold 24 oranges each. All the oranges are shared equally among 16 stalls. How many oranges does each stall get?
