Discover Mathematics P5: Term 1, Unit 4, Lessons 1–7
GoalEstimate a quotient with compatible numbers and divide by a two-digit number with the standard algorithm.
New words
compatible numbers · numbers near the real ones that divide easilyremainder · what is left over when the division is not exactbring down · to write the next digit beside the remainder
Explanation
Estimate first. For 1,848 ÷ 24 use compatible numbers: 1,850 ÷ 25 = 74, so the quotient will be near 74. Then use the standard algorithm, one step for each digit. Look at the first digits that are big enough to hold the divisor: 24 does not go into 18, so use 184. Divide: 184 ÷ 24 is 7 (7 × 24 = 168). Subtract: 184 − 168 = 16. Bring down the next digit 8 to make 168. Divide again: 168 ÷ 24 = 7. Subtract: 168 − 168 = 0. The quotient is 77 and nothing is left. Each step is: divide, multiply, subtract, bring down. The remainder must always be smaller than the divisor.
Step
Divide
Multiply
Subtract
Bring down
1
184 ÷ 24 → 7
7 × 24 = 168
184 − 168 = 16
8 → 168
2
168 ÷ 24 → 7
7 × 24 = 168
168 − 168 = 0
—
Worked examples
Divide 1,848 ÷ 24. Estimate: 1,850 ÷ 25 = 74. Step 1: 184 ÷ 24 is 7 (168), remainder 16. Bring down 8: 168. Step 2: 168 ÷ 24 = 7, remainder 0. The quotient is 77. Check: 24 × 77 = 1,848. The estimate 74 is close.
Step
Divide
Multiply
Subtract
Bring down
1
365 ÷ 42 → 8
8 × 42 = 336
365 − 336 = 29
4 → 294
2
294 ÷ 42 → 7
7 × 42 = 294
294 − 294 = 0
—
Divide 3,654 ÷ 42. Estimate: 3,600 ÷ 40 = 90. Step 1: 42 does not go into 36, so use 365. 365 ÷ 42 is 8 (336), remainder 29. Bring down 4: 294. Step 2: 294 ÷ 42 = 7, remainder 0. The quotient is 87.
Step
Divide
Multiply
Subtract
Bring down
1
100 ÷ 36 → 2
2 × 36 = 72
100 − 72 = 28
0 → 280
2
280 ÷ 36 → 7
7 × 36 = 252
280 − 252 = 28
—
Divide 1,000 ÷ 36. Step 1: use 100. 100 ÷ 36 is 2 (72), remainder 28. Bring down 0: 280. Step 2: 280 ÷ 36 is 7 (252), remainder 28. The quotient is 27 with remainder 28. The remainder 28 is smaller than 36, so we stop.
Class activity
Long division relay. Write a division such as 2,394 ÷ 42 on a card. The first player estimates and writes the first step (divide, multiply, subtract), the second player brings down the next digit and does the next step, and so on. Check at the end by multiplying the quotient by the divisor.
Practice
1
Estimate 2,394 ÷ 42 with compatible numbers, then divide exactly.
