Explanation:
We are estimating quotients by finding two whole numbers the actual quotient lies between, then picking a reasonable estimate.
Let’s go one problem at a time:
1.
23 ÷ 4
We know:
4 × 5 = 20
4 × 6 = 24
So 23 is between 20 and 24 → quotient is between 5 and 6.
Since 23 is closer to 24 than to 20, estimate =
6 (already given — correct).
2.
51 ÷ 6
6 × 8 = 48
6 × 9 = 54
51 is between 48 and 54 → quotient between 8 and 9.
51 − 48 = 3, 54 − 51 = 3 → exactly halfway. Usually we round to nearest whole number: 8.5 → round to
9.
So estimated quotient =
9.
3.
76 ÷ 9
9 × 8 = 72
9 × 9 = 81
76 is between 72 and 81 → quotient between 8 and 9.
76 − 72 = 4, 81 − 76 = 5 → closer to 72, so estimate =
8.
4.
154 ÷ 12
12 × 12 = 144
12 × 13 = 156
154 is between 144 and 156 → quotient between 12 and 13.
154 − 144 = 10, 156 − 154 = 2 → much closer to 156, so estimate =
13.
5.
109 ÷ 7
7 × 15 = 105
7 × 16 = 112
109 is between 105 and 112 → quotient between 15 and 16.
109 − 105 = 4, 112 − 109 = 3 → closer to 112, so estimate =
16.
6.
125 ÷ 8
8 × 15 = 120
8 × 16 = 128
125 is between 120 and 128 → quotient between 15 and 16.
125 − 120 = 5, 128 − 125 = 3 → closer to 128, so estimate =
16.
7.
225 ÷ 16
Let’s try:
16 × 14 = 224
16 × 15 = 240
225 is just 1 more than 224 → quotient between 14 and 15, very close to 14.
So estimate =
14.
8.
210 ÷ 13
Try multiples of 13:
13 × 16 = 208
13 × 17 = 221
210 − 208 = 2, 221 − 210 = 11 → much closer to 208.
So quotient between 16 and 17, estimate =
16.
9.
105 ÷ 12
12 × 8 = 96
12 × 9 = 108
105 is between 96 and 108 → difference: 105−96=9, 108−105=3 → closer to 108.
So estimate =
9.
10.
342 ÷ 15
Try:
15 × 22 = 330
15 × 23 = 345
342 − 330 = 12, 345 − 342 = 3 → much closer to 345.
So quotient between 22 and 23, estimate =
23.
Let me double-check each:
2. 51 ÷ 6 = 8.5 → round to 9
✔
3. 76 ÷ 9 ≈ 8.44 → round to 8
✔
4. 154 ÷ 12 ≈ 12.83 → round to 13
✔
5. 109 ÷ 7 ≈ 15.57 → round to 16
✔
6. 125 ÷ 8 = 15.625 → round to 16
✔
7. 225 ÷ 16 = 14.0625 → round to 14
✔
8. 210 ÷ 13 ≈ 16.15 → round to 16
✔
9. 105 ÷ 12 = 8.75 → round to 9
✔
10. 342 ÷ 15 = 22.8 → round to 23
✔
All good.
Final Answer:
2. 9
3. 8
4. 13
5. 16
6. 16
7. 14
8. 16
9. 9
10. 23
Parent Tip: Review the logic above to help your child master the concept of estimating division worksheet.
