Chapter 5 — worked answers and marking guidance
All chapter review and practice examination items
Chapter review solutions
Calculate 68 ÷ 4 by breaking apart the dividend.
Decompose 68 into convenient multiples of 4; the resulting quotients sum to 17.
Estimate 1213 ÷ 8 to the nearest ten in the quotient.
The exact quotient has whole-number part 151; rounding that to the nearest ten gives 150.
Divide 1,861 by 3. Give the quotient and remainder.
1,861 = 3 × 620 + 1; the remainder 1 is less than 3.
795 pencils are packed 2 per box. How many full boxes can be filled, and how many pencils remain?
Group by 2: 795 = 397 full groups of 2, plus 1 left.
A club has 435 tickets. After buying 49 more, they bundle tickets into packs of 7. How many full packs and tickets left?
Add first: 484. Divide by 7: 69 packs, with 1 tickets remaining.
Calculate 117 ÷ 9 by breaking apart the dividend.
Decompose 117 into convenient multiples of 9; the resulting quotients sum to 13.
Is 2498 ÷ 6 closer to 420 or 440?
Compare compatible products with 6; the quotient is near 416, which is closer to 420.
Divide 1,671 by 3. Give the quotient and remainder.
1,671 = 3 × 557 + 0; the remainder 0 is less than 3.
1,746 pencils are packed 8 per box. How many full boxes can be filled, and how many pencils remain?
Group by 8: 1,746 = 218 full groups of 8, plus 2 left.
A club has 599 tickets. After buying 16 more, they bundle tickets into packs of 2. How many full packs and tickets left?
Add first: 615. Divide by 2: 307 packs, with 1 tickets remaining.
Calculate 160 ÷ 8 by breaking apart the dividend.
Decompose 160 into convenient multiples of 8; the resulting quotients sum to 20.
Estimate 2013 ÷ 8 to the nearest ten in the quotient.
The exact quotient has whole-number part 251; rounding that to the nearest ten gives 250.
Divide 1,827 by 3. Give the quotient and remainder.
1,827 = 3 × 609 + 0; the remainder 0 is less than 3.
744 pencils are packed 4 per box. How many full boxes can be filled, and how many pencils remain?
Group by 4: 744 = 186 full groups of 4, plus 0 left.
A club has 848 tickets. After buying 20 more, they bundle tickets into packs of 2. How many full packs and tickets left?
Add first: 868. Divide by 2: 434 packs, with 0 tickets remaining.
Calculate 88 ÷ 8 by breaking apart the dividend.
Decompose 88 into convenient multiples of 8; the resulting quotients sum to 11.
Estimate 1474 ÷ 6 to the nearest ten in the quotient.
The exact quotient has whole-number part 245; rounding that to the nearest ten gives 250.
Divide 2,793 by 9. Give the quotient and remainder.
2,793 = 9 × 310 + 3; the remainder 3 is less than 9.
3,165 pencils are packed 8 per box. How many full boxes can be filled, and how many pencils remain?
Group by 8: 3,165 = 395 full groups of 8, plus 5 left.
A club has 1,328 tickets. After buying 40 more, they bundle tickets into packs of 4. How many full packs and tickets left?
Add first: 1,368. Divide by 4: 342 packs, with 0 tickets remaining.
Calculate 198 ÷ 9 by breaking apart the dividend.
Decompose 198 into convenient multiples of 9; the resulting quotients sum to 22.
Is 1781 ÷ 7 closer to 250 or 270?
Compare compatible products with 7; the quotient is near 254, which is closer to 250.
Divide 5,199 by 7. Give the quotient and remainder.
5,199 = 7 × 742 + 5; the remainder 5 is less than 7.
270 pencils are packed 3 per box. How many full boxes can be filled, and how many pencils remain?
Group by 3: 270 = 90 full groups of 3, plus 0 left.
A club has 656 tickets. After buying 60 more, they bundle tickets into packs of 6. How many full packs and tickets left?
Add first: 716. Divide by 6: 119 packs, with 2 tickets remaining.
Calculate 279 ÷ 9 by breaking apart the dividend.
Decompose 279 into convenient multiples of 9; the resulting quotients sum to 31.
Estimate 2919 ÷ 7 to the nearest ten in the quotient.
The exact quotient has whole-number part 417; rounding that to the nearest ten gives 420.
A student solves 156 ÷ 6 by computing 120 ÷ 6 and 36 ÷ 6 and adding. Is this a valid mental strategy? Explain.
156 is 120 + 36, and both parts divide by 6. The quotients 20 and 6 add to 26.
Estimate 2,462 ÷ 6 as about 400 or about 4,000. Explain the best estimate.
2,400 ÷ 6 = 400, a close compatible-number estimate for 2,462 ÷ 6.
A student claims 4,315 ÷ 7 equals 616 remainder 4. Check using multiplication, and correct the remainder.
7 × 616 = 4,312. To make 4,315, add remainder 3, which is less than 7.
807 children ride vans seating 4 children each. A student says 201 vans are sufficient because the quotient is 201 remainder 3. Explain and find the necessary number of vans.
The 3 remaining children still need a van. The number of vans must be rounded up to 202.
1077 children ride vans seating 8 children each. A student says 134 vans are sufficient because the quotient is 134 remainder 5. Explain and find the necessary number of vans.
The 5 remaining children still need a van. The number of vans must be rounded up to 135.
Calculate 225 ÷ 9 by breaking apart the dividend.
Decompose 225 into convenient multiples of 9; the resulting quotients sum to 25.
Practice examination solutions and scoring
Calculate 203 ÷ 7 by breaking apart the dividend.
Decompose 203 into convenient multiples of 7; the resulting quotients sum to 29.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Divide 1,881 by 6. Give the quotient and remainder.
1,881 = 6 × 313 + 3; the remainder 3 is less than 6.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A club has 1,482 tickets. After buying 40 more, they bundle tickets into packs of 4. How many full packs and tickets left?
Add first: 1,522. Divide by 4: 380 packs, with 2 tickets remaining.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Estimate 188 ÷ 3 to the nearest ten in the quotient.
The exact quotient has whole-number part 62; rounding that to the nearest ten gives 60.
Scoring (2 points): Award one point for a sound method and one for the correct result.
1,082 pencils are packed 8 per box. How many full boxes can be filled, and how many pencils remain?
Group by 8: 1,082 = 135 full groups of 8, plus 2 left.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Is 1665 ÷ 9 closer to 190 or 210?
Compare compatible products with 9; the quotient is near 185, which is closer to 190.
Scoring (2 points): Award one point for a sound method and one for the correct result.
662 pencils are packed 2 per box. How many full boxes can be filled, and how many pencils remain?
Group by 2: 662 = 331 full groups of 2, plus 0 left.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Calculate 324 ÷ 9 by breaking apart the dividend.
Decompose 324 into convenient multiples of 9; the resulting quotients sum to 36.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Divide 2,507 by 5. Give the quotient and remainder.
2,507 = 5 × 501 + 2; the remainder 2 is less than 5.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A club has 626 tickets. After buying 60 more, they bundle tickets into packs of 6. How many full packs and tickets left?
Add first: 686. Divide by 6: 114 packs, with 2 tickets remaining.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Divide 6,371 by 9. Give the quotient and remainder.
6,371 = 9 × 707 + 8; the remainder 8 is less than 9.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A club has 2,131 tickets. After buying 90 more, they bundle tickets into packs of 9. How many full packs and tickets left?
Add first: 2,221. Divide by 9: 246 packs, with 7 tickets remaining.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Estimate 1253 ÷ 6 to the nearest ten in the quotient.
The exact quotient has whole-number part 208; rounding that to the nearest ten gives 210.
Scoring (2 points): Award one point for a sound method and one for the correct result.
1,592 pencils are packed 5 per box. How many full boxes can be filled, and how many pencils remain?
Group by 5: 1,592 = 318 full groups of 5, plus 2 left.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Calculate 64 ÷ 2 by breaking apart the dividend.
Decompose 64 into convenient multiples of 2; the resulting quotients sum to 32.
Scoring (2 points): Award one point for a sound method and one for the correct result.
944 pencils are packed 3 per box. How many full boxes can be filled, and how many pencils remain?
Group by 3: 944 = 314 full groups of 3, plus 2 left.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Calculate 60 ÷ 6 by breaking apart the dividend.
Decompose 60 into convenient multiples of 6; the resulting quotients sum to 10.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Divide 3,132 by 7. Give the quotient and remainder.
3,132 = 7 × 447 + 3; the remainder 3 is less than 7.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A club has 1,922 tickets. After buying 25 more, they bundle tickets into packs of 5. How many full packs and tickets left?
Add first: 1,947. Divide by 5: 389 packs, with 2 tickets remaining.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Estimate 847 ÷ 6 to the nearest ten in the quotient.
The exact quotient has whole-number part 141; rounding that to the nearest ten gives 140.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A club has 2,625 tickets. After buying 42 more, they bundle tickets into packs of 6. How many full packs and tickets left?
Add first: 2,667. Divide by 6: 444 packs, with 3 tickets remaining.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Estimate 2022 ÷ 5 to the nearest ten in the quotient.
The exact quotient has whole-number part 404; rounding that to the nearest ten gives 400.
Scoring (2 points): Award one point for a sound method and one for the correct result.
3,155 pencils are packed 8 per box. How many full boxes can be filled, and how many pencils remain?
Group by 8: 3,155 = 394 full groups of 8, plus 3 left.
Scoring (3 points): Award one point for identifying the quantities or relationship, one for the correct method, and one for a correct justified result.
Calculate 76 ÷ 4 by breaking apart the dividend.
Decompose 76 into convenient multiples of 4; the resulting quotients sum to 19.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Divide 1,755 by 3. Give the quotient and remainder.
1,755 = 3 × 585 + 0; the remainder 0 is less than 3.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 228 ÷ 6 by breaking apart the dividend.
Decompose 228 into convenient multiples of 6; the resulting quotients sum to 38.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Divide 4,847 by 5. Give the quotient and remainder.
4,847 = 5 × 969 + 2; the remainder 2 is less than 5.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 44 ÷ 4 by breaking apart the dividend.
Decompose 44 into convenient multiples of 4; the resulting quotients sum to 11.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Estimate 647 ÷ 5 to the nearest ten in the quotient.
The exact quotient has whole-number part 129; rounding that to the nearest ten gives 130.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Divide 1,100 by 2. Give the quotient and remainder.
1,100 = 2 × 550 + 0; the remainder 0 is less than 2.
Scoring (2 points): Award one point for a sound method and one for the correct result.
1670 children ride vans seating 6 children each. A student says 278 vans are sufficient because the quotient is 278 remainder 2. Explain and find the necessary number of vans.
The 2 remaining children still need a van. The number of vans must be rounded up to 279.
Scoring (4 points): Award one point for a sound method and one for the correct result.
587 children ride vans seating 3 children each. A student says 195 vans are sufficient because the quotient is 195 remainder 2. Explain and find the necessary number of vans.
The 2 remaining children still need a van. The number of vans must be rounded up to 196.
Scoring (4 points): Award one point for a sound method and one for the correct result.
Calculate 154 ÷ 7 by breaking apart the dividend.
Decompose 154 into convenient multiples of 7; the resulting quotients sum to 22.
Scoring (2 points): Award one point for a sound method and one for the correct result.