← 3-2 · Round the quotient up to carry the remainder · Divisibility and Remainder Reasoning

Round the quotient up to carry the remainder · 9 practice problems

3.OA.A.33.MD.A.2

Generated variants — 9

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 5 trucks

A warehouse needs to load $23$ sacks of rice onto trucks, where each sack weighs $350\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 23 sacks of rice, each weighing 350 lb. A truck can carry at most 2000 lb (1 ton). Find the least number of trucks needed.

Givens

There are 23 sacks of rice.
Each sack weighs 350 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 23 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 23 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 350 lb sacks fit under 2000 lb per truck, then divide the 23 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 350 lb and the limit is 2000 lb. Since 5 x 350 = 1750 lb (under the limit) but 6 x 350 = 2100 lb (over the limit), one truck can carry at most 5 sacks.

5 \times 350 = 1750 \le 2000,\quad 6 \times 350 = 2100 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 5 sacks per truck, 23 sacks need 23 divided by 5, which is 4 trucks carrying 20 sacks with 3 sacks left over.

23 \div 5 = 4\ \text{R}\ 3

4 full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 3 leftover sacks still need a truck, so add 1 more: 4 + 1 = 5 trucks.

4 + 1 = 5\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 5 trucks

Review

5 trucks can carry up to 5 x 5 = 25 sacks, which is enough for 23; 4 trucks carry only 20, which is too few. So 5 is the least number.

Guess and check by total weight (tool 6): 23 sacks weigh 23 x 350 = 8050 lb; 8050 / 2000 rounds up to 5 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!

Variant 2 answer: 4 trucks

A warehouse needs to load $47$ sacks of rice onto trucks, where each sack weighs $130\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 47 sacks of rice, each weighing 130 lb. A truck can carry at most 2000 lb (1 ton). Find the least number of trucks needed.

Givens

There are 47 sacks of rice.
Each sack weighs 130 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 47 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 47 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 130 lb sacks fit under 2000 lb per truck, then divide the 47 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 130 lb and the limit is 2000 lb. Since 15 x 130 = 1950 lb (under the limit) but 16 x 130 = 2080 lb (over the limit), one truck can carry at most 15 sacks.

15 \times 130 = 1950 \le 2000,\quad 16 \times 130 = 2080 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 15 sacks per truck, 47 sacks need 47 divided by 15, which is 3 trucks carrying 45 sacks with 2 sacks left over.

47 \div 15 = 3\ \text{R}\ 2

3 full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 2 leftover sacks still need a truck, so add 1 more: 3 + 1 = 4 trucks.

3 + 1 = 4\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 4 trucks

Review

4 trucks can carry up to 4 x 15 = 60 sacks, which is enough for 47; 3 trucks carry only 45, which is too few. So 4 is the least number.

Guess and check by total weight (tool 6): 47 sacks weigh 47 x 130 = 6110 lb; 6110 / 2000 rounds up to 4 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!

Variant 3 answer: 5 trucks

A warehouse needs to load $35$ sacks of rice onto trucks, where each sack weighs $240\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 35 sacks of rice, each weighing 240 lb. A truck can carry at most 2000 lb (1 ton). Find the least number of trucks needed.

Givens

There are 35 sacks of rice.
Each sack weighs 240 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 35 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 35 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 240 lb sacks fit under 2000 lb per truck, then divide the 35 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 240 lb and the limit is 2000 lb. Since 8 x 240 = 1920 lb (under the limit) but 9 x 240 = 2160 lb (over the limit), one truck can carry at most 8 sacks.

8 \times 240 = 1920 \le 2000,\quad 9 \times 240 = 2160 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 8 sacks per truck, 35 sacks need 35 divided by 8, which is 4 trucks carrying 32 sacks with 3 sacks left over.

35 \div 8 = 4\ \text{R}\ 3

4 full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 3 leftover sacks still need a truck, so add 1 more: 4 + 1 = 5 trucks.

4 + 1 = 5\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 5 trucks

Review

5 trucks can carry up to 5 x 8 = 40 sacks, which is enough for 35; 4 trucks carry only 32, which is too few. So 5 is the least number.

Guess and check by total weight (tool 6): 35 sacks weigh 35 x 240 = 8400 lb; 8400 / 2000 rounds up to 5 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!

Variant 4 answer: 6 trucks

A warehouse needs to load $60$ sacks of rice onto trucks, where each sack weighs $180\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 60 sacks of rice, each weighing 180 lb. A truck can carry at most 2000 lb (1 ton). Find the least number of trucks needed.

Givens

There are 60 sacks of rice.
Each sack weighs 180 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 60 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 60 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 180 lb sacks fit under 2000 lb per truck, then divide the 60 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 180 lb and the limit is 2000 lb. Since 11 x 180 = 1980 lb (under the limit) but 12 x 180 = 2160 lb (over the limit), one truck can carry at most 11 sacks.

11 \times 180 = 1980 \le 2000,\quad 12 \times 180 = 2160 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 11 sacks per truck, 60 sacks need 60 divided by 11, which is 5 trucks carrying 55 sacks with 5 sacks left over.

60 \div 11 = 5\ \text{R}\ 5

5 full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 5 leftover sacks still need a truck, so add 1 more: 5 + 1 = 6 trucks.

5 + 1 = 6\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 6 trucks

Review

6 trucks can carry up to 6 x 11 = 66 sacks, which is enough for 60; 5 trucks carry only 55, which is too few. So 6 is the least number.

Guess and check by total weight (tool 6): 60 sacks weigh 60 x 180 = 10800 lb; 10800 / 2000 rounds up to 6 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!

Variant 5 answer: 5 trucks

A warehouse needs to load $41$ sacks of rice onto trucks, where each sack weighs $190\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 41 sacks of rice, each weighing 190 lb. A truck can carry at most 2000 lb (1 ton). Find the least number of trucks needed.

Givens

There are 41 sacks of rice.
Each sack weighs 190 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 41 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 41 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 190 lb sacks fit under 2000 lb per truck, then divide the 41 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 190 lb and the limit is 2000 lb. Since 10 x 190 = 1900 lb (under the limit) but 11 x 190 = 2090 lb (over the limit), one truck can carry at most 10 sacks.

10 \times 190 = 1900 \le 2000,\quad 11 \times 190 = 2090 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 10 sacks per truck, 41 sacks need 41 divided by 10, which is 4 trucks carrying 40 sacks with 1 sacks left over.

41 \div 10 = 4\ \text{R}\ 1

4 full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 1 leftover sacks still need a truck, so add 1 more: 4 + 1 = 5 trucks.

4 + 1 = 5\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 5 trucks

Review

5 trucks can carry up to 5 x 10 = 50 sacks, which is enough for 41; 4 trucks carry only 40, which is too few. So 5 is the least number.

Guess and check by total weight (tool 6): 41 sacks weigh 41 x 190 = 7790 lb; 7790 / 2000 rounds up to 5 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!

Variant 6 answer: 4 trucks

A warehouse needs to load $50$ sacks of rice onto trucks, where each sack weighs $150\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 50 sacks of rice, each weighing 150 lb. A truck can carry at most 2000 lb (1 ton). Find the least number of trucks needed.

Givens

There are 50 sacks of rice.
Each sack weighs 150 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 50 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 50 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 150 lb sacks fit under 2000 lb per truck, then divide the 50 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 150 lb and the limit is 2000 lb. Since 13 x 150 = 1950 lb (under the limit) but 14 x 150 = 2100 lb (over the limit), one truck can carry at most 13 sacks.

13 \times 150 = 1950 \le 2000,\quad 14 \times 150 = 2100 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 13 sacks per truck, 50 sacks need 50 divided by 13, which is 3 trucks carrying 39 sacks with 11 sacks left over.

50 \div 13 = 3\ \text{R}\ 11

3 full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 11 leftover sacks still need a truck, so add 1 more: 3 + 1 = 4 trucks.

3 + 1 = 4\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 4 trucks

Review

4 trucks can carry up to 4 x 13 = 52 sacks, which is enough for 50; 3 trucks carry only 39, which is too few. So 4 is the least number.

Guess and check by total weight (tool 6): 50 sacks weigh 50 x 150 = 7500 lb; 7500 / 2000 rounds up to 4 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!

Variant 7 answer: 5 trucks

A warehouse needs to load $52$ sacks of rice onto trucks, where each sack weighs $170\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 52 sacks of rice, each weighing 170 lb. A truck can carry at most 2000 lb (1 ton). Find the least number of trucks needed.

Givens

There are 52 sacks of rice.
Each sack weighs 170 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 52 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 52 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 170 lb sacks fit under 2000 lb per truck, then divide the 52 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 170 lb and the limit is 2000 lb. Since 11 x 170 = 1870 lb (under the limit) but 12 x 170 = 2040 lb (over the limit), one truck can carry at most 11 sacks.

11 \times 170 = 1870 \le 2000,\quad 12 \times 170 = 2040 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 11 sacks per truck, 52 sacks need 52 divided by 11, which is 4 trucks carrying 44 sacks with 8 sacks left over.

52 \div 11 = 4\ \text{R}\ 8

4 full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 8 leftover sacks still need a truck, so add 1 more: 4 + 1 = 5 trucks.

4 + 1 = 5\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 5 trucks

Review

5 trucks can carry up to 5 x 11 = 55 sacks, which is enough for 52; 4 trucks carry only 44, which is too few. So 5 is the least number.

Guess and check by total weight (tool 6): 52 sacks weigh 52 x 170 = 8840 lb; 8840 / 2000 rounds up to 5 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!

Variant 8 answer: 5 trucks

A warehouse needs to load $29$ sacks of rice onto trucks, where each sack weighs $300\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 29 sacks of rice, each weighing 300 lb. A truck can carry at most 2000 lb (1 ton). Find the least number of trucks needed.

Givens

There are 29 sacks of rice.
Each sack weighs 300 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 29 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 29 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 300 lb sacks fit under 2000 lb per truck, then divide the 29 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 300 lb and the limit is 2000 lb. Since 6 x 300 = 1800 lb (under the limit) but 7 x 300 = 2100 lb (over the limit), one truck can carry at most 6 sacks.

6 \times 300 = 1800 \le 2000,\quad 7 \times 300 = 2100 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 6 sacks per truck, 29 sacks need 29 divided by 6, which is 4 trucks carrying 24 sacks with 5 sacks left over.

29 \div 6 = 4\ \text{R}\ 5

4 full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 5 leftover sacks still need a truck, so add 1 more: 4 + 1 = 5 trucks.

4 + 1 = 5\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 5 trucks

Review

5 trucks can carry up to 5 x 6 = 30 sacks, which is enough for 29; 4 trucks carry only 24, which is too few. So 5 is the least number.

Guess and check by total weight (tool 6): 29 sacks weigh 29 x 300 = 8700 lb; 8700 / 2000 rounds up to 5 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!

Variant 9 answer: 5 trucks

A warehouse needs to load $37$ sacks of rice onto trucks, where each sack weighs $250\ \text{lb}$ . If each truck can carry up to $1$ ton ( $2000\ \text{lb}$ ), at least how many trucks are needed?

Show solution

Understand

A warehouse must move 37 sacks of rice, each weighing 250 lb. A truck can carry at most 2000 lb (1 ton). Find the least number of trucks needed.

Givens

There are 37 sacks of rice.
Each sack weighs 250 lb.
Each truck can carry up to 2000 lb (1 ton).

Unknowns

The least number of trucks needed to carry all 37 sacks.

Constraints

A truck cannot exceed 2000 lb, and a sack cannot be split.
All 37 sacks must be moved.

Plan

#8 Analyze the Units · also uses: #6 Guess and Check

Find how many whole 250 lb sacks fit under 2000 lb per truck, then divide the 37 sacks by that capacity and round up so no sacks are left behind.

Execute

#8 Analyze the Units 3.MD.A.2

Each sack is 250 lb and the limit is 2000 lb. Since 8 x 250 = 2000 lb (under the limit) but 9 x 250 = 2250 lb (over the limit), one truck can carry at most 8 sacks.

8 \times 250 = 2000 \le 2000,\quad 9 \times 250 = 2250 > 2000

We can only load whole sacks, so we stop at the most that stays under the weight limit.

#8 Analyze the Units 3.OA.A.3

With 8 sacks per truck, 37 sacks need 37 divided by 8, which is 4 trucks carrying 32 sacks with 5 sacks left over.

37 \div 8 = 4\ \text{R}\ 5

4 full trucks still leave some sacks behind.

#6 Guess and Check 3.OA.A.3

The 5 leftover sacks still need a truck, so add 1 more: 4 + 1 = 5 trucks.

4 + 1 = 5\ \text{trucks}

Any leftover that won't fit on the full trucks forces one extra truck.

Answer: 5 trucks

Review

5 trucks can carry up to 5 x 8 = 40 sacks, which is enough for 37; 4 trucks carry only 32, which is too few. So 5 is the least number.

Guess and check by total weight (tool 6): 37 sacks weigh 37 x 250 = 9250 lb; 9250 / 2000 rounds up to 5 trucks, matching the answer.

Standards · min grade 3

3.OA.A.3 Solve multiplication and division word problems within 100 — Dividing sacks among trucks and rounding up the remainder.
3.MD.A.2 Measure and estimate liquid volumes and masses of objects — Comparing sack weights against the 2000 lb truck limit.

💡 This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!