Problem
Round the quotient up to carry the remainder
A warehouse must move 60 sacks of rice, each weighing 180 lb. A truck can carry at most 1 ton (2000 lb). Find the least number of trucks needed.
OperationsMeasurement & data
Your answer
trucks
Watch out Dividing 60 by 11 and stopping at 5 trucks ignores the 5 leftover sacks that still need a truck of their own.
How to solve
Strategy Analyze the Units — 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.
1STEP 1
Find how many sacks fit on one truck
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 × 180 = 1980 at most 2000, 12 × 180 = 2160 greater than 2000
We can only load whole sacks, so we stop at the most that stays under the weight limit.
3.MD.A.2Analyze The Units2STEP 2
Divide the sacks among trucks
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 ÷ 11 = 5 R 5
Five full trucks still leave some sacks behind.
3.OA.A.3Analyze The Units3STEP 3
Round up for the leftover sacks
The 5 leftover sacks still need a truck, so add 1 more: 5 + 1 = 6 trucks.
5 + 1 = 6 trucks
Any leftover that won't fit on the full trucks forces one extra truck.
3.OA.A.3Guess And CheckThe warehouse needs 6 trucks, because the 5 sacks left after 5 full trucks still have to be carried.
Why?
Five trucks loaded to their limit of 11 sacks carry 55 sacks, leaving 5 of the 60 sacks behind.
Why?
Five equal truckloads of 11 sacks is 5 x 11 = 55 sacks.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
The 60 sacks split with no overlap into the 55 that are loaded and the 5 that are left, so 60 - 55 leaves 5.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
Those 5 leftover sacks cannot ride on the full trucks, so they make one more truckload, and 5 loads plus 1 load is 6 trucks.
Why?
A full truck already holds all it can, 11 sacks weighing 1980 lb, because a 12th sack would make 12 x 180 = 2160 lb, past the 2000 lb limit.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
The 60 sacks split with no overlap into the 5 full truckloads and the 1 leftover truckload (the 5 spare sacks fit easily under the 11-sack limit), so the truckloads count 5 plus 1.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Answer
6 trucks
5 + 1 = 6
Six trucks can carry up to 6 x 11 = 66 sacks, which is enough for 60; five trucks carry only 55, which is too few. So 6 is the least number.
Takeaway
This only needs Grade 3 division with a remainder: leftover sacks always need one extra truck!
- Find how many sacks fit on one truck
- Divide the sacks among trucks
- Round up for the leftover sacks
Where next?
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