A group of \(23\) students are going on a field trip. Each van can hold \(6\) students. How many vans are needed? (\(23 \div 6 = 3 \text{ R } 5\))
You need \(4\) vans. \(3\) vans will be full, but you need one more van for the remaining \(5\) students. In this case, you round the quotient up.
A baker has \(38\) cookies to put into bags. Each bag holds \(4\) cookies. How many full bags can the baker make? (\(38 \div 4 = 9 \text{ R } 2\))
The baker can make \(9\) full bags. In this case, the remainder is ignored, and the quotient is the answer.
A coach has \(50\) tennis balls and wants to put them in cans that hold \(3\) balls each. After filling as many cans as possible, how many balls will be left over? (\(50 \div 3 = 16 \text{ R } 2\))
There will be \(2\) balls left over. In this case, the remainder itself is the answer to the question.
What are the three main ways to interpret a remainder in a word problem?
1. Round up to the next whole number (add one to the quotient). 2. Drop the remainder (use only the quotient). 3. Use the remainder as the answer.
You have $30 to spend on books that cost $7 each. How many books can you buy? (\(30 \div 7 = 4 \text{ R } 2\))
You can buy \(4\) books. You don't have enough money for a fifth book, so you drop the remainder. The quotient is the answer.
\(46\) people are waiting for a ride that holds \(8\) people at a time. How many trips will the ride have to make to carry everyone? (\(46 \div 8 = 5 \text{ R } 6\))
The ride will need to make \(6\) trips. \(5\) trips for the first \(40\) people and one more trip for the remaining \(6\) people. You round up.
I am making party favor bags. I have \(53\) stickers to share equally among \(7\) bags. How many stickers will be in each bag? (\(53 \div 7 = 7 \text{ R } 4\))
Each bag will have \(7\) stickers. You drop the remainder because the question asks how many are *in each bag*, not what's left over.
Now, for the same party favor problem (\(53\) stickers, \(7\) bags), how many stickers will be left over? (\(53 \div 7 = 7 \text{ R } 4\))
There will be \(4\) stickers left over. Here, the remainder is the answer.
A school needs to buy new desks. Desks come in packs of \(10\). The school needs \(124\) desks. How many packs should they buy? (\(124 \div 10 = 12 \text{ R } 4\))
They should buy \(13\) packs. Buying \(12\) packs would only give them \(120\) desks, which isn't enough. They must round up.
A farmer collects \(80\) eggs and puts them into cartons that hold a dozen (\(12\)) eggs. How many full cartons can he make? (\(80 \div 12 = 6 \text{ R } 8\))
He can make \(6\) full cartons. The quotient is the answer.
A ribbon is \(100\) cm long. You need to cut as many \(8\) cm pieces as you can. How much ribbon will be left? (\(100 \div 8 = 12 \text{ R } 4\))
There will be \(4\) cm of ribbon left. The remainder is the answer.
When a word problem asks "How many are needed for everyone?" or "How many trips/vehicles are required?", what do you usually do with the remainder?
You usually need to round up by adding \(1\) to the quotient to make sure everyone or everything is included.
