Discover what happens when numbers don't divide evenly. This stack introduces the concept of a 'remainder,' how to find it, and how to interpret it in word problems.
A remainder is the amount 'left over' when a number cannot be divided into equal whole groups. It must always be less than the divisor.
Solve \(13 \div 3\).
The answer is \(4\) with a remainder of \(1\). You can make \(4\) groups of \(3\), and you will have \(1\) left over. This is written as \(4\) R\(1\).
If you have \(17\) toys to share equally among \(3\) friends, how many toys does each friend get, and how many are left over?
Each friend gets \(5\) toys, and there are \(2\) toys left over. The problem is \(17 \div 3 = 5\) R\(2\).
How do you check a division problem with a remainder, like \(22 \div 5 = 4\) R\(2\)?
Multiply the quotient by the divisor, then add the remainder. \((4 \times 5) + 2 = 20 + 2 = 22\). The result should equal the dividend.
True or False: When solving \(14 \div 5\), the answer is \(2\) R\(4\).
True. \(5 \times 2 = 10\), and \(14 - 10 = 4\). The remainder \(4\) is less than the divisor \(5\), so it is correct.
Can the remainder ever be larger than or equal to the divisor?
No. If your remainder is larger than the divisor, it means you could have made at least one more full group.
What is the remainder of \(38 \div 7\)?
The remainder is \(3\). \(7 \times 5 = 35\), and \(38 - 35 = 3\). The full answer is \(5\) R\(3\).
What does a remainder of \(0\) mean?
A remainder of \(0\) means the dividend was divided perfectly by the divisor with nothing left over. For example, \(12 \div 4 = 3\) R\(0\), which is just written as \(3\).
\(29\) students need to be put into teams of \(6\). How many full teams can be made? How many students are left without a team?
\(29 \div 6 = 4\) R\(5\). Four full teams can be made, and \(5\) students will be left over.
