Division

Division With a Remainder

Divide 23 ÷ 4. Four goes into 23 five times (4 × 5 = 20), and 3 is left over. That leftover is the remainder — always smaller than the divisor.

Example

Divide 23 by 4 and find the remainder. When the total will not split into equal whole groups, we take the largest whole number of full groups possible and call the leftover the remainder. The quotient counts the complete groups, and the remainder, always smaller than the divisor, is the part too small to form one more group.

highlighted = computed this step

Step 1 — Set up

Start with the division sentence.

23÷423\div 4
Make groups of 4 from 23 counters.group 14group 24group 34group 44group 54left over--Try complete groups of 4.Full groups must use no more than 23.

Step 2 — Try multiplication

4 x 5 = 20, so try quotient 5.

4×5=204\times \hl{5}=20
5 full groups of 4 use 20 counters.group 14group 24group 34group 44group 54left over--4 x 5 = 20Full groups must use no more than 23.

Step 3 — Find remainder

Subtract: 23 - 20 = 3.

23−20=323 - 20 = \hl{3}
23 - 20 leaves remainder 3.group 14group 24group 34group 44group 54left over34 x 5 = 2020 grouped + 3 left over = 23

Step 4 — Result

Read the result: 23 ÷ 4 = 5 remainder 3.

23÷4=5 r 323\div 4=5\text{ r }3
23 divided by 4 is 5 remainder 3.group 14group 24group 34group 44group 54left over34 x 5 = 2020 grouped + 3 left over = 23
remainder When a dividend does not divide evenly, the leftover after taking out as many full groups as possible is called the remainder. The remainder is always less than the divisor.