Dividing whole numbers and remainders

Short division, division with remainders, writing remainders as fractions, and deciding what to do with a remainder in word problems.

The language of division

In $37 \div 5 = 7$ remainder $2$: $37$ is the dividend, $5$ is the divisor, $7$ is the quotient and $2$ is the remainder.

A remainder can also be written as a fraction of the divisor: $37 \div 5 = 7\tfrac{2}{5}$.

Example 1●

Find $1735 \div 4$.

$17 \div 4 = 4$ remainder $1$. Carry the $1$ to make $13$.

$13 \div 4 = 3$ remainder $1$. Carry to make $15$.

$15 \div 4 = 3$ remainder $3$.

$1735 \div 4 = 433$ remainder $3$, or $433\tfrac{3}{4}$.

Example 2●●

$150$ students go on an excursion. Each bus holds $42$. How many buses are needed?

$150 \div 42 = 3$ remainder $24$.

Round up: $4$ buses.

The 24 extra students still need a bus.

Flashcards

Quotient

The answer to a division (the whole-number part).

Check $a div b = q$ r $r$

$a = b \times q + r$

$23 div 4$ as a mixed numeral

$5\tfrac{3}{4}$

Practice