Long division and remainders

$47 \div 5$ asks how many fives fit in 47. Nine fit, since $5 \times 9 = 45$ , and 2 are left. So $47 = 5 \times 9 + 2$ . Every division fits that shape, and it's also how you check your answer.

Dividend = divisor × quotient + remainder, and the remainder must be smaller than the divisor.

Long division repeats four moves, one place at a time: divide, multiply, subtract, bring down. It works from the left because the biggest places are shared out first.

Work through it

$852 \div 6$

Hundreds: 6 goes into 8 once.write 1, and $8 - 6 = 2$ left

Bring down the 5 to make 25. 6 goes in 4 times.write 4, and $25 - 24 = 1$ left

Bring down the 2 to make 12. 6 goes in 2 times.write 2, and nothing left

Check it. $142 \times 6 = 852$

$730 \div 7$

7 goes into 7 once.write 1, nothing left

Bring down 3. 7 doesn't fit into 3, and you must say so.write 0

Bring down 0 to make 30. 7 goes in 4 times, with 2 left. $104$ remainder $2$

38 students ride in vans that hold 8. How many vans?

Divide. $38 \div 8 = 4$ remainder $6$

Read the story: 6 students still need a seat, so they need another van. $5$ vans

Watch out for this

$730 \div 7 = 14$ remainder 2, by skipping the 0.

When the divisor doesn't fit, write a 0 in the answer. Without it, every digit shifts to the wrong place. It's $104$ R $2$ .

The short version
Ask how many full groups fit. The remainder is what's left, and it's always smaller than the divisor.

Your turn

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