Math Core

How do you split 156 stickers among 6 friends? No multiplication fact gives you the answer right away. But place value lets you divide a big number one chunk at a time, and that works for dividends all the way up to the thousands.

Dividing with place value

Start with numbers that end in zeros. Think about what you are dividing:

$800 \div 4$ : 8 hundreds split into 4 groups is 2 hundreds each. So $800 \div 4 = 200$ .
$120 \div 3$ : 120 is 12 tens. 12 tens split into 3 groups is 4 tens. So $120 \div 3 = 40$ .
$2{,}400 \div 6$ : 2,400 is 24 hundreds. 24 hundreds split into 6 groups is 4 hundreds. So $2{,}400 \div 6 = 400$ .

Each one is a basic fact ( $8 \div 4$ , $12 \div 3$ , $24 \div 6$ ) with a place value name attached.

Partial quotients

For numbers that don't end in zeros, take away easy groups one chunk at a time. Here is $156 \div 6$ :

Take away	How many 6s	What's left
$10 \times 6 = 60$	10	$156 - 60 = 96$
$10 \times 6 = 60$	10	$96 - 60 = 36$
$6 \times 6 = 36$	6	$36 - 36 = 0$
Total	26

You took away $10 + 10 + 6 = 26$ sixes, so $156 \div 6 = 26$ . Check: $26 \times 6 = 156$ . ✓

Big chunks save time. With $20 \times 6 = 120$ you could do it in two steps: $156 - 120 = 36$ , then $36 \div 6 = 6$ , for a total of $20 + 6 = 26$ .

Dividing place by place

A shorter way is to divide one place at a time, starting with the largest place. The steps repeat: divide, multiply, subtract, bring down.

Dividing place by place

Divide the digit (or digits) in the largest place you can.
Multiply that part of the quotient by the divisor.
Subtract to see what is left in that place.
Bring down the next digit and repeat.

Whatever is left after the ones place is the remainder.

Worked example: Two digits, no remainder

Find $84 \div 4$ .

Tens: 8 tens $\div$ 4 = 2 tens, with nothing left over.
Ones: 4 ones $\div$ 4 = 1 one.

So $84 \div 4 = 21$ . Check: $21 \times 4 = 84$ . ✓

Worked example: Three digits with a remainder

Find $437 \div 3$ .

\begin{array}{r} 145 \\ 3\,\overline{)\,437} \\ \underline{-\,3\phantom{00}} \\ 13\phantom{0} \\ \underline{-\,12\phantom{0}} \\ 17 \\ \underline{-\,15} \\ 2 \end{array}

Hundreds: 4 hundreds $\div$ 3 = 1 hundred. $1 \times 3 = 3$ , and $4 - 3 = 1$ hundred is left.
Tens: 1 hundred is 10 tens. Bring down the 3 to get 13 tens. 13 tens $\div$ 3 = 4 tens. $4 \times 3 = 12$ , and $13 - 12 = 1$ ten is left.
Ones: Bring down the 7 to get 17 ones. $17 \div 3 = 5$ . $5 \times 3 = 15$ , and $17 - 15 = 2$ is left.

Nothing is left to bring down, so 2 is the remainder. $437 \div 3 = 145 \text{ R } 2$ .

Check: $145 \times 3 + 2 = 435 + 2 = 437$ . ✓

Worked example: Four digits

Find $1{,}245 \div 5$ .

Thousands: There is only 1 thousand, not enough to give each of 5 groups a thousand. Trade it: 1 thousand and 2 hundreds make 12 hundreds.
Hundreds: 12 hundreds $\div$ 5 = 2 hundreds. $2 \times 5 = 10$ , and $12 - 10 = 2$ hundreds are left.
Tens: Bring down the 4 to get 24 tens. 24 tens $\div$ 5 = 4 tens. $4 \times 5 = 20$ , and $24 - 20 = 4$ tens are left.
Ones: Bring down the 5 to get 45 ones. $45 \div 5 = 9$ , with nothing left.

$1{,}245 \div 5 = 249$ . Check: $249 \times 5 = 1{,}245$ . ✓

Common mistake

Don't skip a place when it has a zero in the quotient. For $624 \div 3$ : 6 hundreds $\div$ 3 = 2 hundreds. Then 2 tens $\div$ 3 = 0 tens (2 tens are left). Then 24 ones $\div$ 3 = 8. The answer is 208, not 28. Write the 0 so the other digits stay in the right places.

Tip

Estimate first so you can catch big mistakes. $437 \div 3$ is a little less than $450 \div 3 = 150$ , so an answer of about 145 makes sense.

Practice

Practice 1

Find $900 \div 3$ .

Type a number.

Practice 2

Find $3{,}500 \div 7$ .

Type a number.

Practice 3

Find $96 \div 4$ .

Type a number.

Practice 4

A school has 378 chairs. They are set up in 6 equal rows. How many chairs are in each row?

Type a number.

Practice 5

Find $529 \div 4$ . Write your answer like 12 R 3.

Type your answer

Practice 6

Find $624 \div 3$ .

Type a number.

Practice 7

A factory packs 2,184 batteries into 8 equal boxes. How many batteries go in each box?

Type a number.

Practice 8

Find $3{,}062 \div 7$ . Write your answer like 12 R 3.

Type your answer