Long division beyond the Ones

The idea

Division using place value (long division) extends to decimal quotients: whatever remains is regrouped into the next smaller place, Ones into tenths, tenths into hundredths, and so on, and division continues.

One left over

Share 1324 equally among 4: each part gets 3 hundreds, 3 tens and 1 one. That is 331. Now share 1325. Each part gets the same, but 1 one is left over.

What can we do with the 1 one left over?

• Stop: the answer is 331 and 1 is left
• Break the 1 one into 10 tenths and share those
• Throw the 1 one away

Share and regroup

Set how many each share gets at every place, then tap Share. If something is left over, regroup it into the next smaller place.

Ones into tenths, tenths into hundredths

1 one is the same as 10 tenths. 1 tenth is the same as 10 hundredths. So what is left over can always be regrouped and shared on.

Together: 3 hundreds + 3 tens + 1 one + 2 tenths + 5 hundredths = 331.25. Check with fractions: 1325/4 = (1325 × 25)/(4 × 25) = 33125/100 = 331.25.

Division using place value (long division) goes on past the Ones place. Whatever is left is regrouped into the next smaller place: Ones into tenths, tenths into hundredths, and so on, and the division continues.

• Share among 4 | Each gets
• 13 hundreds | 3 hundreds, 1 left
• 12 tens | 3 tens, none left
• 5 ones | 1 one, 1 left
• 1 one = 10 tenths | 2 tenths, 2 left
• 2 tenths = 20 hundredths | 5 hundredths, none left

Notes

When the Ones are used up and something is left, regroup it into tenths (1 one = 10 tenths), then tenths into hundredths, and keep sharing until nothing is left.

Check yourself

After sharing, 2 tenths are left over. To share them among 4, we regroup them as ...

After sharing, 3 ones are left. Regrouped into tenths that is how many tenths?

Answer: 30 tenths

3 ones × 10 = 30 tenths.

Find 7 ÷ 2. Each gets 3 ones and 1 one is left. Regroup it and carry on. Type the answer as a decimal.

Answer: 3.5

7 ones ÷ 2 = 3 ones, 1 left. 1 one = 10 tenths ÷ 2 = 5 tenths. So 7 ÷ 2 = 3.5.

Find 27 ÷ 4 by sharing and regrouping. Type the answer as a decimal.

Answer: 6.75

6 each (24), 3 left = 30 tenths: 7 each (28), 2 tenths left = 20 hundredths: 5 each. So 6.75.

• 20 tenths. That makes the amount bigger. We need a smaller place: hundredths, where 1 tenth = 10 hundredths.
• 20 hundredths — correct. 1 tenth is 10 hundredths, so 2 tenths are 20 hundredths. Then each of 4 gets 5 hundredths.
• 2 hundredths. One tenth is worth 10 hundredths, not 1. So 2 tenths are 20 hundredths.