☰ Course contents
📐 Mathematics Course
Mathematics › 🌉 Grade 5 › Fair Share Exchange: Dividing Decimals by Regrouping
🌉 Grade 5 · Lesson 2 of 11

Fair Share Exchange: Dividing Decimals by Regrouping

Split a decimal amount into equal groups, and when it does not divide evenly, trade each leftover for ten smaller pieces — that is regrouping.

Grade 5Elementary
Fair Share Exchange: Dividing Decimals by Regrouping — illustration
💡
The big idea: Dividing a decimal amount fairly works the same way as dividing whole numbers, one place value at a time. When an amount will not split evenly at one place value, you regroup the leftover into ten smaller pieces of the next place value — a whole dollar becomes ten dimes, a dime becomes ten pennies — and keep sharing.
🎯 By the end, you'll be able to
  • Explain division as sharing a quantity into equal-sized groups
  • Divide a decimal amount by a whole number, regrouping tenths and hundredths as needed
  • Use regrouping to divide amounts that do not split evenly using only whole units
  • Check a decimal division answer by multiplying the quotient back
📎 You should already know
  • Decimal place value (tenths and hundredths)
  • Whole-number division facts

Splitting a bill fairly

Suppose 4 friends want to share $9.20 equally. If you only handed out whole dollars, each friend would get $2 — that uses $8 — but $1.20 would still be sitting on the table. Not enough left for another whole dollar each, but far too much to ignore. What now?

The answer is the same trick you already use with whole numbers: regroup the leftover into smaller pieces and keep sharing.

🔑 Regrouping trades one big piece for ten smaller ones
When an amount will not divide evenly at one place value, trade the leftover for ten pieces of the next smaller place value — one leftover dollar becomes ten dimes, one leftover dime becomes ten pennies — and keep dividing.
\[ 1 = 10 \times 0.1 \qquad\qquad 0.1 = 10 \times 0.01 \]
One whole regroups into ten tenths; one tenth regroups into ten hundredths — trade a bigger piece for ten smaller ones so the sharing can continue.

Sharing one place value at a time

Decimal division moves through the place values in order: divide the whole ones first, regroup whatever is left into tenths, divide the tenths, regroup whatever is left into hundredths, and divide the hundredths. You stop once nothing is left over — or once you have divided as far as the problem needs.

🎮 Fair-Share Division LIVE
Share a money amount equally among the groups. When a place value will not split evenly, trade one piece for ten of the next-smaller place — that is decimal division by regrouping.

From dollars to dimes to pennies

Picture the chain: a dollar that cannot be shared whole becomes 10 dimes; a dime that cannot be shared whole becomes 10 pennies. Each trade is fair — nothing is gained or lost, the amount just gets sliced into pieces small enough to hand out evenly.

✨ You already know this trick
This is the very same regrouping you use when subtracting and need to “borrow” — trading 1 ten for 10 ones. Decimal division just keeps that trade going past the ones place, into tenths and hundredths.
📝 Worked example: Share $9.20 equally among 4 friends.
  1. Divide the whole dollars first: 9 ÷ 4 = 2, remainder 1. Each friend has $2 so far, with $1 left over.
  2. Regroup the leftover $1 into 10 dimes, and combine with the 2 dimes already in $9.20: 10 + 2 = 12 tenths.
  3. Divide the tenths: 12 ÷ 4 = 3, remainder 0. Each friend gets 3 more dimes, or $0.30, with nothing left over.
  4. Total per friend: $2 + $0.30.
✓ Each friend gets <strong>$2.30</strong>. Check: 4 &times; $2.30 = $9.20.
📝 Worked example: Share $7.45 equally among 5 friends.
  1. Divide the whole dollars: 7 ÷ 5 = 1, remainder 2. Each friend has $1 so far, with $2 left over.
  2. Regroup the $2 into 20 tenths, plus the 4 tenths already in $7.45: 20 + 4 = 24 tenths.
  3. Divide the tenths: 24 ÷ 5 = 4, remainder 4. Each friend gets 4 more dimes ($0.40), with 4 tenths left over.
  4. Regroup the 4 leftover tenths into 40 hundredths, plus the 5 hundredths already in $7.45: 40 + 5 = 45 hundredths.
  5. Divide the hundredths: 45 ÷ 5 = 9, remainder 0. Each friend gets 9 more pennies ($0.09).
  6. Total per friend: $1 + $0.40 + $0.09.
✓ Each friend gets <strong>$1.49</strong>. Check: 5 &times; $1.49 = $7.45.
⚠️ Do not stop early
If you stop dividing while there is still an amount left over, you have not finished the trade. Keep regrouping into the next place value until nothing remains — otherwise part of the money never gets shared out.

Check your understanding

1. One whole regroups into how many tenths?
Regrouping always trades one piece for ten of the next smaller place value: 1 whole = 10 tenths.
2. You share $6.30 among 3 friends. How much does each friend get?
6 ÷ 3 = 2 with 0 left over; 30 tenths (0.30) ÷ 3 = 0.10. Each friend gets $2.10.
3. After sharing whole dollars, $1 is left over with more sharing still to do. What should you do?
A leftover dollar regroups into 10 dimes (tenths) so the sharing can continue evenly.
4. In the worked example, sharing $7.45 among 5 friends, what does each friend get?
Dividing ones, then tenths, then hundredths gives $1 + $0.40 + $0.09 = $1.49 per friend.
5. One tenth regroups into how many hundredths?
Each regrouping step trades one piece for ten of the next smaller place value: 1 tenth = 10 hundredths.
✅ Key takeaways
  • Division shares a quantity into equal-sized groups.
  • When a whole does not split evenly among the groups, regroup it into ten smaller pieces of the next place value and keep dividing.
  • One whole regroups into 10 tenths; one tenth regroups into 10 hundredths.
  • Divide one place value at a time &mdash; ones, then tenths, then hundredths &mdash; regrouping any leftover before moving on.
  • Check a decimal division by multiplying the answer by the number of groups; it should rebuild the original amount.