The Big Idea
Division asks: "How many groups?" or "How many in each group?"
If you know 6 x 8 = 48, then you also know 48 / 6 = 8 and 48 / 8 = 6!
Method 1: Partial Quotients
Subtract "chunks" until you reach zero (or have a remainder).
Example: 846 / 6
846
- 600 (That's 6 x 100) --> 100
---
246
- 240 (That's 6 x 40) --> 40
---
6
- 6 (That's 6 x 1) --> 1
---
0 ----
Answer: 141
Tip: You can use ANY multiples you know! Some students might subtract 6 x 50 = 300 first. There's no wrong way as long as you add up all your chunks!
Method 2: Standard Algorithm (Long Division)
Divide, Multiply, Subtract, Bring down - repeat!
141
-----
6 | 846
6 (How many 6s in 8? 1. Write 1.)
-- (1 x 6 = 6. Subtract from 8.)
24 (Bring down 4. Now you have 24.)
24 (How many 6s in 24? 4. Write 4.)
-- (4 x 6 = 24. Subtract.)
06 (Bring down 6. Now you have 6.)
6 (How many 6s in 6? 1. Write 1.)
-- (1 x 6 = 6. Subtract.)
0 (Done! No remainder.)
What About Remainders?
Sometimes numbers don't divide evenly. The "leftover" is called a remainder.
Example: 157 / 6 = 26 R 1
Check: 26 x 6 = 156, plus 1 leftover = 157
What do you do with remainders? It depends!
Round UP: "45 students need vans that hold 7. How many vans?" 45/7 = 6 R 3. Need 7 vans (can't leave 3 students!)
Drop it: "48 stickers, 7 per page. How many FULL pages?" 48/7 = 6 R 6. Answer: 6 full pages
Use as fraction: "Share 25 cookies equally among 4 friends." 25/4 = 6 R 1. Each gets 6 1/4 cookies
Your Turn: Practice Problems
1. Solve 728 / 4 using any method. Show your work.
Answer:
2. Solve 1,935 / 5 using any method. Show your work.
Answer:
3. Solve 259 / 6. Show your work and include the remainder.
Answer: R
4. A farmer has 175 apples to pack into bags of 8. How many FULL bags can he make? How many apples are left over?
Full bags: Left over:
5. A class of 29 students needs to split into groups of 4 for a project. How many groups will there be? (Remember: everyone needs a group!)
Answer: groups