Finding the Number of Items
Learn to find how many items when you know total and average
1. When Do We Use This?
The Third Formula
When you know the total and the average, you can find how many items there are!
Number of items = Total ÷ Average
All Three Average Formulas
Now you know all three formulas!
Average = Total ÷ Number
Total = Average × Number
Number = Total ÷ Average ← NEW!
When to use it: the question gives the total and the average, and asks how many items there are.
2. Worked Examples
Example 1: Raju's T-shirts
Raju spent $45 on some T-shirts. The average cost of the T-shirts is $9. How many T-shirts did he buy?
Given: Total = $45, Average = $9
Find: Number of T-shirts
Solution:
Number of T-shirts = Total ÷ Average
= $45 ÷ $9 = 5 T-shirts
Check: 5 T-shirts × $9 average = $45 total ✓
Example 2: Sally's Tarts
Sally has 24 tarts. She packs the tarts into some boxes. The average number of tarts in each box is 6. How many boxes of tarts are there?
Number of boxes = Total ÷ Average
= 24 ÷ 6 = 4 boxes
Question: Do all the boxes have the same number of tarts?
Answer: Not necessarily! One box might have 5 tarts, another 7, another 6, another 6. The average is 6, but individual boxes can differ.
Example 3: James's Books
James bought some books for $72. The average cost of a book was $8. How many books did he buy?
Number of books = Total ÷ Average
= $72 ÷ $8 = 9 books
Check: 9 books × $8 = $72 ✓
Example 4: Fruit Seller's Papayas
A fruit seller has some papayas. The total mass of the papayas is 70 kg. The average mass of a papaya is 2 kg. How many papayas does the fruit seller have?
Number of papayas = Total mass ÷ Average mass
= 70 kg ÷ 2 kg = 35 papayas
3. Watch Out!
Common Mistake
✗ WRONG: Average ÷ Total
✓ CORRECT: Total ÷ Average
Remember: The total is never smaller than the average, so the total goes first: Total ÷ Average.
How to Remember
Ask yourself: "How many $9s are in $45?"
This is just like asking: "45 ÷ 9 = ?" The answer is 5!
4. Try These!
Practice Problem 1
A farmer collected 180 eggs. The average number of eggs per basket is 15. How many baskets did the farmer use?
Click to see solution
Number of baskets = 180 ÷ 15 = 12 baskets
Check: 12 × 15 = 180 ✓
Practice Problem 2
A shop sold stickers for a total of $156. The average price per pack is $12. How many packs were sold?
Click to see solution
Number of packs = $156 ÷ $12 = 13 packs
Check: 13 × $12 = $156 ✓
Practice Problem 3
The total length of some ribbons is 63 m. The average length is 9 m. How many ribbons are there?
Click to see solution
Number of ribbons = 63 ÷ 9 = 7 ribbons
Check: 7 × 9 = 63 ✓
Key Points to Remember
- ✓Number = Total ÷ Average
- ✓Use this when you need to find "how many" items
- ✓Remember: Total ÷ Average (NOT Average ÷ Total)
- ✓Always verify: Number × Average should equal Total
- ✓Think: "How many averages fit into the total?"