Finding Total Value
Learn to find the total when you know the average
1. Reversing the Formula
The Key Insight
If we know the average and the number of items, we can find the total!
Total = Average × Number of items
The Three Average Formulas
The three formulas are all connected:
Average = Total ÷ Number
Total = Average × Number
Number = Total ÷ Average
Think of it like this: If we "evened out" the values, we get the average. To find the total, we "gather back" all those equal shares!
2. Worked Examples
Example 1: Stickers in Packets
The average number of stickers in 3 packets is 18. What is the total number of stickers in the 3 packets?
Given: Average = 18, Number of packets = 3
Find: Total number of stickers
Solution: Total = Average × Number = 18 × 3 = 54 stickers
Example 2: Water in Cups
The average volume of water in 5 cups is 120 ml. What is the total volume of water in the 5 cups?
Total volume = Average × Number of cups
Total volume = 120 ml × 5 = 600 ml
Important: Does this mean all 5 cups have exactly 120 ml each? No! One cup might have 100 ml, another 140 ml. The average is 120 ml, but individual cups can differ.
Example 3: Mobile Phones
The average cost of 8 mobile phones is $315.75. What is the total cost of the 8 mobile phones?
Given: Average = $315.75, Number = 8
Solution:
Total = $315.75 × 8 = $2526
3. Using a Bar Model
Example: Joan's Project Time
Joan spent an average of 2 hours a day on a project from Monday to Thursday. What was the total time Joan spent on her project?
Monday to Thursday = 4 days
Total time = 2 hours × 4 = 8 hours
4. Try These!
Practice Problem 1
The average of 6 numbers is 25. What is the sum of the 6 numbers?
Click to see solution
Sum = Average × Number = 25 × 6 = 150
Practice Problem 2
The average height of 7 students is 1.45 m. What is the total height of the 7 students?
Click to see solution
Total height = 1.45 m × 7 = 10.15 m
Practice Problem 3
The average mass of 4 parcels is 2.5 kg. What is the total mass of the 4 parcels?
Click to see solution
Total mass = 2.5 kg × 4 = 10 kg
Key Points to Remember
- ✓Total = Average × Number of items
- ✓Use this when you know the average and need to find the total
- ✓Think of it as "gathering back" all the evened-out shares
- ✓Individual values don't need to equal the average - they just need to add up to the total
- ✓Works with decimals too (e.g., $315.75 × 8)