Find the Average: Dividing Sum of 40 by 4 Numbers

Q: Why do I divide the sum by the number of values?

The average represents the typical value if all numbers were equal. Dividing spreads the total sum equally across all values, showing what each number would be if they were all the same.

Q: What if the division doesn't come out evenly?

That's perfectly normal! Averages can be decimal numbers. For example, if three numbers sum to 10, the average is $ \frac{10}{3} = 3.33... $

Q: Do all the individual numbers have to equal the average?

No! The individual numbers can be different. The average is just the balance point - some numbers can be higher, others lower, as long as they total to the given sum.

Q: What's the difference between sum and average?

The sum is when you add all numbers together (like 40). The average is the sum divided by how many numbers you have (like $ \frac{40}{4} = 10 $).

Average Calculation with Given Sum

What is the average of four numbers that have a sum of 40?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the average of the numbers

00:03 To calculate the average, sum up and divide by the number of occurrences

00:06 We already have the sum, so let's substitute and divide by the quantity of numbers

00:09 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the average of four numbers that have a sum of 40?

Step-by-step solution

To solve this problem, we need to find the average of four numbers whose total sum is 40.

We will apply the formula for finding the average, which is:

$\text{Average} = \frac{\text{Sum of values}}{\text{Number of values}}$

Here, the sum of the numbers is given as 40, and the number of values (numbers) is 4.

Substitute these values into the formula:

$\text{Average} = \frac{40}{4}$

Perform the division:

$\frac{40}{4} = 10$

Therefore, the average of these four numbers is $10$ .

Final Answer

$10$

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum divided by number of values
Technique: Use $\frac{40}{4} = 10$ for four numbers totaling 40
Check: Multiply answer by count: $10 \times 4 = 40$ matches given sum ✓

Common Mistakes

Avoid these frequent errors

Using sum as the final answer instead of dividing
Don't write 40 as your answer = confusing sum with average! The sum is what you start with, not the final answer. Always divide the sum by the number of values to find the average.

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 10 $$ and $$ 12 $$ .

FAQ

Everything you need to know about this question

Why do I divide the sum by the number of values?

The average represents the typical value if all numbers were equal. Dividing spreads the total sum equally across all values, showing what each number would be if they were all the same.

What if the division doesn't come out evenly?

That's perfectly normal! Averages can be decimal numbers. For example, if three numbers sum to 10, the average is $\frac{10}{3} = 3.33...$

How can I check if my average is correct?

Multiply your answer by the number of values. If you get back the original sum, your average is right! Like $10 \times 4 = 40$ ✓

Do all the individual numbers have to equal the average?

No! The individual numbers can be different. The average is just the balance point - some numbers can be higher, others lower, as long as they total to the given sum.

What's the difference between sum and average?

The sum is when you add all numbers together (like 40). The average is the sum divided by how many numbers you have (like $\frac{40}{4} = 10$ ).

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