Find the Arithmetic Mean: Three Numbers with Sum of 9

Arithmetic Mean with Known Sum

What is the average of three numbers given that their sum is 9?

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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
00:02 To calculate the average, we sum and divide by the number of occurrences
00:05 We already have the sum, so we'll substitute and divide by the quantity of numbers
00:08 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the average of three numbers given that their sum is 9?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information: The sum of the three numbers is 9 9 .
  • Step 2: Apply the formula for average.
  • Step 3: Perform the necessary calculation to find the average.

Now, let's work through each step:
Step 1: The problem gives us the sum of the three numbers as 9 9 .
Step 2: We'll use the formula for average:
Average=Sum of the numbersNumber of values \text{Average} = \frac{\text{Sum of the numbers}}{\text{Number of values}} Step 3: Plugging in our values, we have: Average=93=3 \text{Average} = \frac{9}{3} = 3

Therefore, the solution to the problem is 3 3 .

3

Final Answer

3 3

Key Points to Remember

Essential concepts to master this topic
  • Formula: Average equals sum divided by number of values
  • Technique: Apply 93=3 \frac{9}{3} = 3 for three numbers
  • Check: Three numbers averaging 3 must sum to 9 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing sum with average
    Don't think the sum of 9 IS the average = wrong answer of 9! The sum is the total before dividing. Always divide the sum by the count of numbers to find the average.

Practice Quiz

Test your knowledge with interactive questions

If the balls below are divided so that each column in the table contains an equal number, then how many balls will there be in each column?

FAQ

Everything you need to know about this question

Why do I divide by 3 and not multiply?

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The average formula requires division! You're splitting the total sum equally among all the numbers. Think of it as: How much does each number get if we share 9 equally among 3 numbers?

What if the numbers aren't all the same?

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The average is still 3! The individual numbers could be 1, 2, and 6, or 0, 4, and 5. As long as they add up to 9, their average will always be 3.

Can I use this method for any number of values?

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Absolutely! Whether you have 2 numbers, 10 numbers, or 100 numbers, the formula stays the same: Average=SumCount \text{Average} = \frac{\text{Sum}}{\text{Count}}

What if I get a decimal or fraction as the average?

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That's completely normal! Not all averages are whole numbers. For example, if two numbers sum to 5, their average would be 52=2.5 \frac{5}{2} = 2.5

How can I check if my average is reasonable?

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Multiply your average by the number of values. You should get back the original sum! In this case: 3×3=9 3 \times 3 = 9

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