Calculate the Average of Three Numbers: 2, 5, and 9

Q: Why is the answer a mixed number instead of a decimal?

Both forms are correct! $ 5\frac{1}{3} $ is the exact answer, while 5.333... is the decimal approximation. Mixed numbers are often preferred because they show the precise value.

Q: How do I convert the improper fraction to a mixed number?

Divide 16 by 3: 16 ÷ 3 = 5 remainder 1. The whole number (5) becomes the whole part, and the remainder (1) over the divisor (3) becomes the fraction: $ 5\frac{1}{3} $.

Q: What if I accidentally add the numbers wrong?

Always double-check your addition! Try adding in a different order: 5 + 9 = 14, then 14 + 2 = 16. If you get a different sum, recalculate carefully.

Q: Can I use a calculator for this problem?

Yes, but be careful with the division! 16 ÷ 3 = 5.333... on most calculators. To get the mixed number, you need to recognize that 0.333... = $ \frac{1}{3} $.

Q: Is there a faster way to find the average?

Not really! The average formula always requires adding all numbers and dividing by the count. This is the standard method that works for any set of numbers.

Arithmetic Mean with Mixed Numbers

Calculate the average

of $2,5,$ and $9$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the average

00:03 To calculate the average, we need to divide the sum by the number of occurrences

00:07 Let's sum up the numbers

00:13 And divide by the number of occurrences (3)

00:14 Let's break down 16 into 15 plus 1

00:39 Let's break it down into whole fraction and remainder

00:44 Convert from whole fraction to whole number

00:52 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

Calculate the average

of $2,5,$ and $9$ .

Step-by-step solution

To solve for the average of the numbers 2, 5, and 9, we will follow these steps:

Step 1: Add the numbers together.
Step 2: Count the number of values.
Step 3: Divide the sum by the count to find the average.

We start by calculating the sum of the numbers:

$2 + 5 + 9 = 16$

Next, we count the number of values, which is 3.

Now, we calculate the average using the formula for the arithmetic mean:

$\text{Average} = \frac{16}{3} = 5\frac{1}{3}$

Therefore, the average of the numbers 2, 5, and 9 is $5\frac{1}{3}$ .

This matches choice 2 from the provided options.

Final Answer

$5\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Formula: Add all numbers then divide by count of numbers
Technique: Sum: 2 + 5 + 9 = 16, then divide 16 ÷ 3
Check: Convert $5\frac{1}{3}$ to decimal: 5.333... matches 16 ÷ 3 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all numbers when dividing
Don't just add the numbers and stop = incomplete calculation! Students often forget the division step or miscount how many numbers they have. Always count your numbers first, then divide the sum by that exact count.

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 11 $$ and $$ 7 $$ .

FAQ

Everything you need to know about this question

Why is the answer a mixed number instead of a decimal?

Both forms are correct! $5\frac{1}{3}$ is the exact answer, while 5.333... is the decimal approximation. Mixed numbers are often preferred because they show the precise value.

How do I convert the improper fraction to a mixed number?

Divide 16 by 3: 16 ÷ 3 = 5 remainder 1. The whole number (5) becomes the whole part, and the remainder (1) over the divisor (3) becomes the fraction: $5\frac{1}{3}$ .

What if I accidentally add the numbers wrong?

Always double-check your addition! Try adding in a different order: 5 + 9 = 14, then 14 + 2 = 16. If you get a different sum, recalculate carefully.

Can I use a calculator for this problem?

Yes, but be careful with the division! 16 ÷ 3 = 5.333... on most calculators. To get the mixed number, you need to recognize that 0.333... = $\frac{1}{3}$ .

Is there a faster way to find the average?

Not really! The average formula always requires adding all numbers and dividing by the count. This is the standard method that works for any set of numbers.

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