Averages for 5th Grade: Calculating the average of non-whole numbers

To solve this problem, we need to calculate the average of the numbers 1 and 12. The average can be calculated using the formula:
$\text{average} = \frac{\text{sum of numbers}}{\text{number of values}}$.

Now, let's work through the steps:
Step 1: Calculate the sum of the numbers:
$1 + 12 = 13$.

Step 2: Determine the number of values, which is 2 in this case.
Step 3: Apply the average formula:
$\text{average} = \frac{13}{2} = 6.5$.

Therefore, the average of the numbers 1 and 12 is $6.5$.

Considering the given answer choices, choice 1 with $6.5$ is the correct answer as per our calculations.

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.

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

• Step 1: Calculate the sum of the numbers.
• Step 2: Count the number of numbers given.
• Step 3: Divide the sum by the count to find the average.

Now, let's work through each step:

Step 1: Add the numbers $10 + 3 + 2 + 4$.

$10 + 3 + 2 + 4 = 19$.

Step 2: Count the number of numbers, which is 4.

Step 3: Divide the total sum by the number of numbers: $\frac{19}{4}$.

$\frac{19}{4}$ can be written as a mixed number, which is $4\frac{3}{4}$.

Therefore, the average of 10, 3, 2, and 4 is $4\frac{3}{4}$.

To solve this problem, we will calculate the average of the numbers 0, 0, and 8.

We follow these steps:

• Step 1: Add the numbers together:

The sum of $0 + 0 + 8$ is $8$.

• Step 2: Divide the sum by the number of terms:

There are 3 numbers, so we divide the sum by 3:
$\frac{8}{3}$

This results in the fraction $\frac{8}{3}$, which is equivalent to the mixed number $2\frac{2}{3}$.

Therefore, the average of the numbers 0, 0, and 8 is $2\frac{2}{3}$.

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

• Step 1: Calculate the sum of the numbers.
• Step 2: Determine the count of the numbers.
• Step 3: Use the formula for the average.

Now, let's work through each step:
Step 1: Sum of the numbers = $7 + 6 + 5 + 5 = 23$.
Step 2: Count of the numbers = 4.
Step 3: Apply the average formula:
$\text{Average} = \frac{23}{4} = 5.75$ This can be expressed as a mixed number, $5\frac{3}{4}$.

Therefore, the average of 7, 6, 5, and 5 is $5\frac{3}{4}$.

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

• Step 1: Calculate the sum of the numbers.
• Step 2: Divide the sum by the number of values to find the average.

Now, let's work through each step:
Step 1: The numbers given are 11, 13, 4, and 9. We calculate the sum as follows:
$11 + 13 + 4 + 9 = 37$.
Step 2: To find the average, divide the sum by 4 (the number of values):
$\frac{37}{4} = 9.25$ or $9\frac{1}{4}$ when expressed as a mixed number.

Therefore, the average of 11, 13, 4, and 9 is $9\frac{1}{4}$.

To solve this problem, we need to find the average of four identical numbers: $10\frac{1}{2}$. We will follow these steps:

• Step 1: Recognize that the problem involves calculating the average of identical numbers.
• Step 2: Choose to convert the mixed number $10\frac{1}{2}$ into a more convenient form, such as a decimal or improper fraction.
• Step 3: Compute the sum of these numbers and divide by the total number of terms.

Let's proceed with these steps:
Step 1: Each number is the same, $10\frac{1}{2}$. A mixed number like $10\frac{1}{2}$ can either be expressed as $10.5$ (decimal form) or as the improper fraction $\frac{21}{2}$.
Step 2: There are four numbers, each valued at $10.5$. The sum of these numbers is $4 \times 10.5 = 42$.
Step 3: Divide this sum by the number of numbers (4):
$\text{Average} = \frac{42}{4} = 10.5$

Therefore, the average of the numbers $10\frac{1}{2}, 10\frac{1}{2}, 10\frac{1}{2},$ and $10\frac{1}{2}$ is $10\frac{1}{2}$.

To solve this problem, we'll follow these steps to find the average:

• Step 1: Calculate the sum of the given numbers.
• Step 2: Determine the total number of numbers provided.
• Step 3: Use the formula for the average to find the solution.

Now, let's work through each step:
Step 1: Sum the numbers given: $21 + 0 + 0 + 0 = 21$.
Step 2: Count the total number of numbers: There are $4$ numbers in total.
Step 3: Calculate the average using the formula:
$\text{Average} = \frac{\text{Sum of numbers}}{\text{Total number of numbers}} = \frac{21}{4} = 5.25$

This can be written as a mixed number: $5\frac{1}{4}$.

Thus, the solution to the problem is $5\frac{1}{4}$, corresponding to choice 4.