Examples with solutions for Averages for 5th Grade: Determining the average of given a sum

Exercise #1

What is the average of four numbers that have a sum of 20?

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the number of values for which we are calculating the average. In this case, it is 44.
  • Step 2: Identify the given total sum, which is 2020.
  • Step 3: Use the average formula to calculate: Average = SumTotal Count\frac{\text{Sum}}{\text{Total Count}}.

Now, let's work through each step:
Step 1: We know that we are dealing with 44 numbers.
Step 2: The total sum of these numbers is given as 2020.
Step 3: Using the formula for the average, we calculate:
Average=204=5\text{Average} = \frac{20}{4} = 5.

Therefore, the solution to the problem is 5 5 .

Answer

5 5

Exercise #2

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

Video Solution

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 .

Answer

3 3

Exercise #3

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

Video Solution

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:

  • Average=Sum of valuesNumber of values \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:

Average=404 \text{Average} = \frac{40}{4}

Perform the division:

404=10 \frac{40}{4} = 10

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

Answer

10 10

Exercise #4

What is the average of seven numbers with a sum of 28?

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the given data
  • Step 2: Use the average formula
  • Step 3: Perform the division to find the average

Now, let's work through each step:

Step 1: The total sum of the numbers is given as 2828, and there are 77 numbers.

Step 2: We'll use the formula for calculating the average:

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

Step 3: Plugging in the values, we have:

Average=287\text{Average} = \frac{28}{7}

Average=4\text{Average} = 4

Therefore, the solution to the problem is that the average of these seven numbers is 4\mathbf{4}.

Answer

4 4

Exercise #5

What is the average of ten numbers that have a sum of 5?

Video Solution

Step-by-Step Solution

To solve this problem, we'll apply the formula for the average:

  • Step 1: The total number of numbers is 10 10 .
  • Step 2: The sum of all these numbers is 5 5 .
  • Step 3: Use the average formula to find the average.

Now, using the formula, the average is calculated as:
Average=Sum of all numbersNumber of numbers=510=12 \text{Average} = \frac{\text{Sum of all numbers}}{\text{Number of numbers}} = \frac{5}{10} = \frac{1}{2}

Therefore, the solution to the problem is 12 \frac{1}{2} .

Answer

12 \frac{1}{2}

Exercise #6

What is the average of four numbers that have a sum of 15?

Video Solution

Step-by-Step Solution

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

  • Step 1: Identify the given information
  • Step 2: Apply the appropriate formula to find the average
  • Step 3: Perform the calculation to find the result

Now, let's go through each step:

Step 1: The problem tells us the sum of four numbers is 15.

Step 2: We will use the formula for average: Average=Sum of numbersn\text{Average} = \frac{\text{Sum of numbers}}{n}, where n n is the number of numbers.

Step 3: Substituting into the formula, we have:

Average=154 \text{Average} = \frac{15}{4}

Calculating this gives:

154=3.75 \frac{15}{4} = 3.75

We can express 3.753.75 as a mixed number: 334 3\frac{3}{4} .

Therefore, the average of the four numbers is 334 3\frac{3}{4} .

Answer

334 3\frac{3}{4}

Exercise #7

What is the average of three numbers that have a sum of 10?

Video Solution

Step-by-Step Solution

To solve this problem, we need to find the average of three numbers that sum up to 10.

We will follow these steps:

  • Step 1: Identify the sum of the numbers, which is given as 10.
  • Step 2: Identify the number of terms, which in this case is 3.
  • Step 3: Apply the average formula Average=Sum of numbersn \text{Average} = \frac{\text{Sum of numbers}}{n} .

Now, let's perform the calculations:
Step 1: The sum of the three numbers is 10 10 .
Step 2: There are 3 3 numbers to consider.
Step 3: Calculate the average:Average=103=3.3333 \text{Average} = \frac{10}{3} = 3.3333\ldots .

We can express 3.3333 3.3333\ldots as a mixed number: 313 3\frac{1}{3} .

Therefore, the average of three numbers that sum to 10 is 313 3\frac{1}{3} .

Answer

313 3\frac{1}{3}

Exercise #8

What is the average of ten numbers that have an average of 90?

Video Solution

Answer

9 9