Examples with solutions for Averages for 5th Grade: Finding the sum given the average and number of terms

Exercise #1

There are 10 cages in a zoo.

If the average number of animals in each cage is 3, then how many animals are there in total?

Step-by-Step Solution

To calculate the total number of animals in the zoo, we need to follow these steps:

  • Step 1: Identify the given average number of animals per cage, which is 33.
  • Step 2: Identify the total number of cages, which is 1010.
  • Step 3: Use the formula for total calculation: Total=Average×Number of cages\text{Total} = \text{Average} \times \text{Number of cages}.

Now, applying the formula:
Total=3×10=30 \text{Total} = 3 \times 10 = 30

Therefore, the total number of animals in all cages at the zoo is 3030.

Answer

30 30

Exercise #2

Roni has 5 bags.

If the average number of pens in each bag is 4, then how many pens in total does Roni have?

Step-by-Step Solution

To solve this problem, we'll apply the concept of the average:

  • Step 1: Identify the given information. The average number of pens in each bag is 44 and there are 55 bags.
  • Step 2: Use the formula for the total sum based on the average: Total Sum=Average×Number of Terms\text{Total Sum} = \text{Average} \times \text{Number of Terms}.
  • Step 3: Substitute the given values into the formula: Total Sum=4×5\text{Total Sum} = 4 \times 5.
  • Step 4: Perform the multiplication: 4×5=204 \times 5 = 20.

Therefore, the total number of pens Roni has is 2020.

Answer

20 20

Exercise #3

A sports center has 5 halls.

If the average number of seats in each hall is 30, then how many seats are there in total in the center?

Step-by-Step Solution

To solve this problem, we'll begin by applying the steps outlined previously.

  • Step 1: Identify the given information. We know that there are 5 halls in the sports center, and the average number of seats per hall is 30.
  • Step 2: Use the formula for calculating the total from an average. The formula is:

Total=Average×Number of Halls \text{Total} = \text{Average} \times \text{Number of Halls}

  • Step 3: Plug in the given values into the formula. We have:

Total=30×5 \text{Total} = 30 \times 5

Calculate the result:

  • Perform the multiplication: 30×5=150 30 \times 5 = 150 .

Therefore, the total number of seats in the sports center is 150 150 .

Answer

150 150

Exercise #4

There are 4 streets in a neighbourhood.

If the average number of houses on each street is 20, then how many houses are there in the neighborhood altogether?

Step-by-Step Solution

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

  • Step 1: Determine the number of streets.
  • Step 2: Determine the average number of houses per street.
  • Step 3: Calculate the total number of houses by multiplying these two values.

Now, let's work through each step:

  • Step 1: The number of streets is given as 4.
  • Step 2: The average number of houses per street is 20.
  • Step 3: Using the formula Total number of houses=Average number of houses×Number of streets\text{Total number of houses} = \text{Average number of houses} \times \text{Number of streets}, we have:

Total number of houses=20×4=80 \text{Total number of houses} = 20 \times 4 = 80

Therefore, the solution to the problem is 80 80 .

Answer

80 80

Exercise #5

Danny's house has 3 rooms.

If the average number of windows in each room is 2, then how many windows are there in total?

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
  • Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem gives us 3 rooms and an average of 2 windows per room.
Step 2: We'll use the formula: Total number of windows=(Average number per room)×(Number of rooms) \text{Total number of windows} = (\text{Average number per room}) \times (\text{Number of rooms}) .
Step 3: Plugging in our values, we get 2×3=6 2 \times 3 = 6 .

Therefore, the solution to the problem is 6 6 .

Answer

6 6

Exercise #6

In the zoo there are 12 animals.

If the average number of legs that each animal has is 3, then how many legs in total do all the animals in the zoo have?

Step-by-Step Solution

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

  • Step 1: Identify the given information: There are 12 animals, and the average number of legs is 3.
  • Step 2: Use the formula for the total sum based on the average: Total Sum=Average×Number of Terms\text{Total Sum} = \text{Average} \times \text{Number of Terms}.
  • Step 3: Perform the calculation using the given numbers.

Now, let's work through each step:
Step 1: We know there are 12 animals and the average number of legs per animal is 3.
Step 2: We'll use the formula Total Sum=Average×Number of Terms\text{Total Sum} = \text{Average} \times \text{Number of Terms}. In this context: Total Sum of legs=3×12\text{Total Sum of legs} = 3 \times 12.
Step 3: Calculating gives us 3×12=363 \times 12 = 36.

Therefore, the total number of legs that all the animals in the zoo have is 36 36 .

Answer

36 36

Exercise #7

There are 20 shops in a shopping mall.

If the average number of employees in each shop is 5, then how many employees are there in the shopping mall altogether?

Step-by-Step Solution

To solve this problem, we'll proceed as follows:

  • Step 1: Use the formula for finding the total number of employees based on the average and the number of shops.
  • Step 2: Substitute the values given in the problem into the formula.
  • Step 3: Perform the multiplication to find the total number of employees.

Now, let's implement these steps:
Step 1: The formula used is: Total employees = Average number of employees per shop ×\times Number of shops.
Step 2: Substitute the given values: Total employees = 5×205 \times 20.
Step 3: Calculate the result: 5×20=1005 \times 20 = 100.

Therefore, the total number of employees in the shopping mall is 100 100 .

Answer

100 100

Exercise #8

In the warehouse there are 10 shelves.

If the average number of boxes on each shelf is 612 6\frac{1}{2} , then how many boxes are there in the warehouse in total?

Step-by-Step Solution

To solve this problem, we will follow a series of logical steps:

  • Step 1: Identify the given information
  • Step 2: Convert the mixed number to a decimal or improper fraction
  • Step 3: Use the appropriate formula to calculate the total number of boxes

Let's work through these steps:

Step 1: We know there are 10 shelves and the average number of boxes per shelf is 612 6\frac{1}{2} .

Step 2: Convert 612 6\frac{1}{2} to an improper fraction or decimal for calculation. As an improper fraction, it becomes 132\frac{13}{2}, and as a decimal, it is 6.56.5.

Step 3: Using the formula:

Total number of boxes=Average×Number of shelves \text{Total number of boxes} = \text{Average} \times \text{Number of shelves}

Substituting the values, we get:

Total number of boxes=6.5×10 \text{Total number of boxes} = 6.5 \times 10

Perform the multiplication:

6.5×10=65 6.5 \times 10 = 65

Therefore, the total number of boxes in the warehouse is 65 65 .

Answer

65 65