Find the average

### 1.1. Knowledge to remember

**Problem 1: **Pour into the first orange 6l of oil, pour into the second can of 4l of oil. If that number of liters of oil is evenly poured into 2 cans, how many liters of oil are in each can?

*Solution*

The total number of liters of oil in 2 cans is:

6 + 4 = 10 (l)

The number of liters of oil evenly poured into the can is:

10 : 2 = 5 (l)

Answer: 5l of oil

**Comment :**

– Take the total number of liters of oil divided by 2 to get the number of liters of oil evenly poured into each can:

(6+4): 2 = 5 (l)

We call the number 5 the average of the two numbers 6 and 4 .

– We say: The first can has 6 liters, the second can has 4 liters, the same can has 5 liters each.

**Problem 2: **The number of students in 3 classes is 25 students, 27 students, and 32 students, respectively. On average, how many students are there in each class?

*Solution:*

Total number of students in 3 classes:

25 + 27 + 32 = 84 (students)

On average, each class has:

84 : 3 = 28 (student)

Answer 28 students

*Comment :* The number 28 is the average of the three numbers 25, 27 and 32

We write: (25 + 27 + 32) : 3 = 28

*To find the average of many numbers, we calculate the sum of the numbers and then divide that sum by the terms.*

### 1.2. Textbook exercise solution page 27

**Lesson 1:** Find the average of the following numbers

a) 42 and 52 b) 36 ; 42 and 57.

c) 34 ; 43 ; 52 and 39 d) 20 ; 35 ; 37 ; 65 and 73

**Solution guide:**

- To find the average of many numbers, we calculate the sum of the numbers and then divide that sum by the number of terms.

a) The average of 42 and 52 is:

(42 + 52) : 2 = 47

b) the average of 36 ; 42 and 57 are:

(36 + 42 + 57) : 3 = 45

c) the average of 34 ; 43 ; 52 and 39 are:

(34 + 43 + 52+ 39) : 4 = 42

d) the average of 20 ; 35 ; 37 ; 65 and 73 are:

(20 + 35 + 37 + 65 + 73) : 5 = 46

**Lesson 2: **Four children Mai, Hoa, Hung, Thinh, respectively, weigh 36 kg; 38 kg; 40kg; 34kg. On average, how many kilograms does each child weigh?

__Solution guide:__

- To find the average weight of each child, we calculate the total weight of 4 children and divide that sum by 4.

*Solution*

All four children weigh in kilograms:

36 + 38 + 40 + 34 = 148 (kg)

The average weight of each child in kilograms is:

148 : 4 = 37 (kg)

Answer: 37kg.

**Lesson 3:** Find the average of consecutive natural numbers from 1 to 9.

__Solution guide:__

- To find the average of many numbers, we calculate the sum of those numbers and then divide that sum by the number of terms.

The average of consecutive natural numbers from 1 to 9 is:

(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) : 9 = 5

### 1.3. Textbook exercise solution page 28

**Lesson 1:** Find the average of the following numbers

a) 96 ; 121 and 143. b) 35 ; twelfth ; 24 ; 21 and 43.

__Solution guide:__

- To find the average of many numbers, we calculate the sum of the numbers and then divide that sum by the number of terms.

a) the average of 96 ; 121 and 143 are:

(96 + 121 + 143) : 3 = 120

b) the average of 35 ; twelfth ; 24 ; 21 and 43 are:

(35 + 12 + 24 + 21 + 43): 5 = 27

**Lesson 2: **The population of a commune in 3 consecutive years increased by: 96 people, 82 people, 71 people, respectively. The average population of that commune increases by how many people each year?

__Solution guide:__

- To find the average number of people who increased each year, we add up the total number of people that increased in those 3 years and divide that total by 3.

*Solution*

The total number of people added in 3 consecutive years is:

96 + 82 + 71 = 249 (person)

On average, each year the commune’s population increases, the number of people is:

249 : 3 = 83 (person)

Answer: 83 people.

**Lesson 3:** The height measurements of 5 fourth graders are 138cm, 132cm, 130cm, 136cm, 134cm respectively. What is the average height of each child in centimeters?

__Solution guide:__

- To find the average height of each child, we calculate the sum of the height measurements of 5 students and divide by 5.

*Solution*

The sum of the height measurements of 5 students is:

138 + 132 + 130 + 136 + 134 = 670 (cm)

The average height of each student is:

670 : 5 = 134 (cm)

Answer: 134cm.

**Lesson 4: **There are 9 cars transporting food into the city, in which there are 5 cars in the lead, 36 quintals each and 4 rear cars, 45 quintals each. On average, how many tons of food does each car carry?

__Solution guide:__

- Calculate the number of quintals of food the first 5 cars can carry = the number of quintals of food the first 1 car can carry x 5.
- Calculate the number of food quintals that can be carried by the following 4 cars = the number of food quintals that can be carried by the following 4 cars x 4.
- Calculate the total number of cars: 4 + 5 = 9 cars.
- Calculate the total number of food quintals that 9 trucks can carry = the number of food quintals the first 5 cars can carry + the number of food quintals the last 4 cars can carry.
- Calculate the average number of weights of food each truck can carry = total weights of food 9 trucks can carry: 9.
- Convert the measurement you just found to the unit of measurement is tons, note we have: 1 ton = 10 quintals.

*Solution*

The first 5 cars that can transfer food weights are:

36 x 5 = 180 (weights)

The following 4 cars can transfer the weight of food:

45 x 4 = 180 (weights)

The company’s total number of cars is:

5 + 4 = 9 (car)

9 cars can transfer the weight of food is:

180 + 180 = 360 (weights)

The average number of pounds of food transported by the car is:

360 : 9 = 40 (weight)

40 quintals = 4 tons

Answer: 4 tons.

**Lesson 5:**

a) The average of two numbers is 9. Knowing one of them is equal to 12, find the other.

b) The average of two numbers is 28. Knowing one of them is 30, find the other number.

__Solution guide:__

- To find the sum of the numbers, we multiply the average by the number of terms.
- To find the unknown term, subtract the known term from the sum.

a) The sum of two numbers is: 9 x 2 = 18

The number to find is: 18 – 12 = 6

b) Sum of two numbers is: 28 x 2 = 56

The number to find is: 56 – 30 = 26

Answer: a) 6; b) 26.

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