Practice solving math problems

### 1.1. Practice solving math problems

**Lesson 1 page 176:** Two years ago the population of a commune was 5236 people, last year the population of the commune increased by 87 people, this year increased by 75 people. Calculate the population of the commune this year.

__Solution guide:__

*Summary*

Two years ago : 5236 people

Last year: increased by 87 people

This year: increase by 75 people

All : ? people.

__Method 1:__

- Find the population of the commune in the last year.
- Find the population of the commune this year equal to the population of the commune last year plus the additional number of people.

*Solution*

The population of the commune last year was:

5236 + 87 = 5323 (person)

The population of the commune this year is:

5323 + 75 = 5398 (person)

Answer: 5398 people.

__Method 2:__

- Find the number of people added after 2 years.
- Find the population of the commune this year equal to the original number of people plus the number just calculated.

*Solution*

The commune that increases in number of people in two years is:

87 + 75 = 162 (person)

This year the commune has a population of:

5236 + 162 = 5398 (person)

Answer: 5398 people.

**Lesson 2 page 176:** A store has 1245 shirts, the store sold \(\frac{1}{3}\) shirt number. How many shirts are left in that store?

__Solution guide:__

*Summary*

Yes : 1245 pieces

Sold : \(\frac{1}{3}\) shirt number

Rest : ? shirt.

- Find the number of shirts sold by the store by dividing 1245 by 3.
- Find the number of shirts that the store has left by subtracting the number of shirts from the original shop that sold.

*Solution*

The store that sold the number of shirts is:

1245 : 3 = 415 (shirt)

The rest of the store has the number of shirts:

1245 โ 415 = 830 (shirt)

Answer: 830 shirts.

**Lesson 3 page 176:** According to the plan, a group of workers had to plant 20 500 trees, the group planted \(\frac{1}{5}\) the number of trees. According to the plan, how many more trees will the group have to plant?

__Solution guide:__

*Summary*

Plan : 20 500 trees

Planted : \(\frac{1}{5}\) number of trees

Rest : ? tree

- Find the number of trees the worker’s nest has planted.
- Find the number of trees that the team needs to plant to complete the plan.

*Solution*

The number of trees planted by the workers’ group is:

20 500 : 5 = 4100 (tree)

The workers’ group also has to plant the number of trees to complete the plan:

20500 โ 4100 = 16400 (tree)

Answer: 16400 trees.

**Lesson 4 page 176:** Enter T or WILL

a) 96 : 4 x 2 = 24 x 2 = 48

b) 96 : 4 x 2 = 96 : 8 = 12

c) 96 : (4 x 2 ) = 96 : 8 = 12

__Solution guide:__

- Expressions with brackets : Calculate in parentheses first, outside brackets after.
- Expressions without brackets and only multiplication and division should be done in order from left to right.

a) Right

b) Wrong. Because it needs to be calculated in order from left to right.

c) Right

### 1.2. Reviewing on problem solving (continued)

**Lesson 1 page 176:** A rope 9135cm long is cut into two segments. The first segment is equal to \(\frac{1}{7}\) the length of the string. Calculate the length of each piece of string?

__Solution guide:__

*Summary*

- The length of the first segment is equal to the length of the string divided by 7.
- The length of the second segment is equal to the length of the string minus the length of the first line.

*Solution*

The length of the first string is:

9135 : 7 = 1305 (cm)

The length of the second string is :

9135 โ 1305 = 7830 (cm)

Answer: the first segment: 1305m;

second segment: 7830 cm.

**Lesson 2 page 176:** It is planned to transport 15,700 kg of salt to the mountainous areas by 5 trucks with evenly spaced loads. In the first phase, 2 trucks were on the road. How many kilograms of salt did the first batch carry?

__Solution guide:__

*Summary*

5 cars: 15 700kg

2 cars: ? kg

- Find how many kilograms of salt a truck can carry.
- Find how many kilograms of salt can be carried by two trucks.

*Solution*

The number of kilograms of salt each truck can carry is:

15 700 : 5 = 3140 (kg)

In the first batch, the number of kilograms of salt transferred was:

3140 x 2 = 6280 (kg)

Answer: 6280 kg.

**Lesson 3 page 176:** There are 42 identical cups arranged in 7 boxes. If there are 4572 cups of the same type, how many such boxes can be placed?

__Solution guide:__

*Summary*

42 cups : 7 boxes

4572 cups : ? box

- Find how many cups are in each box.
- Find the number of boxes by dividing 4572 by the number found in the previous step.

*Solution*

The number of cups in each box is:

42 : 7 = 6 (cup)

Number of boxes to hold all 4572 cups is:

4572 : 6 = 762 (box)

Answer: 762 boxes.

**Lesson 4 page 176:** Choose a letter that has a right answer

a) The expression 4 + 16 x 5 has a value of:

A. 100 B. 320 C. 84 D. 94

b) The expression 24 : 4 x 2 has the value of:

A. 3 B. 12 C. 4 D. 48

**Solution guide:**

- Expressions with multiplication and addition calculate the value of the multiplication first and then the addition.
- Expressions with multiplication and division are calculated from left to right, respectively.

a) We have: 4 + 16 x 5 = 4 + 80 = 84

Circle the letter C.

b) We have: 24 : 4 x 2 = 6 x 2 = 12

Circle the letter B.

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