Review and supplement on math problem solving

### * Review and supplement on math problem solving

a) Example: An average person walks 4km . per hour

The table below shows the distance traveled by the bugger in 1 hour, 2 hours, 3 hours:

Time | 1 hour | 2 o’clock | 3 o’clock |

Distance traveled | 4km | 8km | 12km |

*Comment: As time increases many times, the distance traveled will also increase many times*

b) Problem: A car travels 90km in 2 hours. How many kilometers did the car travel in 4 hours – 0 meters?

Summary:

2 hours: 90km

4 hours: …km?

Method 1:

Solution:

In 1 hour the car can travel is:

90 : 2 = 45 (km)

In 4 hours the car can travel is:

45 x 4 = 180 (km)

Answer: 180km

This step is the “retract to units” step.

Method 2:

Solution

4 hours is 2 hours the number of times is:

4: 2 = 2 (times) (**)

In 4 hours the car can travel is:

90 x 2 = 180 (km)

Answer: 180km

### (**) This step is the “find the score” step.

Note: When doing the test, students can solve the problem in one of two ways

* Review and supplement on problem solving (continued)

20kg

5 bags

Number of kilograms of rice in each bag | 5kg | 10kg | |

Number of bags of rice | 20 bags | 10 bags |

Comment: When the number of kilograms of rice in each bag is multiplied, the number of bags of rice is reduced by that many times.

b) Problem: To complete the foundation of the house in 2 days, 12 people are required. How many people would it take to build the floor in 4 days? (Each person’s level of work is the same)

Summary:

2 days: 12 people

4 days: … people?

Way 1

Solution

To finish building the floor in 1 day, the number of people needed is:

12 x 2 = 24 (person)

To complete the foundation in 4 days, the number of people needed is:

24 : 4 = 6 (person)

Answer: 6 people

This step is the “withdraw to units” step.

Method 2:

Solution

4 days is 2 days the number of times is:

4: 2 = 2 (times) (**)

To complete the foundation in 4 days, the number of people needed is:

## 12 : 2 = 6 (person)

- Answer: 6 people
- (**) This step is the “find the score” step.

### Note: When doing the test, students can solve the math in one of the two ways above

Instructions for solving textbook exercises

Review and supplement on math problem solving

Lesson 1 of the textbook page 19:

Buy 5m of fabric for 80,000 VND. How much does it cost to buy 7m of that kind of fabric?

Solution

Summary:

5m : 80000 VND

7m: … dong?

To buy 1m of fabric, the total amount is:

**80 000 : 5 = 16 000 (VND)**

To buy 7m of fabric, the total amount is:

**16 000 × 7 = 112 000 (VND)**

Answer: 112,000 VND.

Lesson 2 Textbook page 19:

An average afforestation team can plant 1200 pine trees every 3 days. How many pine trees did the team plant in 12 days?

Solution

Summary

3 days: 1200 pine trees

12 days: … pine tree?

Solution

Method 1:

12 days is 3 times as many times as:

12 : 3 = 4 (times)

The number of pine trees that the team can plant in 12 days is:

1200 × 4 = 4800 (pine tree)

Method 2:

The number of pine trees that the team can plant in a day is:

**1200 : 3 = 400 (tree)**

In 12 days that team can plant the number of pine trees is:

400 × 12 = 4800 (pine tree)

Answer: 4800 pine trees.

**Lesson 3 Textbook page 19:**

The current population of a commune is 4000 people.

a) With an annual increase of 21 people for every 1000 people, calculate how many people will increase the population of that commune a year later.

b) If the annual increase is reduced to 15 people for every 1000 people, how many people will the population of that commune increase after a year?

Solution

a) Summary:

1000 people : increase 21 people

4000 people : increase … people ?

Solution

4000 people is 1000 times as many times as:

4000 : 1000 = 4 (times)

After one year, the population of that commune increases by:

21 × 4 = 84 (person)

Answer: 84 people.

b) Summary:

1000 people: an increase of 15 people

4000 people increase … people?

Solution:

4000 people is 1000 times as many times as:

**4000 : 1000 = 4 (times)**

After one year, the population of that commune increases by:

**15 × 4 = 60 (person)**

Answer: 60 people.

Lesson 1 Textbook page 19 (Practice):

Buy 12 notebooks for 24000 VND. How much does it cost to buy 30 such books?

Solution

The amount to buy 1 book is:

**24000 : 12 = 2000 (VND)**

The amount to buy all 30 books is:

**2000 × 30 = 60000 (VND)**

Answer: 60000 VND.

Lesson 2 Textbook page 19 (Practice)

Ha bought two dozen pencils for 30,000 VND. Ask Mai, if you want to buy 8 such pencils, how much do you have to pay the seller?

Solution

The number of pencils Ha bought is:

12 × 2 = 24 (piece)

The cost to buy 1 pencil is:

**30000 : 24 = 1250 (VND)**

The amount to buy 8 pencils is:

**1250 × 8 = 10000 (VND)**

Answer: 10000 VND.

Lesson 3 Textbook page 20 (Practice)

A school organizes for students to visit historical sites. The first phase requires 3 cars to carry 120 students. How many cars do you need to use in the second round to carry 160 students for sightseeing?

Solution

The number of students in each car is:

**120 : 3 = 40 (students)**

Number of cars to carry students for the second batch is:

**160 : 40 = 4 (car)**

Answer: 4 cars.

Lesson 4 Textbook page 20 (Practice):

A worker for 2 days is paid 72 000 VND. With such a salary, if he works for 5 days, how much will he be paid?

Solution

The salary for 1 day is:

- 72 000 : 2 = 36 000 (VND)
- The wages for 5 days are:

### 36 000 x 5 = 180 000 (VND)

Answer: 180 000 VND

Review and supplement on problem solving (continued)

Lesson 1 of the textbook page 21:

10 people to complete a job takes 7 days. Now, how many people would it take to finish the job in 5 days? (Each person’s level of work is the same)

Solution

To complete the work in 1 day, the number of people needed is:

10 x 7 = 70 (person)

To complete the work in 5 days, the number of people needed is:

70 : 5 = 14 (person)

Answer: 14 people.

Lesson 2 Textbook page 21:

A kitchen stocked rice enough to feed 120 people for 20 days, actually 150 people ate. How many days will that reserve of rice be enough to eat? (Everyone’s food level is the same)

Solution

A person eats all that rice in the number of days is:

20 × 120 = 2400(days)

150 people will eat all that rice in the number of days is:

2400 : 150 = 16 (days)

Answer: 16 days.

Lesson 3 Textbook page 21:

To suck water in a lake, 3 pumps must be used continuously for 4 hours. Because they wanted the work to be completed sooner, six such pumps were used. How many hours will it take to absorb all the water in the lake?

Solution

6 pumps 3 times the number of pumps is :

6: 3 = 2 (times)

6 pumps suck out all the lake water after the number of hours is:

4: 2 = 2 (hours)

Answer: 2 hours.

Lesson 1 Textbook page 21 (Practice):

A person buys 25 notebooks, priced at 3,000 VND each, and has just run out of money. With the same amount, if you buy a notebook for 1500 VND a book, how many books can that person buy?

Solution

The person’s amount is:

3000 x 25 = 75 000 (VND)

The number of notebooks of 1500 VND to buy is:

75 000 : 1500 = 50 (book)

Answer: 50 books.

Lesson 2 Textbook page 21 (Practice):

A family consists of 3 people (father, mother and one child). Average monthly income is 800,000 VND per person. If the family has one more child and the total income of the family does not change, how much will the average monthly income of each person decrease?

Solution

The family’s monthly income is:

800000 × 3 = 2400000 (VND)

If there is one more child, the average income of each person will be:

2400000 : (3 + 1) = 600000 (VND)

The average income of each person reduced by the amount is:

800000 − 600000 = 200000 (VND)

Answer: 200,000 VND.

Lesson 3 Textbook page 21 (Practice):

A team of 10 people in one day dug 35 m of ditch. If 20 people are added to dig together, how many meters of ditches can be dug in a day? (Each person’s mining level is the same)

Solution

After adding, the team has the following number of people:

10 + 20 = 30 (person)

30 people is 10 times as many people as:

30 : 10 = 3 (times)

In one day the team can dig the number of ditches is:

35 × 3 = 105 (m)

Answer: 105m

Lesson 4 Textbook page 21 (Practice):

A truck can only carry 300 bags of rice, each bag is 50 kg. If loaded on that truck with 75kg bags of rice, how much can the truck carry?

Solution

The number of kilograms of rice that the truck can carry is:

50 × 300 = 15000(kg)

If the truck is loaded with 75 kg bags of rice, the maximum number of bags of rice that can be loaded by the truck is

15000 : 75 = 200 (bag)

Lesson 1 Textbook page 22 (Common practice):

A class has 28 students, where the number of boys is equal to \(\frac{2}{5}\) the number of girls. How many girls and how many boys are there in that class?

Solution

Solving Math 5| To study well Math 5

According to the diagram, the total number of equal parts is:

2 + 5 = 7 (parts)

The number of boys in that class is:

28 : 7 × 2 = 8 (em)

The number of girls in that class is:

28 − 8 = 20 (em)

Answer: 8 boys; 20 girls

Find the perimeter of a rectangular piece of land whose length is 2 times its width and 15 meters more than its width.

Solution

Solve Maths 5| To study well in Math 5

According to the diagram, the equal part difference is:

2 – 1 = 1 (parts)

The width of the plot is:

15 : 1 x 1 = 15 (m)

The length of the plot is:

15 x 2 = 30 (m)

The perimeter of the plot is:

(30 + 15) x 2 = 90 (m)

Answer: 90 m.

Lesson 3 Textbook page 21 (Common practice):

A car uses 12 liters of gasoline every 100 km. If the car has traveled 50 km, how many liters of gasoline will it consume?

Solution

100km is 50km the number of times is:

100 : 50 = 2 (times)

The number of liters of gasoline consumed by a car when traveling 50 km is:

12 : 2 = 6 (liters)

Answer: 6 liters of gasoline.

Lesson 4 Textbook page 21 (Common practice):

As planned, a carpentry workshop must work in 30 days, each day can build 12 sets of tables and chairs to complete the plan. Due to technical improvement, the factory can build 18 sets of tables and chairs every day. How many days does the carpentry workshop take to complete the plan?

Solution

The number of tables and chairs that need to be closed is:

12 x 30 = 360 (set)

360: 18 = 20 (days)

Answer: 20 days

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Chapter 1: Review And Supplement Of Fractions. Solve Maths Related to Ratios. Area Unit Table

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