# Tìm hai số khi biết tổng và tỉ số của hai số đó: Lý Thuyết & Bài Tập

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## Find two numbers when the sum and ratio of the two numbers are known: Theory & Exercise

Math form of finding two numbers when knowing the sum and ratio of those two numbers (Total – Billing problem) is a good form of problem solving, students learn in Math 4 and Math 5 programs. This is a part of knowledge and knowledge. important appears in most of the exam questions. To better understand how to solve basic and incremental problems, please share the following article of Cmm.edu.vnboos.com!

I. GENERAL FORMULA

The steps to solve the problem of finding two numbers when the sum and ratio of those two numbers are known (or the Sum – Ratio problem) generally go through the following steps:

Step 1: Find the sum of two numbers (if the sum is hidden)

Step 2: Find the ratio (if the ratio is unknown)

Step 3. Draw a diagram according to the given data.

Step 4. Find the total number of equal parts

Step 5. Find small and large numbers (You can find big numbers first or search later and vice versa

Small number = (Sum: equal parts) x number of parts of small number (Or Sum – large number)

Large number = (Sum: equal parts) x number of parts of large number (Or sum – small number)

Step 6. Conclusion of the answer

(Students can take an extra step of retrying to verify their results.)

Example 1: Lan and Mai have 25 notebooks. Minh’s notebooks are 2/3 of Khoi’s books. How many notebooks does each person has?

Prize:

Line diagram

Number of Lan’s notebooks: |—–|—––|

Number of Mai’s notebooks: |—–|—–|—–|

The total number of equal parts is: 2 + 3 = 5 (parts)

Lan’s notebooks are: 25 : 5 x 2 = 10 (notebooks)

Mai’s notebooks are: 25 : 5 x 3 = 15 (notebooks)

Mai: 15 notebooks

Example 2: Lan and Mai have 25 notebooks. Minh’s notebooks are 2/3 of Khoi’s books. How many notebooks does each person has?

Prize

Line diagram

Number of Lan’s notebooks: |—–|—––|

Number of Mai’s notebooks: |—–|—–|—–|

The total number of equal parts is: 2 + 3 = 5 (parts)

Lan’s notebooks are: 25 : 5 x 2 = 10 (notebooks)

Mai’s notebooks are: 25 : 5 x 3 = 15 (notebooks)

Mai: 15 notebooks

II. SPECIAL TOTAL – BILLION FORMS

The multi-problem problem does not give complete data about sums and ratios, but can give the following data:

• Missing (hidden) total (Indicates score, does not give total)
• Missing (hidden) billion (Indicate total, do not give score)
• For the data to add, subtract numbers, create a total (billion) to find the original number.

For problems with similar data, it is necessary to make an extra step back to the basic problem.

1. Total hidden math

This is a form of math that lacks (hidden) the sum (indicates the ratio, not the sum of the two numbers). To solve the problem, we perform the finding of the sum of two numbers and then solve the problem in the form of sum and ratio math.

A rectangle has a perimeter of 460 cm. Calculate the width and length of that rectangle knowing that the length is 4 times the width.

Solution steps:

Step 1: Find the sum of two numbers

The problem says that the perimeter of the rectangle is 460 cm. However, to find the length and width of the rectangle, we have to find the half circumference (divide the circumference by 2).

Step 2: Find the ratio: The length is 4 times the width, that is, for the ratio ¼, ie the width (small number) is 1 part and the length (large number) is 4 equal parts.

Step 3: Draw the diagram Step 4: Find the total number of equal parts:

Looking at the diagram, we see that the width is 1 part, the length is 4 parts and the total length + width (total equal parts) = 5 parts.

Step 5: Find the small number value (width), large number value (length)

Step 6: Answer and try again

Solution:

Half perimeter of rectangle is: 460 : 2 = 230 (cm)

Looking at the diagram we see that the total number of equal parts is: 5 + 1 = 5

The length of the rectangle is: 230 : 5 x 4 = 184 (cm)

The length of the rectangle is: 230 : 5 x 1 = 46 (cm)

Answer: length: 180cm and width: 46cm

Retry:

We see 46/184 = 1/4

Perimeter of the rectangle is: (184 + 46) x 2 = 460 (cm) satisfying the proposition.

2. Mathematical form

This is the missing (hidden) form of math (indicates the sum of two numbers, not the ratio). To solve the problem, we need to find the ratio of two numbers and then solve the problem in the form of sum and ratio math.

Example: The sum of two numbers is 72. Find those two numbers, knowing that if the large number is reduced by 5 times, the smaller number will be obtained.

Comment

– Problem of finding two numbers when the sum and ratio of the two numbers are known.

– The card event is in the form of a hidden score.

Detailed solution

Larger number is 5 times smaller than smaller number => Small number = 1/5 of the big number

Step 2. Draw the diagram

Small number: |—–|

Big numbers: |—–|—–|—–|—–|—–|

Step 3. The number of equal parts is: 1 + 5 = 6

Step 4. Number of babies: 72:6 = 12

Large numbers: 72 : 6 x 5 = 60

Step 5. Answer: Number of children: 12

Large number: 60

3. Math form that hides both sum and ratio

This is a form of math that lacks (hidden) both sum and ratio data. To solve the problem we perform the finding of the sum and ratio of two numbers and then solve the problem in the form of sum and ratio math.

Example Find two numbers, knowing the average of two numbers is 120 and the first number is equal to The second number.

Solution:

+ Step 1: Find the sum and ratio of two numbers

+ Step 2: Find the first and second numbers according to the sum and ratio problem.

Step 3: Conclusion of the problem.

Assignment

The sum of two numbers is:

120 x 2 = 240

The ratio between the first number and the second number is: Diagram: The total number of equal parts is:

3 + 7 = 10 (parts)

The first number is:

240 : 10 x 3 = 72

The second number is:

240 – 72 = 168

Second number: 168

4. General form of math

Example: In a box, there are 48 marbles of 3 types: blue marbles, red marbles, yellow marbles. Given that the number of blue marbles is equal to the sum of the red and yellow marbles, the number of blue marbles plus the number of red marbles is 5 times the number of yellow marbles. How many marbles of each type?

Prize:

We have:

Number of blue marbles + red marbles + yellow marbles = 48 balls

Blue marbles = Red marbles + yellow marbles = 48 or blue marbles = 24 balls

Number of red marbles + yellow marbles = 24 balls

Red marbles + blue marbles = red marbles + yellow marbles + red marbles = 5 yellow marbles

So 2 red balls = 4 yellow balls

Red marbles = 2 yellow balls

Red marble + yellow marble = 24

So 3 golden balls = 24 or yellow balls = 8 balls

So red marbles are 24 – 8 = 16 balls

Answer: Blue marble: 24, red marble: 16, yellow marble: 8

III. APPLICATION EXERCISES

1. Basic math of total billions

Lesson 1: Harvesting from two fields is 10 tons and 7 quintals of rice. Harvest in the first field is much more than in the second field 11 quintals of rice. How many kilograms of rice can be harvested in each field?

Lesson 2: Two tanks hold all 750 liters of water. The small container holds less than the large 112 liters of water. How many liters of water can each container hold?

Exercise 3: A rectangle has a difference of width and length of 16 cm and their sum is 100 cm. Calculate the area of ​​the given rectangle?

Lesson 4: Find two numbers where the sum of the two numbers is 58 and the difference of the two numbers is 10?

Lesson 5: Two classes 4A and 4B planted 620 trees. Class 4A planted 70 trees less than class 4B. Ask how much each class to plant trees?

Lesson 6: A class has 48 students. The number of male students is 10 more than the number of female students. How many male students and how many female students are there in that class?

Lesson 7: A school library lends students 125 books of two types: Textbooks and Extra Information books. The number of textbooks is more than the number of books. Information 17 more books. How many books did the library lend to students of each type?

Lesson 8: Two workshops can make 1460 products. The first workshop made 210 pieces less than the second. How many products can each factory make?

2. Total hidden math

Lesson 1: The first number is 115 more than the second number. Do you know that if you take the first number and add the second number, then add their sum to 2246?

Lesson 2: A subtraction has the sum of the subtracted number, the subtracted number, and the difference being 1920. The difference is 688 units larger than the minus number. Find that subtraction?

Lesson 3: All students in class 3 will get 12 rows. The number of girls is 4 less than the number of boys. How many boys and girls are there in that class?

Lesson 4: The sum of two numbers is the largest 3 digit number that is divisible by 5. If we add 35 units to the small number, we get the big number. Find each number ?

Lesson 5: A rectangular garden has a perimeter of 54m, and its length is 5m more than its width. What is the area of ​​the garden in square meters?

Lesson 6: A subtraction has the sum of the subtracted number, the subtracted number, and the difference being 8622. The difference is 790 units greater than the minus number. Find that subtraction?

3. Mathematical form

Exercise 1: Find two even numbers whose sum is 200 and between them there are 4 odd numbers?

Exercise 2: Find two natural numbers whose sum is 837, knowing that there are all 4 even numbers between them?

Lesson 3: Today the father’s age is 7 times the son’s age. After 10 years, father will be 3 times as old as son. Calculate the age of each person today.

Lesson 4: The sum of present age of father and son is 50 years old. Five years later, the father’s age will be 3 times the son’s age. Calculate the age of each person today?

Lesson 5: The sum of 2 numbers is equal to 385. One of the two numbers ends in 0, if we delete that digit, we get 2 equal numbers. Find two of them.

4. Math form that hides both sum and ratio

Exercise 1: Find two numbers whose sum is the largest 4-digit number and the difference is the smallest 3-digit odd number?

Exercise 2: Find two numbers whose sum is the smallest 4-digit number and the difference is the largest 2-digit even number?

Exercise 3: Find two numbers whose difference is the smallest 2-digit number that is divisible by 3 and whose sum is the largest 2-digit number that is divisible by 2?

Exercise 4: Find two numbers, knowing the sum of two numbers is the largest two-digit number. Difference between two numbers is the smallest two-digit odd number?

Lesson 5: Find two numbers whose difference is the largest one-digit number and the sum of the two numbers is the largest three-digit number?

Lesson 6: Two odd numbers whose sum is the smallest 4-digit number and in between those two odd numbers there are 4 odd numbers. Find two of them ?

5. General math form

Lesson 1: Grandpa is 56 years older than you, knowing that in 3 years, your grandson’s total age will be 80 years old. How old are you today? How old are you?

Lesson 2: Your age and younger brother add up to 36 years old. I am 8 years younger than my sister. How old are you, how old are you?

Lesson 3: Father is 28 years older than son; 3 years from now, the age of both father and son will turn 50. Calculate the present age of each person?

Lesson 4: Two barrels of oil have a total of 82 liters of oil. If 7 liters of oil are poured from the first barrel into the second, the two tanks contain the same amount of oil. How many liters of oil does each tank hold?

Lesson 5: Two rice warehouses have 155 tons. If adding 8 tons to the first warehouse and 17 tons to the second warehouse, the number of rice in each warehouse is the same. How many tons of rice were in each warehouse at first?

Lesson 6: Two weavers weave 270 m of fabric. If the first person weaves 12m more and the second weaves 8m more, the first person will weave 10m more than the second. How many meters of fabric did each person weave?

Lesson 7: The grandson and grandson today have a total age of 68, knowing that 5 years ago, their grandson was 52 years younger than him. Calculated the age of each person ?

Lesson 8: I am 5 years older than you. Given that 5 years from now, the sum of their ages will be 25 years. Calculate the age of each person today?

Lesson 9: The ages of father and son add up to 58 years. I am older than you 38 years old. How old is the father, how old is the son?

Above, Xicxabooks.com has distributed to children the method of solving the problem of finding two numbers when knowing the sum and the ratio (also known as the Total – Bill problem) in basic math and special math forms. Hopefully, by sharing the same article, you have mastered the math of total billions and billions of billions. Hope to see you again in the next posts!

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