# Chuyên Đề toán tìm hai số khi biết tổng và hiệu của hai số đó

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## Math Topic finding two numbers when knowing the sum and difference of those two numbers

The problem of finding two numbers when knowing the sum and difference of those two numbers (Sum-Difference math) students have learned in Math 4 program. This is an important math form in elementary school Math program, appearing many in the math programs. exam. To help students better understand the method of solving math problems to find two numbers when knowing the sum and difference of those two numbers and many application exercises, Cmm.edu.vn has shared the following article. Follow us!

I. Knowledge NEED TO REMEMBER

a. Recipe:

Large number = (sum + difference): 2

Small number = (sum – difference): 2

Or:

Method 1: – Large number = (sum + difference): 2

– Small number = big number – difference (or sum – large number)

Method 2: – Small number = (sum – difference): 2

– Big number = small number + difference (or sum – small number)

b. For example:

Lesson 1: The sum of two numbers is 70. The difference of the two numbers is 10. Find the two numbers.

The first way: Solution:

Twice the small number is:

70 – 10 = 60

The small number is:

60 : 2 = 30

The big number is:

30 + 10 = 40

Lesson 2: Kim Dong Primary School has a total of 1286 students, knowing the number of male students is 48 more than the number of female students. Calculate the number of male and female students in the school?

Solution:

Diagram: The number of male students in the school is:

(1286 + 48) : 2 = 667 (student)

The number of female students in the school is:

1286 – 667 = 619 (student)

Answer: male: 667 students, female: 619 students

II. TYPES OF FINDING TWO NUMBERS WHEN KNOWING THE SUM AND DIFFERENCES OF THESE TWO NUMBERS

1. Form 1: Show both the sum and the difference

This form of math is quite easy, but you can just use the formula we shared above.

a. Example: A school library lends students 68 books of two types: Textbooks and Extra Information books. The number of textbooks is more than the number of books. Information 14 more books. How many books did the library lend to students of each type?

Hint: the problem gives a sum of 68 and a difference of 14 and know there are more textbooks than books More Info. So the number of textbooks is a large number; number of books More information is a small number. apply the formula:

Large number = (sum + difference): 2

Small number = (sum – difference): 2

Solution:

Number of textbooks in the library is : (68 + 14) : 2 = 41 (books)

Number of books Additional information of the library is: (68 – 14) : 2 = 27 (books)

Answer: 41 textbooks; Book of Information 27 more books

b. Exercise

Exercise 1. Find 2 numbers whose sum and difference are respectively:

a) 24 and 6;

b) 60 and 12;

c) 325 and 99.

Lesson 2. The age of sister and 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. A school library lends students 65 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 4. Two workshops can make 1200 products. The first workshop made 120 units less than the second. How many products can each factory make?

2. Form 2: Indicates the sum of the signals

This type of math is a bit complicated, forcing students to find the difference before they can apply the formula to solve it.

a. For example. Hung and Dung have a total of 45 marbles. If Hung has 5 more marbles, Hung has 14 more marbles than Dung. How many marbles did each of you initially have?

if Hung has 5 more marbles, then Hung is 14 more than Dung=> Initially, Hung has more marbles than Dung, the number of marbles is :14 -5 = 9 (balls) Initially Hung has the number of marbles :(45+9 ) : 2 = 27 (marbles)In the beginning Dung has the number of marbles :45 – 27 = 18 (marbles)

Answer: Hung 27 members; Dung 18 tablets

b. Exercise

Exercise 1. Find two numbers whose sum is 234. Know that if the first number is subtracted from the second number and then plus their difference, the result is 172.

Lesson 2. An and Binh have a total of 120 marbles. If An gives Binh 20 pills, Binh will have 16 more than An. How much marbles does each of them have?

Lesson 3. 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 4. Jade has all 48 marbles that are both green and red. Know that if 10 red marbles and two green marbles are drawn, the number of red marbles is equal to the number of blue marbles. How many marbles of each type are there?

Lesson 5. 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?

3. Form 3: Indicates the sign but the sum sign

This form of math is also quite complicated, forcing students to find the sum and then apply the formula to solve it.

a. For example. The rectangular garden has a perimeter of 48m, the length is 4m more than the width. What is the area of ​​the garden in square meters?

Hint: To find the length and width, we must find the half circumference (find the sum).

Solution:

Half perimeter of rectangular garden is: 48 : 2 = 24 (m)

The length of the garden is: (24 + 4 ) : 2 = 14 (m)

The width of the garden is: (24 – 4 ): 2 = 10 (m)

Answer: 14 m in length; 10m width

b. Exercise

Exercise 1. Find two numbers whose difference is 22. Know that if you take the large number plus the small number and add their difference, you get 116.

Exercise 2. Find two numbers whose difference is 132. Know that if you take the large number plus the small number and then subtract their difference, you get 548.

Lesson 3. Lan walks around the stadium for 15 minutes, walking 36 meters per minute. Knowing the length of the stadium is 24 m more than the width. Calculate the area of ​​the stadium.

Lesson 4. Hong has 16000 dong more than Hue. If Hong has 5000 more and Hue has 11000 more, then both of you will have 70000 VND in all. How much money did each of you have at the beginning?

Lesson 5. Hong has 16000 dong more than Hue. If Hong gives 5000 VND and Hue gives 11000 VND, then both of you will have 70000 VND in all. How much money did each of you have at the beginning?

Lesson 6. I’m 5 years older than you. Knowing that 5 years from now, the sum of their ages will be 25. What is the age of each of them today?

4. Form 4: sign both sum and difference

a. For example. A rectangular field has a perimeter of 120m. Calculate the area of ​​that field, knowing that if the width is increased by 5m and the length is decreased by 5m, the field becomes square.

Solution:

The half perimeter of the rectangle is:

120 : 2 = 60 (m)

If the width is increased by 5m and the length is decreased by 5m, the field becomes square, so its length is greater than its width:

5 + 5 = 10 (m)

The length of the rectangle is:

(60 + 10) : 2 = 35 (m)

The width of the rectangle is:

60 – 35 = 25 (m)

The area of ​​the rectangle is:

35 x 25 = 875 (m2)

b. Exercise.

Exercise 1. Find two numbers whose sum is the smallest 4-digit number and the difference is the largest 2-digit even number.

Exercise 2. 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.

Lesson 9. Find two numbers, knowing the sum of the two numbers is the largest two-digit number. The difference between two numbers is the smallest two-digit odd number.

Lesson 3. 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 4. A rectangular garden has a perimeter equal to the perimeter of a square field of side 80m. If the length of the garden is reduced by 30m and the width is increased by 10m, the garden will be square. Calculate the garden area.

III. EXERCISE FIND TWO NUMBERS WHEN KNOWING THE SUM AND DIFFERENCES OF THESE TWO NUMBERS

Lesson 1. The sum of the ages of father and son is 58 years. I am older than you 38 years old. How old is the father, how old is the son?

Lesson 2. A class has 28 students. The number of male students is 4 more than the number of female students. How many male students and how many female students are there in that class?

Lesson 3. A rectangle has the difference of two continuous sides of 24 cm and their sum is 92 cm. Calculate the area of ​​the given rectangle.

Lesson 4. Find two numbers where the sum of the two numbers is 42 and the difference of the two numbers is 10.

Lesson 5. Two classes 4A and 4B planted 600 trees. Class 4A planted 50 trees less than class 4B. Ask how much each class to plant trees?

Lesson 6. Hung and Dung have a total of 45 marbles. If Hung has 5 more marbles, Hung has 14 more marbles than Dung. How many marbles did each of you initially have?

Lesson 7. Class 4A has 32 students. There are 3 girls out of school today, so the number of boys is 5 more than the number of girls. How many girls and boys in class 4A?

Lesson 8. Hung and Dung have a total of 46 marbles. If Hung gives Dung 5 marbles, the number of marbles between the two of you is equal. How many marbles did each of you initially have?

Lesson 9. Two oil tanks have a total of 116 liters. If 6 liters are transferred from the first barrel to the second tank, the amount of oil in the two tanks is the same. Ask how many liters per barrel of oil?

Lesson 10. A rectangular garden has a perimeter of 48m, its length is 4m more than its width. What is the area of ​​the garden in square meters?

Lesson 11. Father is 30 years older than son. In 5 years, the sum of the ages of father and son will be 62 years. Calculate the present age of father and son.

Lesson 12. Father is 32 years older than son. In 4 years, the sum of the ages of father and son will be 64 years. Calculate the present age of father and son.

Lesson 13. Age and poetry contribute cakes to eat together, Age contribute 3 pieces, Tho contribute 5 pieces. Just then, Math came over. Tu and Tho invite Math to eat together. After eating, Math returned to 2 friends 8000 VND. Ask Age and Tho how much money each beneficiary gets?

Answer: 15000 VND; 9 000 dong.

Lesson 14. There are 210 tangerines and oranges in the basket. Mom sold 60 tangerines. At this time, in the basket, there are the remaining tangerines equal to the number of oranges. At the beginning, how many parts of the number of oranges were equal to the number of tangerines?

Answer: 104 balls and 96 balls

Lesson 15. Binh has 22 marbles, including red and blue marbles. The bottle gives you 3 red marbles and 2 blue marbles. An’s friend gave Binh another 7 red marbles. At this time, Binh has twice as many red marbles as blue marbles. How many red marbles and how many green marbles did Binh have at first?

Green Answer : 10 marbles ; red 12 marbles

Lesson 16. In a garden, people grow a total of 120 trees of 3 types: oranges, lemons and mangoes. The number of oranges is equal to the sum of lemons and mangoes, and the number of mangoes is equal to the sum of lemons and oranges. How many trees are there in each?

Lesson 17. Dung has 48 marbles including 3 types: blue marbles, red marbles and yellow marbles. The number of blue marbles is equal to the sum of the red and yellow marbles, and 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?

Address : Green 22 marbles ; Red marble 18; Gold 8 marbles

Lesson 18. Spring day 3 friends: Hue, Hang, Mai go to plant trees. Know that the total number of trees you can grow is 17 trees. The number of trees Hue and Hang can grow is much more than Mai’s 3 trees. Hue’s number of trees is equal to Hang’s number of trees. How many trees can each of you plant?

Lesson 19. The sum of two numbers is 2011. Find those two numbers knowing that there are 40 odd numbers between them.

Lesson 20. For a subtraction of two numbers, the sum of the subtracted number, the subtraction and the difference is 1998. The difference is 135. The difference is 135. Find the subtracted and subtracted numbers of that calculation?

Above, Cmm.edu.vn has introduced to students specializing in math to find two numbers when knowing the sum and difference of those two numbers: both methods of solving each type of math and exercises for application. Hopefully, sharing the same article, you better understand this very important elementary math knowledge. The forms of uniform motion math have also been introduced very specifically by us. guys don’t miss it!

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