Tỉ số phần trăm: Khái niệm, công thức & cách giải bài tập dễ hiểu nhất

Percentages are a part of mathematical knowledge that any student will learn, become familiar with, and solve exercises. However, to solve exercises requires students to clearly understand formula knowledge and calculation methods. Therefore, in the following article, Nguyễn Tất Thành will analyze in the most detail.

What is the percentage?

The ratio of two numbers is known as a fraction, which is the quotient of dividing a by b (b is not 0). Symbol a/b or a : b.

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A percentage is the ratio of two numbers, and here, we will have to reduce the denominators of those ratios to 100. Symbol: %.

For example, 50% is equivalent to 50/100, or 0.5. Reading is fifty percent.

In addition, percentages are often used to express the relative magnitude of one quantity relative to another. For example: 1/100=1%, ​​25/100=25%

To be able to express the percentage of a number a, where a is a decimal number or a natural number, we have a : 100 or a/100 = a%

For example: 15/100 = 15%

Meaning of percentage

In mathematics, percentages are essentially fractions with a denominator of 100. They are used to express the relative magnitude of one quantity compared to another. Specifically, the first quantity will represent the corresponding part or change compared to the second quantity.

For example: An amount of 50,000 VND after interest increases by 3,800 VND, so the amount increases by 3,800 / 50,000 = 0.076 times the original amount. If expressed as a percentage, we say the amount of 50,000 VND has increased interest by 7.6%.

Detailed percentage calculation formulas

To be able to conquer the exercises when learning percentage math, you need to firmly grasp how to calculate percentages in each of the following cases:

Formula to calculate percentage between 2 numbers

To be able to calculate the percentage ratio of A and B, we divide A by dividing B, multiplying by 100 and then adding the % symbol to the result.

Specifically:

A/B x 100%

In essence, the value of multiplying by 100% does not change compared to dividing A and B. Because, when multiplying by 100%, it means x 100/100, which is x 1. Therefore, if you add the % symbol, you will Readers will silently understand that the real value of the A/B ratio must be divided by 100.

For example: A bouquet has 25 flowers, including 6 yellow flowers. Find the percentage of yellow flowers compared to the total number of flowers?

Solution:

Consider number A as 25 flowers in total, number B as 6 yellow flowers. The percentage of yellow flowers in the bouquet is:

(6 : 25) x 100 = 24%

Answer: 24% yellow flowers

Formula to calculate the percentage of a number

To find the percentage of a number, we will divide that number by 100, then multiply by %, or multiply that number by % and then divide by 100.

Specifically:

A far% = A : 100 far

For example: A roll of fabric is 300m long, the tailor can cut 30% of the length of that roll of fabric. How much of the remaining roll of fabric does the tailor need to cut?

Solution:

Cut fabric roll: 30% x 300 = 90 meters

The remaining fabric that needs to be cut is: 300 – 90 = 210 meters

Answer: 210 meters of fabric.

Formula to find a number when knowing the percentage of that number

If the problem shows a percentage of a number and we are looking for the value of that number, we will divide that number by the percentage and then multiply by 100, or we can multiply that value by 100 and divide by the given percentage. know.

Specifically, want to find a number knowing b% of that number is B:

B : b% = B : bx 100

This formula will be the opposite of the formula to find the percentage of a given number.

For example: A book has been read for 120 pages, accounting for 15% of the book’s pages. How many pages does that book have?

Solution:

Because 120 pages account for 15% of the book’s pages, it follows that 1% of the book’s pages are:

120 : 15% = 8 pages

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So the number of pages in the book is: 8 x 100 = 800 pages

Answer: 800 pages of book

Common types of percentage calculation exercises and solution methods

In the elementary math program, children will be introduced to percentage knowledge. Along with that, students will learn and have to conquer the following types of exercises:

Type 1: Problems about addition, subtraction, multiplication, and division of percentages

To solve exercises about calculating percentages, we apply the following formulas:

Addition formula: a% + b% = (a + b)%.

For example: 5% + 12% = (5 + 12)% = 18%

Subtraction math formula a% – b% = (a – b)%.

For example: 42% – 8% = (42 – 8)% = 34%

Multiplication formula a% × b = (a × b)%.

For example: 5% × 7 = (5 × 7)% = 35%

Math division formula a% : b = (a : b)%

For example: 27% : 9 = (27 : 9) = 3%

Form 2: Find the percentage ratio of two numbers

Solution method: With this type of exercise, you will only apply the formula to find the percentage of both numbers given above, then follow the instructions and give the correct answer.

For example: A store plans to sell 12 tons of rice this month, but in reality the store sells 15 tons of rice. Ask:

a. How much of the plan has the store implemented?

b. How many percent has the store exceeded plan?

Solution instructions:

a. The store’s performance compared to the plan is: (15 : 12) x 100 = 125% (plan)

b. The store has exceeded the plan: 125% – 100% = 25% (plan)

Answer:

a. 125% of plan

b. 25% of the plan

Form 3: Find percent of a number

Solution method: You will also apply the formula to divide the number by 100 and multiply it by %, or take the given number and multiply it by % then divide by 100 to be able to calculate the % value of a corresponding number. Exactly.

For example: Class 5A has 30 students, of which 60% are female students. Ask how many female students there are.

Solution instructions:

The number of students in class 5A is: 30 : 100 x 60 = 18 (students)

Answer: 18 (female student)

Form 4: Find a number when you know the percentage value of that number

Solution method: To calculate the value of a number when we know the % of that number, we divide that value by the % and then multiply by 100, or we can take the given value, multiply by 100 and divide by the % already know.

For example: A class has 25% good students, 55% good students and the remaining average students. Calculate the number of students in that class if the average number of students is 5?

Solution instructions:

If we consider the total number of students in the class as 100%, the average number of students compared to the number of students in the class is:

100% – (25% + 55%) = 20%

The number of students in the class is:

5 : 20 x 100 = 25 (students)

Answer: 25 students

Type 5: Problems about calculating interest and capital

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Solution method: To calculate the percentage of profit and capital, we divide the percentage of the selling price by the percentage of the purchase price.

For example: A store sets the purchase price at 75% of the selling price. Ask what percentage of the purchase price the store sets the selling price for?

Solution instructions

Considering the selling price is 100%, the buying price is 75%.

So the selling price compared to the buying price as a percentage is: 100 : 75 = 133.33%

Answer: 133.33% of purchase price

Form 6: The problem is brought to a familiar mathematical form

Solution method: With this type of exercise, students will reduce the math format to familiar forms such as sum – billion, difference – billion,… to find the correct answer more quickly.

For example: The sum of two numbers is 25% and the quotient of those two numbers is also 25%. Find those two numbers.

Solution instructions:

25% = 0.25

The first number is: 0.25 : (1+4) = 0.05

The second number is: 0.25 – 0.05 = 0.2

Answer: 0.05 and 0.2

Exercises to calculate percentages for students to practice

After firmly grasping the theory of percentage knowledge, students will surely feel more secure in conquering related exercises. So, below Nguyễn Tất Thành will summarize some exercises and questions for you to practice together.

Question 1: A class has 28 students, including 7 boys. Find the percentage of male students compared to the class size?

Question 2: In the chicken coop there are 12 hens and 28 roosters. Find the ratio of the number of hens to the number of chickens in the garden?

Question 3: The area of ​​a flower garden is 100m2, of which 35m2 is planted with lilies. Find the ratio of the area planted with lilies and the area of ​​the flower garden.

Question 4: The first faucet every hour flows into 1/6 of the tank’s volume, the second faucet every hour flows into 1/3 of the tank’s volume. What percentage of the tank’s volume will both taps flow into the tank in one hour?

Question 5: The car has traveled 40% of the length of the 250 km road. Calculate the distance traveled by the car.

Question 6: The number of excellent students in an elementary school is 64, accounting for 12.8% of the entire school’s students. How many students does that school have?

Question 7: A person spends 42,000 VND in capital to buy vegetables. After selling all the vegetables, that person earned 52,500 VND.

a.The money from selling vegetables is equal to what percentage of the capital?

b.What percentage of profit does that person earn?

Question 8: If a product’s price has been reduced by 20%, if you want to sell that product at its original price, how much more percentage must you increase the price?

Question 9: The teacher divides the apples with the students. If each child has 9 balls, there are 9 balls missing. If each child is divided into 10 apples, 25% of the original number of apples will be missing. Calculate the number of apples she divided and the number of students who received apples.

Question 10: A person sells eggs: in the morning he sells 50% of the eggs, in the afternoon he sells the remaining 20%. Then that person sold 40 more fruits. At night, that person found that the number of eggs brought back was 120% of the number of eggs taken away. How many eggs did he bring?

Question 11: The amount of salt contained in sea water is 5%. How many kg of plain water must be added to 200kg of seawater to get a solution containing 2% salt?

Question 12: In the school, 68% of students know Russian, 5% know both English and Russian. The rest only know English. What percentage of students in the school know English?

Question 13: On March 26, a souvenir shop sells 10% off compared to normal days. However, they still profit 8% compared to the cost price. Ask what percentage of profit they make on a normal day compared to the cost price?

Question 14: A fruit store orders 4.5 tons of oranges at a price of 18,000 VND per kilogram. Shipping cost is 1,600,000 VND. Suppose 10% of the oranges are damaged during shipping and all the oranges are sold. Calculate how much each kilogram of oranges needs to be sold to earn a profit of 8%?

Question 15: Dad bought 2 pairs of shoes for Hung, but they were both too small, so Mom had to sell them. Each pair of shoes sells for 300,000 VND. One pair sells 20% more than the purchase price, the other pair sells 20% less than the purchase price. Ask Tien’s mother how much profit or loss she made when she sold it?

Apply the percentage calculation formula into practice

The percentage formula is a simple mathematical formula but can be widely applied in practice. Specifically:

• In the field of economics and finance, percentages are used to calculate interest rates, taxes, revenue, costs, profits,… For example: Bank interest is calculated as a percentage of the deposit amount.
• In the field of education, percentages are used to calculate test scores, average scores, student classification,… For example: A student’s test score is calculated by the total number of points achieved divided by the total maximum number of points.
• In the medical field, percentages are used to calculate disease incidence, mortality rate,… For example: Disease incidence is calculated as the number of people infected with the disease divided by the total number of people in a community.
• In the field of science, percentages are used to calculate the content of a substance in a mixture,… For example: The water content in an orange is calculated as the weight of water divided by the overall weight of the orange.

Conclude

Above is information shared about knowledge of percentages, one of the basic forms of mathematics, as well as very high practical applicability. Therefore, parents can master this knowledge to support their work, as well as help guide their children to learn and conquer this type of exercise better.

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