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## Math types to find percentages: formulas and exercises

Math types to find percentages of students have been studied in Math 5 program. Each form has a specific solution. However, to distinguish each form of math to find percentages to apply to the solution, not all students are fluent. In today’s article, Trinh Hoai Duc High School will provide specific instructions for you to easily distinguish! Just share!

1. METHODS FOR FINDING THE PERcentage

FORM 1: FIND THE PERFORMANCE OF TWO NUMBERS

 Formula: To find the ratio of number A to number B, divide A by number B and multiply by 100.

Example 1: The amount of water in fresh seeds is 16%. People take 200 kg of fresh seeds to dry, the amount of seeds is reduced by 20 kg. Calculate the percentage of water in the dried seeds?

Suggest: First we need to find the amount of water in the original fresh seeds and then find the remaining water in the dried seeds to finally find the percentage of water in the dried seeds.

Prize:

The initial amount of water in the fresh seed is:
200 x 16% = 32 (kg)
After drying 200 kg of fresh seeds, the amount of seeds is 20 kg lighter, so the remaining amount in the dried seeds is:
32 – 20 = 12 (kg)
The remaining amount of dried seeds is:
200 – 20 = 180 (kg)
The percentage of water in the dried seeds is:
12 : 180 = 6.7%

Example 2:

A person spends 42,000 VND of capital to buy vegetables. After selling all the vegetables, that person earns VND 52,500.
a.What is the percentage of the capital from selling vegetables?
b. How much profit does that person earn?

Prize:

a) Money from selling vegetables compared to capital is:

52500 : 42000 = 1.25 = 1.25 x100% = 125%.

b) The profit is:

125 – 100 = 25(%)

Example 3:

At the end of the school year, a store reduces the price of notebooks by 20%. With the same amount of money, how much more will a student buy more books?

Suggest: See the previous price of a book is 100% to calculate when the price is reduced, from which to calculate the number of books to buy more.

Because it has been sold at a 20% discount, to buy a notebook that previously needed to pay 100% of the amount, now must pay:

100% – 20% = 80% (amount)

The remaining 20% ​​can be purchased:

20 : 80 = 25% (number of notebooks)

Example 4:

In the garden there are 12 orange trees and 28 lemon trees. Find the ratio of the number of orange trees to the number of trees in the garden?

Suggest: We have to find the ratio of the number of orange trees to the number of trees in the garden. Thus, we must first find the number of trees in the garden and then find the percentage as required.

Prize: The number of trees in the garden is:

12 + 28 = 40 (tree)

The ratio of the number of orange trees to the number of trees in the garden is:

12 : 40 = 0, 3 = 0, 3 x 100 % = 30%

FORM 2: FIND THE PERFECT VALUE OF A NUMBER

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

Example 1: A bicycle costs 400,000 VND, now 15% off. What is the price of the bike now?

Suggest: This problem has two solutions: find the discount amount and deduce the new selling price, or find the percentage of the new price to the original price and find the new selling price.

Prize:

Reduced selling price:

15% x 400 000 = 60 000 (VND)

Bike prices are now:

400 000 – 60 000 = 340 000 (VND)

Example 2: A construction contractor accepted to build a house at a cost of 360 000 000 VND but the owner asked for a reduction of 2.5%, the contractor agreed. Calculate the amount the contractor received to build the house?

Suggest: This problem also has 2 solutions, here we show only one way, there is another way you practice more!

Solution:

If we consider the initial amount of money the contractor received to build the house is 100%, the amount to build the house after being reduced from the original amount is:

100% – 2.5% = 97.5%

The amount the contractor receives to build the house is:

360 000 000 x 97.5 : 100 = 351 000 000 (VND)

Example 3. A library has 6,000 books. The number of library books increases by 20% every year (compared to the previous year). How many books are there in the library after two years?

Suggest: 20% is the percentage increase in the number of books each year compared to the number of books the previous year. Therefore, to know the increase in the number of books in the second year, we must know the number of books available after the first year.

Prize:

After the first year, the number of books increased is:

20% x 6 000 = 1 200 (book)

After the first year, the number of books in the library is:

6 000 + 1 200 = 7 200 (book)

After the second year the number of books increased is:

20% x 7 200 = 1 440 (book)

After two years, the number of books in the library is:

7 200 + 1 440 = 8 640 (book)

FORM 3: FIND A NUMBER WHEN KNOWING THE PERMIT OF THE NUMBER

 To find a number when we know the percentage value of that number, we divide that value by the percentage and then multiply by 100 or take that value and multiply by 100 and then divide by the percentage.

Example 1. A tourist car on the first day traveled 28%, on the second day traveled 32% of the entire intended distance, on the third day traveled the remaining 240km. How far did the car travel in three days?

Suggest: 240 km is the distance left after traveling 2 days so we have to find the percentage of the distance traveled on the third day to the total distance traveled. From there will find out the distance traveled by the car in 3 days.

Prize:

After 2 days, the car has covered the percentage of distance compared to the intended distance:

28% + 32% = 60%

So on the third day the car will travel the distance is:

100% – 60% = 40%

1% of the intended distance traveled is:

240 : 40% = 6 (km)

The distance traveled in 3 days is:

6 x 100 = 600 (km).

Example 2. The number of excellent students in a primary school is 64, accounting for 12.8% of the total number of students in the whole school. How many students does that school have?

Suggest: 64 is 12.8% we have to find the number of students in the whole school ie find 100%? It is possible to follow the method of withdrawing to units (calculate 1%) and from there get 100% (multiply 100).

Prize:

1% of the school’s students are:

64 : 12.8% = 5 (em)

The total number of students in the school is:

5 x 100 = 500 (em)

Example 3.

Calculating the age of two brothers know that 62.5% of his age is 75% more than her age, and he is 2 years old and 50% of his age is 37.5% more than his younger brother is 7 years old.

Suggest: According to the question, 50% of my age is 37.5% older than you are 7 years old or (50% x 2) my older brother (37.5% x 2) is 14 years old.

Solution:

Because 50% of my age is more than 37.5 years old and I am 7 years old, 100% of my age is more than 75% of my age, I am 14 years old.

100% more than 62.5% is:

100% – 62.5% = 37.5%

14 years old over 2 years old is:

14 – 2 = 12 (age)

12 : 37.5 x 100 = 32 (age).

75% of my age is:

32 – 14 = 18 (age).

My age is:

18 : 75 x 100 = 24 (age)

I’m 32 years old

FORM 4: PROBLEM ON PROFIT AND CAPITAL CALCULATION

Example 1: A bicycle costs 1 700 000 VND, now 15% off. What is the price of the bike now?

Solution:

See the price of the bike at first is 100%, after reduced to only:

100% – 15% = 85%

The current price of the bike is:

1 700 000 x 85 : 100 = 1 445 000 (VND)

FORM 5: PROBLEM BRINGING TO SUMMARY – TRIAL TYPES

Example 1: The sum of two numbers is 25% the quotient of the two numbers is also 25%. Find two of them.

Suggest: Convert 25% to a fraction, the problem is returned to the form of finding two numbers when the sum and the ratio are known.

Solution:

Change 25% = 0.25

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

The second number is: 0.25 – 0.05 = 0.2

Example 2: Find two numbers, knowing that 25% of the first number is 1/3 of the second number and the difference of the two numbers is 15/37.

Solution:

Change 25% = 1/4

According to the problem, 1/4 of the first number is 1/3 of the second number:

The first number is: 15/37 : (4 – 3) x 4 = 60/37

The second number is: 60/37 – 15/37 = 45/37

FORM 6: EXTENSIVE PROBLEMS RELATED TO OTHER FORMS OF MATH

Example 1: A car intends to travel from A to B in 2 hours. But due to bad weather, the car had to reduce its speed by 10% compared to the expected speed and the number of hours to go was increased to 30 minutes to reach C, exceeding B by 26 km. Calculate the distance from A to B.

Suggest: The distance from A to B is unchanged. If the speed is reduced, of course the travel time will have to increase. We will take the estimated velocity and time as the standard (100%) to calculate the real speed and time.

Prize:

The actual velocity relative to the expected velocity is:

100% – 10% = 90%

Real time travel:

2 hours + 30 minutes = 2 hours 30 minutes = 2.5 hours = 140% of the scheduled time

Actual distance traveled relative to the distance from A to B:

90% x 140% = 126%

The distance from B to C that the car travels more than the distance from A to B:

126% – 100% = 26%

So the distance from A to B is:

26 : 26% x 100 = 100 (km).

Example 2. The orange yield of Uncle An’s garden is 26% higher than that of Uncle Cuc’s, although the area of ​​Uncle An’s garden is only 5% higher than that of Uncle Cuc’s. What percentage is the yield of Uncle An’s garden more than that of Uncle Cuc’s garden?

Suggest: We take the area and yield of Uncle Cuc’s garden as the standard (100%) to calculate the area and yield of Uncle An’s garden.

Prize:

Considering the yield of Uncle Cuc’s garden is 100%, then the output of Uncle An’s garden is:

100% + 26% = 126%

Considering the area of ​​Uncle Cuc’s orange garden is 100%, the area of ​​Uncle An’s orange garden is:

100% + 5% = 105%

The yield of Uncle An’s orange garden is:

126 : 105 = 120%

The yield of Uncle An’s orange garden is more than that of Uncle Cuc’s orange garden.

120% – 100% = 20%

2. ACTIVITIES ON PER % NUMBERS

Lesson 1: The amount of water in fresh grass is 55%, in dry grass it is 10%. How many kg of hay will we get when drying 100kg of fresh grass?

Lesson 2: A grocery store, after selling out of goods, collected an amount of

24 200 000 VND. Calculating a profit of 21% compared to the capital invested. How much capital did the store spend to purchase?

lesson 3: Gasoline price from 20 000 VND to 21 700 VND per liter. By what percentage increase in the price of gasoline?

Lesson 4: The amount of salt contained in sea water is 5%. How many kilograms of water must be added to 200kg of seawater to get a solution containing 2% salt?

Lesson 5: 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?

Lesson 6: On the occasion of March 26, a souvenir shop sells 10% off compared to weekdays. However, they still make a profit of 8% compared to the cost price. Ask them what percentage of their profit on weekdays compared to the cost price?

Lesson 7: A fruit shop ordered 4.5 tons of oranges for 18,000 VND per kilogram. Shipping fee is 1 600 000 VND. Assume 10% of the oranges are damaged in transit and all oranges are sold. Calculate how much each kg of oranges need to be sold to earn 8% profit?

Lesson 8: Dad bought 2 pairs of shoes for Tien but they were both small, so mom had to sell them 2 pairs of shoes. Each pair of shoes is sold for 300,000 VND. In which one pair sells for 20% more than the purchase price, the other pair sells for 20% less than the purchase price. Ask Tien’s mother how much profit or loss can she sell?

Lesson 9: A retailer buys a number of boxes of powdered milk for 24 000 VND/box, when paying, the owner has reduced to the shopper an amount equal to 12.5% ​​of the price of a box. After that, he resells the milk for a profit equal to 33% of the cost price after reducing 20% ​​of the listed price. How much is the listed price on a carton of milk?

Lesson 10: A liquid A is evaporated according to the law: Every 4 hours and 10 minutes, 50% of its capacity is lost. If 256 liters of liquid A are evaporated, how many liters will remain in 1 day and 1 hour of liquid A?

So you have just reviewed the knowledge of the mathematical forms of finding percentages which are extremely useful. Hopefully, after sharing the same article, you have a better grasp of this extremely important part of math knowledge. Share more divisibility sign of a natural number at this link too! Love !!!

Posted by: Trinh Hoai Duc High School

Category: General Knowledge

Source: THOMO
Categories: Giáo dục