Interest. Converting Fractions to Percentages

Percentage is one of the interesting and often used tools in practice. Percentages are partially or fully used in any science, in any job, and even in everyday communication. A person who is good at percentages gives the impression of being smart and educated. In this lesson we will learn what a percentage is and what actions you can perform with it.

Lesson content

What is percentage?

Fractions are most common in everyday life. They even got their own names: half, third and quarter, respectively.

But there is another fraction that also occurs frequently. This is a fraction (one hundredth). This fraction is called percent. What does the fraction one hundredth mean? This fraction means that something is divided into one hundred parts and one part is taken from there. So a percentage is one hundredth of something.

A percentage is one hundredth of something

For example, one meter is 1 cm. One meter is divided into one hundred parts, and one part is taken (remember that 1 meter is 100 cm). And one part of these hundred parts is 1 cm. This means that one percent of one meter is 1 cm.

One meter is already 2 centimeters. This time, one meter was divided into one hundred parts and not one, but two parts were taken from there. And two parts out of a hundred are two centimeters. So two percent of one meter is 2 centimeters.

Another example: one ruble equals one kopeck. The ruble was divided into one hundred parts, and one part was taken from there. And one part of these hundred parts is one kopeck. This means that one percent of one ruble is one kopeck.

Percentages were so common that people replaced the fraction with a special icon that looks like this:

This entry reads "one percent." It replaces a fraction. It also replaces the decimal fraction 0.01 because if we convert a regular fraction to a decimal fraction, we get 0.01. Therefore, between these three expressions we can put an equal sign:

1% = = 0,01

Two percent in fractional form will be written as , in decimal form as 0.02, and using a special icon, two percent is written as 2%.

2% = = 0,02

How to find the percentage?

The principle of finding a percentage is the same as the usual finding of a fraction from a number. To find a percentage of something, you need to divide it into 100 parts and multiply the resulting number by the desired percentage.

For example, find 2% of 10 cm.

What does the entry 2% mean? The 2% entry replaces the . If we translate this task into a more understandable language, it will look like this:

Find from 10 cm

And we already know how to solve such tasks. This is the usual way of finding a fraction from a number. To find a fraction of a number, you need to divide this number by the denominator of the fraction, and multiply the resulting result by the numerator of the fraction.

So, divide the number 10 by the denominator of the fraction

We got 0.1. Now we multiply 0.1 by the numerator of the fraction

0.1 × 2 = 0.2

We received an answer of 0.2. This means that 2% of 10 cm is 0.2 cm. And if , then we get 2 millimeters:

0.2 cm = 2 mm

This means that 2% of 10 cm is 2 mm.

Example 2. Find 50% of 300 rubles.

To find 50% of 300 rubles, you need to divide these 300 rubles by 100, and multiply the resulting result by 50.

So, we divide 300 rubles 100

300: 100 = 3

Now multiply the result by 50

3 × 50 = 150 rub.

This means that 50% of 300 rubles is 150 rubles.

If at first it is difficult to get used to the notation with the % sign, you can replace this notation with a regular fractional notation.

For example, the same 50% can be replaced with the entry . Then the task will look like this: Find from 300 rubles, but solving such problems is still easier for us

300: 100 = 3

3 × 50 = 150

In principle, there is nothing complicated here. If difficulties arise, we advise you to stop and re-examine and.

Example 3. The garment factory produced 1,200 suits. Of these, 32% are suits of a new style. How many new style suits did the factory produce?

Here you need to find 32% of 1200. The found number will be the answer to the problem. Let's use the rule for finding percentage. Let's divide 1200 by 100 and multiply the resulting result by the desired percentage, i.e. at 32

1200: 100 = 12

12 × 32 = 384

Answer: The factory produced 384 suits of a new style.

Second way to find percentage

The second method of finding the percentage is much simpler and more convenient. It lies in the fact that the number from which the percentage is being sought will immediately be multiplied by the desired percentage, expressed as a decimal fraction.

For example, let's solve the previous problem using this method. Find 50% of 300 rubles.

The entry 50% replaces the entry , and if we convert these to a decimal fraction, we get 0.5

Now, to find 50% of 300, it will be enough to multiply the number 300 by the decimal fraction 0.5

300 × 0.5 = 150

By the way, the mechanism for finding percentage on calculators works on the same principle. To find a percentage using a calculator, you need to enter into the calculator the number from which the percentage is being sought, then press the multiplication key and enter the desired percentage. Then press the percentage key %

Finding a number by its percentage

Knowing the percentage of a number, you can find out the entire number. For example, an enterprise paid us 60,000 rubles for work, and this amounts to 2% of the total profit received by the enterprise. Knowing our share and what percentage it is, we can find out the total profit.

First you need to find out how many rubles make up one percent. How to do it? Try to guess by carefully studying the following figure:

If two percent of the total profit is 60 thousand rubles, then it is easy to guess that one percent is 30 thousand rubles. And to get these 30 thousand rubles, you need to divide 60 thousand by 2

60 000: 2 = 30 000

We found one percent of the total profit, i.e. . If one part is 30 thousand, then to determine one hundred parts, you need to multiply 30 thousand by 100

30,000 × 100 = 3,000,000

We found the total profit. It is three million.

Let's try to formulate a rule for finding a number by its percentage.

To find a number by its percentage, you need to divide the known number by the given percentage, and multiply the resulting result by 100.

Example 2. The number 35 is 7% of some unknown number. Find this unknown number.

Let's read the first part of the rule:

To find a number by its percentage, you need to divide the known number by the given percentage.

Our known number is 35, and the given percentage is 7. Divide 35 by 7

35: 7 = 5

Read the second part of the rule:

and multiply the result by 100

Our result is the number 5. Multiply 5 by 100

5 × 100 = 500

500 is an unknown number that needed to be found. You can do a check. To do this, we find 7% of 500. If we did everything correctly, we should get 35

500: 100 = 5

5 × 7 = 35

We got 35. So the problem was solved correctly.

The principle of finding a number by its percentage is the same as the usual finding of a whole number by its fraction. If percentages are confusing and confusing at first, then the percentage entry can be replaced with a fractional entry.

For example, the previous problem can be stated as follows: the number 35 is from some unknown number. Find this unknown number. We already know how to solve such problems. This is finding a number using a fraction. To find a number using a fraction, we divide this number by the numerator of the fraction and multiply the resulting result by the denominator of the fraction. In our example, the number 35 must be divided by 7 and the resulting result multiplied by 100

35: 7 = 5

5 × 100 = 500

In the future we will solve problems involving percentages, some of which will be difficult. In order not to complicate learning at first, it is enough to be able to find the percentage of a number, and the number by percentage.

Tasks for independent solution

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Numbers, fractions, and decimals are converted to percentages in many industries, including engineering, economics, and business. This transformation is also used in everyday life; for example, we know that we need to leave a 15% tip, but how quickly can each of us calculate a specific amount? Likewise, the ability to describe a value in terms of percentages allows us to visualize and understand that value.

Steps

Calculating interest without a calculator

Use simple addition and subtraction to quickly calculate percentages. This way you can easily find percentages when you don’t have a calculator at hand. Percentages can only be added and subtracted if they refer to the same quantity (for example, 5% of a 6kg chicken cannot be added to 20% of a 2kg chicken). This method will calculate simple interest.

For example, you want to leave a 20% tip, and the bill for dinner was 2,350 rubles. A few simple steps will allow you to quickly find a specific tip amount.

Move the decimal point one place to the left to calculate 10%. This is the easiest way to find percentages without a calculator. Move the decimal point one digit to the left. In our example, 10% of 2350 rubles is 235 rubles. Remember that any whole number can be expressed as a decimal fraction; for example, the number 25 is equal to the decimal fraction 25.00.

Add and subtract 10% to find the final result. In our example, you want to leave 20% (not 10%) of 2,350 rubles. Since 20% is twice 10%, you can easily calculate a specific amount by doubling the value of 10%.
- 10% from 2350 rubles = 235 rubles
- 20% = 10% + 10%
- 20% = 235 + 235
- 20% tip from 2350 rubles = 470 rubles
- This method works because percentages are essentially fractions. 10% = 10/100. Thus, you need to add 10% ten times to get 100%. If you add 10% twice, you get 20% and so on.
Continue with ten percent to calculate other percentages. Once you understand and remember the basic steps, you will be able to find other percentages. For example, the waiter was slow, so you want to leave a 15% tip. Break this number down into a sum of smaller numbers, like this: 15% = 10% + 5%. Since 5 is half of 10, you can calculate the amount of 5% by dividing the amount of 10% in half. So 15% is equal to 235 + 117 = 352. Other steps:

Converting Fractions to Percentages
1. Remember that percentages are some fraction of 100. Percentages are the simplest representation of fractions, the denominator (the bottom number) of which is always 100. A percentage shows how many items you have if there are exactly 100 such items. For example, 25% of the apple crop is spoiled. This means that out of every 100 apples, 25 are spoiled, that is, 25/100. Converting fractions will allow you to find percentages in everyday life, such as what percentage of apples are bad if for every 2500 apples there are 450 bad apples.
  
  Create a fraction when the problem statement is given as text (not numbers). Sometimes a fraction is not given, that is, it needs to be created. Here it is important not to confuse which number to write in the numerator and which in the denominator. The denominator (lower number) always contains the original value (the overall “integer”). For example, the apple harvest, the amount from a restaurant bill, the total number of slices of pie, and so on. This is the number from which the percentage is calculated. The following examples show how to create fractions:
  - The collection of music tracks includes 4000 songs. What percentage are the songs of the Aquarium group, if the collection contains 500 records of this group.
    - Here you need to find the percentage of Aquarium group records from 4000 songs. The fraction will be written like this: 500/4000.
  - Olga deposits 1000 rubles into her bank account. After 3 months, this amount increases to 1342 rubles. Find the percentage by which the initial investment has grown.
    - Since you need to find the percentage by which the initial deposit has grown (1000 rubles), the fraction will be written like this: 1342/1000.
2. Check to see if the denominator can be converted to 100. If the denominator can be converted to 100 by division or multiplication, the resulting fraction will have a numerator equal to a percentage. Remember: any operation with the denominator must be repeated with the numerator.
  - Task: Convert the fraction 3/25 to a percentage.
  - 25 easily turns into 100 since 4x25 = 100.
  - Multiply the numerator and denominator by 4 to get the fraction 12/100.
    - 4 x 3 = 12.
    - 4 x 25 = 100.
  - The numerator is equal to the percentage. In our problem 3/25 = 12/100 = 12%
3. If the denominator cannot be converted to 100, divide the numerator (top number) by the denominator (bottom number). For example, in the fraction 16/64, the denominator (64) cannot be converted to the number 100, so you need to divide the numerator by the denominator: 16/64 = 0.25.
  - Typically, division results in a decimal fraction less than 1, but sometimes the result is greater than one if the numerator is greater than the denominator.
4. Multiply the result by 100 to convert the decimal to a percentage. In the previous example: 16/64 = 0.25. To complete the conversion of 16/64 to a percentage, multiply 0.25 by 100; To do this, move the decimal point two places to the right. So 16/64 = 25%.
  - Since (12/100)*100 = 12, the numerator of a fraction with 100 in its denominator is always equal to a percentage (12%).
  - The decimal point is essentially a percentage of one. By adding 0.1 at a time, you get closer to one (0.9 + 0.1 = 1.0). So if you move the decimal point in decimals, you can turn them into percentages. Remember: you are looking for how much of a whole, say a “whole” crop of 2,566 apples, is made up of smaller parts of that whole.
5. Solve the following problem to practice converting fractions. It is recommended that a person consume 2000 calories per day. Let's say you got that many calories, but then you ate pie and ice cream, which added another 1,500 calories. What percentage of your recommended calories did you consume today?

Modern science cannot be imagined without the concept of “percentage”. Percentages are all over the place in mathematics, physics, chemistry, economics, biology, medicine, and the list goes on forever. Many people do not understand how to work with percentages and what it means. To begin with, to understand the meaning of percentages, you should not immediately solve problems or pick up a calculator. It's worth using your imagination. Take, for example, a huge birthday cake. Let its mass be 100 kilograms. Now it was cut into 100 equal parts, 1 kilogram each. Each such piece can be called a percentage. The whole cake consists of one hundred pieces, that is, one hundred percent. For clarity, let’s take 50 pieces out of a hundred. It will be exactly half, but, on the other hand, it is exactly 50 percent. Hence the conclusion: 50% is half. A beginner has a question: “How to convert percentages into numbers?”

The question is not entirely correct: a percentage is a number. One percent is equal to one hundredth of the whole. Another relevant question is: “How to write percentages as numbers?” To do this, it’s worth remembering school and the topic of ordinary and decimal fractions. When cutting the cake, we agreed to call one hundredth part a percentage. Let's write one hundredth as a common fraction: 1/100. Obviously, if we divide 1 by 100, we get 0.1, which can be verified on a calculator. Now you need to go step by step. Two percent is 0.1 + 0.1 = 0.2. Or two percent is 0.1 * 2 = 0.2. In the same way, it turns out that 3% is 0.3, 10% = 0.1, 27% = 0.7 and so on until 100% = 1 = integer. Of course, the cake could be cut into either 77 pieces or 123. But for ease of counting, people agreed to cut all the “cakes” into one hundred pieces and call one part a percentage. Now it’s common for the reader to ask the question “How to convert a number into a percentage?”

This operation is commutative. This means that all actions are fair in the other direction. It is quite obvious that if 0.2 is 42%, then 42% is 0.2. As you can see, in order to convert a number into a percentage it is necessary and sufficient to multiply this number by 100%. In fact, multiplying by 100% does not change anything, because a percentage is a hundredth part, and multiplication is done by one hundred hundredths, that is, by one. Everything is very simple and clear in one line: 73% = 73*0.1 = 0.3 = 0.3*100% = 73%. Simple, like everything ingenious. All examples were given for numbers from 0.1 to 1 with a step length of 0.1. What if you need to calculate half a percent? Or one tenth of it? The scheme described above is universal and works for absolutely any numbers. Half a percent is 0.5% = 0.5*0.1 = 0.5. But how to calculate percentage for numbers greater than one?

As mentioned above, the scheme is universal. If 1 = 100%, then 2 = 200%, 10 = 1000%. As in other cases, to convert a percentage into a number, you need to remove the percent sign and divide by 100; to convert a number into a percentage, you need to add the “%” sign and multiply the number by 100. Now you need to figure out how to determine the percentage. Let's consider a specific example: 300 people work at the plant, 27 of them are left-handed. Determine the percentage of left-handers in production. If 300 people make up a whole, then one percent will include 300/100 = 3 people. Now if 3 workers = 1%, then 27 workers are 27/3 = 9%. Let's check. 9% = 0.9, 300*0.9 = 27. Everything fits. But a similar problem can be solved in another way. But for this it will be necessary not to convert the percentage into a number, but vice versa.

Let us divide the number of all left-handers by the number of all workers. This will help you find out the attitude of left-handed people to all people, the value will be expressed as a fraction. 27/300 = 0.9. It remains to transfer 0.9 = 9%. The answers are the same, there is no need to check. To consolidate the material, it is worth solving the inverse problem. The philatelist's collection contains 2,400 stamps, of which 2.5% were issued back in the 19th century. Find the number of stamps made in the 19th century. Let's convert the percentages into numbers: 2.5% = 2.5*0.1 = 0.5. Now you should multiply the total number of stamps by the part of the old ones: 2400 * 0.5 = 300. Answer: 300 stamps. Check: 300/2400 = 0.5 = 2.5%.

Using a percentage calculator you can make all kinds of calculations using percentages. Rounds results to the required number of decimal places.

What percentage is number X of number Y. What number is X percent of number Y. Adding or subtracting percentages from a number.

Interest calculator

clear form

How much is % of number

Calculation

0% of number 0 = 0

Interest calculator

clear form

What % is the number from the number

Calculation

Number 15 from number 3000 = 0.5%

Interest calculator

clear form

Add % to number

Calculation

Add 0% to the number 0 = 0

Interest calculator

clear form

Subtract % from the number

Calculation to clear everything

The calculator is designed specifically for calculating interest. Allows you to perform a variety of calculations when working with percentages. Functionally it consists of 4 different calculators. See examples of calculations on the interest calculator below.

In mathematics, a percentage is one hundredth of a number. For example, 5% of 100 is 5.
This calculator will allow you to accurately calculate the percentage of a given number. There are various calculation modes available. You will be able to make various calculations using percentages.

The first calculator is needed when you want to calculate the percentage of the amount. Those. Do you know the meaning of percentage and amount?
The second one is if you need to calculate what percentage X is of Y. X and Y are numbers, and you are looking for the percentage of the first in the second
The third mode is adding a percentage of the specified number to the given number. For example, Vasya has 50 apples. Misha brought Vasya another 20% of the apples. How many apples does Vasya have?
The fourth calculator is the opposite of the third. Vasya has 50 apples, and Misha took 30% of the apples. How many apples does Vasya have left?

Frequent tasks

Task 1. An individual entrepreneur receives 100 thousand rubles every month. He works in a simplified manner and pays taxes of 6% per month. How much tax does an individual entrepreneur have to pay per month?

Solution: We use the first calculator. Enter the bet 6 in the first field, 100000 in the second
We receive 6,000 rubles. - tax amount.

Problem 2. Misha has 30 apples. He gave 6 to Katya. What percentage of the total number of apples did Misha give to Katya?

Solution: We use the second calculator - enter 6 in the first field, 30 in the second. We get 20%.

Task 3. At Tinkoff Bank, for replenishing a deposit from another bank, the depositor receives 1% on top of the replenishment amount. Kolya replenished the deposit with a transfer from another bank in the amount of 30,000. What is the total amount for which Kolya’s deposit will be replenished?

Solution: We use the 3rd calculator. Enter 1 in the first field, 10000 in the second. Click on the calculation and we get the amount of 10,100 rubles.