Rule. To find the percentage of two numbers, divide one number by the other, and multiply the result by 100.
For example, calculate the percentage of 52 of 400.
According to the rule: 52: 400 * 100 - 13 (%).
Typically, such relationships are found in tasks when the values are set, but it is necessary to determine by what percentage the second value is greater or less than the first (in the question of the task: by how many percent overfulfilled the task; by how many percent have completed the work; by how many percent has decreased or increased the price, etc.) etc.).
Percentage problem solutions rarely involve only one action. Most often, the solution of such problems consists of 2-3 actions.
1. The plant was supposed to produce 1,200 items in a month, and produced 2,300 items. By what percentage did the plant exceed the plan?
1,200 items are the plant plan, or 100% of the plan.
1) How many products did the plant produce in excess of the plan?
2 300 - 1 200 = 1 100 (ed.)
2) What percentage of the plan will be overplanned items?
1 100 from 1 200 => 1 100: 1 200 * 100 = 91.7 (%).
1) What percentage is the actual output of products in comparison with the planned?
2,300 from 1,200 => 2,300: 1,200 * 100 = 191.7 (%).
2) By what percentage is the plan overfulfilled?
2. The wheat yield in the farm for the previous year was 42 kg / ha and was included in the plan for the next year. The next year, the yield dropped to 39 kg / ha. By what percentage was the next year's plan fulfilled?
42 kg / ha is a farm plan for this year, or 100% of the plan.
1) How much the yield has decreased in comparison
2) How much, in percent, is the plan not completed?
3 of 42 => 3: 42 * 100 = 7.1 (%).
3) What percentage of this year's plan has been fulfilled?
1) How many percent is the yield of this goal in comparison with the plan?
Percentage of two numbers
The percentage (or ratio) of two numbers is the ratio of one number to another multiplied by 100%.
The percentage of two numbers can be written using the following formula:
For example, there are two numbers: 750 and 1100.
The percentage of 750 to 1100 is
750 is 68.18% of 1100.
The percentage of 1100 to 750 is
The number 1100 is 146.67% of 750.
The vehicle manufacturing plant's quota is 250 vehicles per month. The plant assembled 315 vehicles in a month. Question: by what percentage did the plant exceed the plan?
Percentage of 315 to 250 = 315: 250 * 100 = 126%.
The plan was fulfilled by 126%. The plan was overfulfilled by 126% - 100% = 26%.
The company's profit for 2011 was $ 126 million, in 2012 the profit was $ 89 million. Question: by what percentage did profit fall in 2012?
The percentage of 89 million to 126 million = 89: 126 * 100 = 70.63%
Profit fell by 100% - 70.63% = 29.37%
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A relationship is called a certain relationship between the entities of our world. These can be numbers, physical quantities, objects, products, phenomena, actions, and even people.
V Everyday life when it comes to ratios we say "The ratio of this and that"... For example, if there are 4 apples and 2 pears in a vase, then we say "Ratio of apples and pears" "The ratio of pears and apples".
In mathematics, the ratio is often used as "The attitude of so-and-so to that-and-so"... For example, the ratio of four apples and two pears, which we considered above, in mathematics will read as "The ratio of four apples to two pears" or if you swap apples and pears, then "The ratio of two pears to four apples".
The ratio is expressed as a To b(where instead of a and b any numbers), but more often you can find an entry that is composed using a colon as a: b... You can read this entry in different ways:
- a To b
- a refers to b
- attitude a To b
Let's write the ratio of four apples to two pears using the ratio symbol:
4: 2
If we swap the places of apples and pears, then we will have a ratio of 2: 4. This ratio can be read as "Two to four" or either "Two pears refer to four apples" .
In what follows, we will call the relation a relation.
Lesson contentWhat is an attitude?
The relation, as mentioned earlier, is written in the form a: b... It can also be written as a fraction. And we know that such a notation in mathematics means division. Then the result of the relationship will be the quotient a and b.
A ratio in mathematics is called the quotient of two numbers.
The ratio allows you to find out how much of one entity falls on the unit of another. Let's go back to the ratio of four apples to two pears (4: 2). This ratio will allow us to find out how many apples are there per unit of pear. A unit means one pear. First, let's write the ratio 4: 2 as a fraction:
This ratio is the division of the number 4 by the number 2. If we perform this division, we will get an answer to the question how many apples are there per unit of pear
Received 2. So four apples and two pears (4: 2) correlate (are interconnected with each other) so that there are two apples per pear
The figure shows how four apples and two pears relate to each other. It can be seen that there are two apples for each pear.
The relationship can be reversed by writing as. Then we get the ratio of two pears to four apples, or "the ratio of two pears to four apples." This ratio will show how many pears are there per unit of apple. The unit of apple means one apple.
To find the value of a fraction, you need to remember how to divide a smaller number by a larger one.
Received 0.5. Let's convert this decimal fraction to an ordinary one:
Reduce the resulting fraction by 5
Received an answer (half a pear). This means that two pears and four apples (2: 4) correlate (are interconnected with each other) so that one apple accounts for half of the pear
The figure shows how two pears and four apples relate to each other. It can be seen that for each apple there is a half of a pear.
The numbers that make up the ratio are called members of the relationship... For example, in a 4: 2 ratio, the members are the numbers 4 and 2.
Let's consider other examples of relationships. To prepare something, a recipe is drawn up. The recipe is built from the relationship between the products. For example, making oatmeal usually requires a glass of cereal for two glasses of milk or water. The ratio is 1: 2 ("one to two" or "one glass of cereal for two glasses of milk").
We convert the ratio 1: 2 to a fraction, we get. Calculating this fraction, we get 0.5. This means that one glass of cereal and two glasses of milk are correlated (interconnected with each other) so that one glass of milk accounts for half a glass of cereal.
If you flip the ratio 1: 2, you get a 2: 1 ratio ("two to one" or "two glasses of milk for one glass of cereal"). Convert the ratio 2: 1 to a fraction, we get. Calculating this fraction, we get 2. So two glasses of milk and one glass of cereals are correlated (interconnected with each other) so that there are two glasses of milk for one glass of cereals.
Example 2. There are 15 students in the class. 5 of them are boys, 10 are girls. You can write down the ratio of girls to boys 10: 5 and convert this ratio to a fraction. Calculating this fraction, we get 2. That is, girls and boys are related to each other in such a way that for every boy there are two girls
The figure shows how ten girls and five boys relate to each other. It can be seen that there are two girls for every boy.
The ratio cannot always be converted into a fraction and the quotient can be found. In some cases, this will not be logical.
So, if you turn over the attitude, it turns out, and this is the attitude of boys to girls. If you calculate this fraction, you get 0.5. It turns out that five boys relate to ten girls in such a way that for every girl there is half a boy. Mathematically, this is of course true, but from the point of view of reality it is not entirely reasonable, because a boy is a living person and you cannot just take and divide him, like a pear or an apple.
Building the right attitude is an important problem solving skill. So in physics, the ratio of the distance traveled to time is the speed of movement.
The distance is denoted by the variable S, time - through the variable t, speed - through the variable v... Then the phrase "The ratio of the distance traveled to time is the speed of movement" will be described by the following expression:
Suppose the car has traveled 100 kilometers in 2 hours. Then the ratio of the traversed one hundred kilometers to two hours will be the speed of the car:
It is customary to call speed the distance traveled by the body per unit of time. The unit of time means 1 hour, 1 minute, or 1 second. And the relation, as mentioned earlier, allows you to find out how much of one entity falls on the unit of another. In our example, the ratio of one hundred kilometers to two hours shows how many kilometers are there for one hour of movement. We see that there are 50 kilometers for every hour of movement.
Therefore, the speed is measured in km / h, m / min, m / s... The fraction symbol (/) indicates the ratio of distance to time: kilometers per hour , meters per minute and meters per second respectively.
Example 2... The ratio of the value of a product to its quantity is the price of one unit of a product
If we took 5 chocolate bars from the store and their total cost was 100 rubles, then we can determine the price of one bar. To do this, you need to find the ratio of one hundred rubles to the number of bars. Then we get that there are 20 rubles per bar
Comparison of quantities
Earlier we learned that the relationship between quantities of different natures form a new quantity. So, the ratio of the distance traveled to time is the speed of movement. The ratio of the value of a commodity to its quantity is the price of one unit of a commodity.
But the ratio can also be used to compare values. The result of such a relationship is a number showing how many times the first value is greater than the second, or how much of the first value is from the second.
To find out how many times the first value is greater than the second, a larger value must be written in the numerator of the ratio, and a smaller value in the denominator.
To find out what part of the first value is from the second, you need to write a smaller value in the numerator of the ratio, and a larger value in the denominator.
Consider the numbers 20 and 2. Let's find out how many times the number 20 is greater than the number 2. To do this, we find the ratio of the number 20 to the number 2. In the numerator of the ratio we write the number 20, and in the denominator - the number 2
The value of this ratio is ten
The ratio of the number 20 to the number 2 is the number 10. This number shows how many times the number 20 is greater than the number 2. So the number 20 is ten times greater than the number 2.
Example 2. There are 15 students in the class. 5 of them are boys, 10 are girls. Determine how many times there are more girls than boys.
We write down the attitude of girls towards boys. We write the number of girls in the numerator of the relationship, and the number of boys in the denominator of the relationship:
The value of this ratio is 2. This means that there are twice as many girls in a class of 15 people.
There is no longer the question of how many girls there are for one boy. V this case the ratio is used to compare the number of girls with the number of boys.
Example 3... How much of the number 2 is from the number 20.
We find the ratio of the number 2 to the number 20. In the numerator of the ratio we write the number 2, and in the denominator - the number 20
To find the meaning of this relationship, you need to remember
The value of the ratio of the number 2 to the number 20 is the number 0.1
In this case, the decimal fraction 0.1 can be converted to an ordinary one. This answer will be easier to understand:
So the number 2 of the number 20 is one tenth.
You can check. To do this, we find from the number 20. If we did everything correctly, then we should get the number 2
20: 10 = 2
2 × 1 = 2
We got the number 2. So one tenth of the number 20 is the number 2. Hence we conclude that the problem is solved correctly.
Example 4. There are 15 people in the class. 5 of them are boys, 10 are girls. Determine what proportion of the total number of schoolchildren are boys.
We write down the ratio of boys to the total number of schoolchildren. We write down five boys in the numerator of the relationship, and the total number of students in the denominator. The total number of schoolchildren is 5 boys plus 10 girls, so we write 15 in the denominator of the relationship
To find the value of this ratio, you need to remember how to divide a smaller number by a larger one. In this case, the number 5 must be divided by the number 15
When you divide 5 by 15, you get a periodic fraction. Let's convert this fraction to an ordinary one
We got the final answer. So boys make up one third of the class.
The figure shows that in a class of 15 students, 5 boys make up a third of the class.
If we find from 15 schoolchildren for verification, then we get 5 boys
15: 3 = 5
5 × 1 = 5
Example 5. How many times is 35 greater than 5?
We write down the ratio of the number 35 to the number 5. In the numerator of the ratio, you need to write the number 35, in the denominator - the number 5, but not vice versa
The value of this ratio is 7. So the number 35 is seven times more than the number 5.
Example 6. There are 15 people in the class. 5 of them are boys, 10 are girls. Determine what proportion of the total number are girls.
We write down the ratio of girls to the total number of schoolchildren. We write ten girls in the numerator of the relationship, and the total number of schoolchildren in the denominator. The total number of schoolchildren is 5 boys plus 10 girls, so we write 15 in the denominator of the relationship
To find the meaning of this ratio, you need to remember how to divide a smaller number by a larger one. In this case, the number 10 must be divided by the number 15
Dividing 10 by 15 produces a periodic fraction. Let's convert this fraction to an ordinary one
Reduce the resulting fraction by 3
We got the final answer. So girls make up two-thirds of the class.
The figure shows that in a class of 15 students, two thirds of the class are 10 girls.
If we find from 15 schoolchildren for verification, then we get 10 girls
15: 3 = 5
5 × 2 = 10
Example 7. What part of 10 cm is 25 cm
We write down the ratio of ten centimeters to twenty-five centimeters. We write 10 cm in the numerator of the ratio, 25 cm in the denominator
To find the value of this ratio, you need to remember how to divide a smaller number by a larger one. In this case, the number 10 must be divided by the number 25
Let's convert the resulting decimal fraction into an ordinary
Reduce the resulting fraction by 2
We got the final answer. This means that 10 cm are from 25 cm.
Example 8. How many times is 25 cm more than 10 cm
We write down the ratio of twenty-five centimeters to ten centimeters. In the numerator of the ratio we write 25 cm, in the denominator - 10 cm
The answer was 2.5. Means 25 cm more than 10 cm 2.5 times (two and a half times)
Important note. When finding a relationship of the same name physical quantities these values must be expressed in one unit of measurement, otherwise the answer will be incorrect.
For example, if we are dealing with two lengths and we want to know how many times the first length is greater than the second, or what part of the first length is from the second, then both lengths must first be expressed in one unit of measurement.
Example 9. How many times is 150 cm more than 1 meter?
First, let's make it so that both lengths are expressed in the same unit of measurement. To do this, let's convert 1 meter to centimeters. One meter is one hundred centimeters
1 m = 100 cm
Now we find the ratio of one hundred and fifty centimeters to one hundred centimeters. In the numerator of the ratio we write 150 centimeters, in the denominator - 100 centimeters
Let's find the value of this ratio
The answer was 1.5. This means that 150 cm is 1.5 times more than 100 cm (one and a half times).
And if they did not convert meters to centimeters and immediately tried to find the ratio of 150 cm to one meter, then we would get the following:
It would turn out that 150 cm is more than one meter one hundred and fifty times, but this is not true. Therefore, it is imperative to pay attention to the units of measurement of physical quantities that are involved in the relationship. If these quantities are expressed in different units of measurement, then to find the ratio of these quantities, you need to go to one unit of measurement.
Example 10. Last month, a person's salary was 25,000 rubles, and this month, the salary has increased to 27,000 rubles. Determine how many times the salary has grown
We write down the ratio of twenty-seven thousand to twenty-five thousand. We write 27000 in the numerator of the ratio, 25000 in the denominator.
Let's find the value of this ratio
The answer was 1.08. This means that the salary has increased by 1.08 times. In the future, when we get to know percentages, we will express such indicators as salaries as percentages.
Example 11... Width apartment building 80 meters and a height of 16 meters. How many times the width of the house is greater than its height?
We write down the ratio of the width of the house to its height:
The value of this ratio is 5. This means that the width of the house is five times its height.
Relationship property
The ratio will not change if its members are multiplied or divided by the same number.
This is one of the most important properties of the relationship follows from the property of the particular. We know that if the dividend and divisor are multiplied or divided by the same number, then the quotient will not change. And since the relation is nothing more than division, the property of the particular works for it too.
Let's go back to girls' attitudes towards boys (10: 5). This attitude showed that there are two girls for every boy. Let's check how the relationship property works, namely, let's try to multiply or divide its members by the same number.
In our example, it is more convenient to divide the members of the relationship by their greatest common divisor (GCD).
The gcd of members 10 and 5 is the number 5. Therefore, you can divide the members of the relationship by the number 5
Got a new attitude. This is a two-to-one ratio (2: 1). This ratio, like the past ratio of 10: 5, shows that there are two girls for one boy.
The figure shows a 2: 1 (two to one) ratio. As in the past, the ratio of 10: 5 per boy has two girls. In other words, the attitude hasn't changed.
Example 2... There are 10 girls and 5 boys in one class. In another class there are 20 girls and 10 boys. How many times are there more girls in the first grade than boys? How many times are there more girls in the second grade than boys?
In both classes, there are twice as many girls as boys, because the relationships and are equal to the same number.
The relationship property allows you to build various models that have similar parameters to real object... Let's pretend that apartment house is 30 meters wide and 10 meters high.
To draw a similar house on paper, you need to draw it in the same ratio of 30: 10.
Divide both terms of this ratio by the number 10. Then we get the ratio 3: 1. This ratio is 3, just like the previous ratio is 3
Let's convert meters to centimeters. 3 meters is 300 centimeters, and 1 meter is 100 centimeters
3 m = 300 cm
1 m = 100 cm
We have a ratio of 300 cm: 100 cm. Divide the terms of this ratio by 100. We obtain a ratio of 3 cm: 1 cm. Now we can draw a house with a width of 3 cm and a height of 1 cm.
Of course, the drawn house is much smaller than the real house, but the ratio of width and height remains unchanged. This allowed us to draw a house as similar as possible to the real one.
Attitude can be understood in other ways as well. Initially, it was said that a real house has a width of 30 meters and a height of 10 meters. The total is 30 + 10, that is, 40 meters.
These 40 meters can be understood as 40 parts. A ratio of 30: 10 means that there are 30 pieces for the width and 10 pieces for the height.
Further, the members of the ratio 30: 10 were divided by 10. The result was a ratio of 3: 1. This ratio can be understood as 4 parts, three of which are for the width, one for the height. In this case, you usually need to find out how many meters are specific to the width and height.
In other words, you need to find out how many meters are in 3 parts and how many meters are in 1 part. First you need to find out how many meters are in one part. To do this, the total 40 meters must be divided by 4, since in a 3: 1 ratio there are only four parts
Let's determine how many meters are in the width:
10 m × 3 = 30 m
Let's determine how many meters are at the height:
10 m × 1 = 10 m
Multiple relationship members
If several members are given in a relation, then they can be understood as parts of something.
Example 1... Purchased 18 apples. These apples were shared between mom, dad and daughter in a relationship. How many apples did each one get?
The attitude suggests that mom received 2 parts, dad - 1 part, daughter - 3 parts. In other words, each member of the relationship is a specific part of 18 apples:
If you add up the members of the relationship, then you can find out how many parts there are in total:
2 + 1 + 3 = 6 (parts)
Find out how many apples are in one part. To do this, divide 18 apples by 6
18: 6 = 3 (apples per slice)
Now let's determine how many apples each got. By multiplying three apples for each member of the relationship, you can determine how many apples mom got, how much dad got, and how much daughter got.
Find out how many apples mom got:
3 × 2 = 6 (apples)
Find out how many apples dad got:
3 × 1 = 3 (apples)
Find out how many apples my daughter received:
3 × 3 = 9 (apples)
Example 2... New silver (alpaca) is an alloy of nickel, zinc and copper in relation to. How many kilograms of each metal do you need to take to get 4 kg of new silver?
4 kilograms of new silver will contain 3 parts nickel, 4 parts zinc and 13 parts copper. First, we find out how many parts will be in four kilograms of silver:
3 + 4 + 13 = 20 (parts)
Let's determine how many kilograms will be in one part:
4 kg: 20 = 0.2 kg
Let's determine how many kilograms of nickel will be contained in 4 kg of new silver. The relation indicates that the three parts of the alloy contain nickel. Therefore, we multiply 0.2 by 3:
0.2 kg × 3 = 0.6 kg nickel
Let's determine how many kilograms of zinc will be contained in 4 kg of new silver. In relation it is stated that the four parts of the alloy contain zinc. Therefore, we multiply 0.2 by 4:
0.2kg × 4 = 0.8kg zinc
Let's determine how many kilograms of copper will be contained in 4 kg of new silver. In relation, thirteen parts of the alloy are stated to contain zinc. Therefore, we multiply 0.2 by 13:
0.2 kg × 13 = 2.6 kg copper
This means that to get 4 kg of new silver, you need to take 0.6 kg of nickel, 0.8 kg of zinc and 2.6 kg of copper.
Example 3... Brass is an alloy of copper and zinc, the weight of which is 3: 2. To make a piece of brass, 120 g of copper is required. How much zinc does it take to make this piece of brass?
Let's determine how many parts an alloy of copper and zinc consists of:
3 + 2 = 5 (parts)
Let's determine how many grams of alloy are in one part. The condition says that 120 g of copper is required to make a piece of brass. It is also said that the three parts of the alloy contain copper. So, dividing 120 by 3, we will determine how many grams of alloy are in one part:
120: 3 = 40 grams per portion
Now let's determine how much zinc is required to make a piece of brass. To do this, multiply 40 grams by 2, since in the ratio of 3: 2 it is indicated that two parts contain zinc:
40 g × 2 = 80 grams of zinc
Example 4... We took two alloys of gold and silver. In one, the amount of these metals is in a ratio of 1: 9, and in the other 2: 3. How much of each alloy should be taken to get 15 kg of a new alloy, in which gold and silver would be in a ratio of 1: 4?
Solution
15 kg of the new alloy should be in a ratio of 1: 4. This ratio suggests that one part of the alloy will be gold, and four parts will be silver. There are five parts in total. This can be schematically represented as follows
Let's determine the mass of one part. To do this, first add all parts (1 and 4), then divide the mass of the alloy by the number of these parts
1 + 4 = 5
15 kg: 5 = 3 kg
One part of the alloy will have a mass of 3 kg. Then 15 kg of gold alloy will contain 3 × 1, that is, 3 kg, and silver 3 × 4, that is, 12 kg.
Therefore, to obtain an alloy weighing 15 kg, we need 3 kg of gold and 12 kg of silver.
Now back to the two alloys. You need to use each of them. We will take 10 kg of the first alloy, and 5 kg of the second. The first alloy, which is in a ratio of 1: 9, will give us 1 kg of gold and 9 kg of silver. The second alloy, which is in a ratio of 2: 3, will give us 2 kg of gold and 3 kg of silver.
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Percentage (which means "per hundred") is compared to 100.
Percentage symbol%. So, for example, 5 percent is written as 5%.
Let's say there are 4 people in the room.
50% is half - 2 people.
25% is a quarter - 1 person.
0% is nothing - 0 people.
It is 100% whole - all 4 people in the room.
If 4 more people enter the room, then their number becomes 200%.
1% is $ \ frac (1) (100) $
If there are 100 people in total, then 1% of them is one person.
To express mathematically the number X as a percentage of Y, you do the following:
$ X: Y \ times 100 = \ frac (X) (Y) \ times 100 $
Example: What percentage of 160 is 80?
Solution:
$ \ frac (80) (160) \ times 100 = 50 \% $
Increase / Decrease Percentage
When a number increases relative to another number, the amount of increase is represented as:
Increase = New number - Old number
However, when the number decreases relative to another number, then this value can be represented as:
Decrease = Old number - New number
Increasing or decreasing a number is always expressed based on the old number.
That's why:
% Increase = 100 ⋅ (New Number - Old Number) Old Number
% Decrease = 100 ⋅ (Old number - New number) Old number
For example, you had 80 postage stamps and started collecting this month while the total number of postage stamps reached 120. The percentage increase in the number of stamps you have equals
$ \ frac (120 - 80) (80) \ times 100 = 50 \% $
When you have 120 stamps, you and your friend agreed to exchange the Lego game for several of these stamps. Your friend took a few stamps that he liked, and when you counted the remaining stamps, you found that you had 100 stamps left. The percentage decrease in the number of stamps can be calculated as:
$ \ frac (120 - 100) (120) \ times 100 = 16.67 \% $
Percentage Calculator
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How percentages help in real life
There are two ways percentages can help solve our everyday problems:
1. We are comparing two different quantities when all quantities refer to the same basic quantity of 100. To explain this, let us consider the following example:
Example: Tom opened a new grocery store. In the first month he bought groceries for \ $ 650 and sold for \ $ 800, and in the second he bought for \ $ 800 and sold for \ $ 1200. It is necessary to calculate whether Tom is making more profit or not.
Solution:
We cannot tell directly from these numbers whether Tom's income is growing or not, because expenses and revenue are different every month. In order to solve this problem, we need to correlate all values to a fixed base value equal to 100. Let's express percentage his income to expenses in the first month:
(800 - 650) 650 ⋅ 100 = 23.08%
This means that if Tom spent \ $ 100, then he made a profit of 23.08 in the first month.
Now let's apply the same to the second month:
(1200 - 800) 800 ⋅ 100 = 50%
So, in the second month, if Tom spent \ $ 100, then his income was \ $ 50 (because \ $ 100⋅50% = \ $ 100⋅50100 = \ $ 50). It is now clear that Tom's income is growing.
2. We can quantify a portion of a larger value if the percentage of that portion is known. To explain this, let's look at the following example:
Example: Cindy wants to buy 8 meters of hose for her garden. She went to the store and found that there was a 30 meter hose reel. However, she noticed that the reel says that 60% has already been sold. She needs to know if the remaining hose is enough for her.
Solution:
The tablet says that
$ \ frac (Sold \ Length) (Total \ Length) \ times 100 = 60 \% $
$ Sold \ Length = \ frac (60 \ times 30) (100) = 18m $
Therefore, the remainder is 30 - 18 = 12m, which is quite enough for Cindy.
Examples:
1. Ryan loves collecting sports cards with his favorite players. He has 32 baseball cards, 25 soccer cards and 47 basketball cards. What is the percentage of cards for each sport in his collection?
Solution:
Total number of cards = 32 + 25 + 47 = 104
Baseball Card Percentage = 32/104 x 100 = 30.8%
Football Cards Percentage = 25/104 x 100 = 24%
Percentage Basketball Cards = 47/104 x 100 = 45.2%
Note that if you add up all the percentages, you get 100%, which represents the total number of cards.
2. There was a math test in the lesson. The test consisted of 5 questions; three of them were given three 3 points each, and the remaining two - four points. You were able to correctly answer two questions for 3 points and one question for 4 points. What percentage of the points did you get on this test?
Solution:
Total = 3x3 + 2x4 = 17 points
Points received = 2x3 + 4 = 10 points
Percentage of points received = 10/17 x 100 = 58.8%
3. You bought a video game for \ $ 40. Then the prices for these games were raised by 20%. What's the new price for a video game?
Solution:
Price increase is 40 x 20/100 = \ $ 8
The new price is 40 + 8 = \ $ 48
Percentage (ratio) - what is it?
Percentage is the ratio of one number to another, expressed as a percentage. If you need to find out how many percent of the number A is the number B, then you need to divide the number B by the number A and multiply by 100 percent. The formula looks like this B: A x 100%. And for clarity, examples: how many percent of 50 is the number 250. 250: 50 X 100% = 500%.
And vice versa: what percentage of 250 is 50? 50: 250 x 100% = 20%
This Comparative characteristics two or more numbers (quantities), which shows
1) What part is one number from another number or from a whole.
2) How many percent will one number be more (less) than other numbers.
There are 2 types of percentages:
1) Percentage of two numbers.
2) The percentage of several elements of one whole.
Below we will consider the calculation methodology.
Percentage of two numbers
This is the ratio of one number to another as a percentage.
Let 2 numbers be given: N and M.
The percentage between them can be calculated using the following formula:
N / M * 100% (the ratio of the first number to the second).
M / N * 100% (the ratio of the second number to the first).
The ratio of the number N to the number M in% = (500/600) * 100% = 83.3%.
The ratio of the number M to the number N in% = (600/500) * 100% = 120%.
Percentage of elements of one whole
This type of ratio shows the structure of the constituent elements of any integer value, it is more clearly displayed in the form of a pie chart.
For example, the percentage of the organization's expenses for a certain period.
Here, the integer (N) is the total cost. Let's say they will be equal to 12 million rubles.
Parts from the whole (N1, N2, N3.) Are separate types of expenses. Let's say material costs are equal to 7 million rubles, labor costs are equal to 1 million rubles, cash costs are equal to 4 million rubles.
The percentage for each element is found by the formula:
It shows how much of the whole (the amount of expenses) is each component (expense item).
Material costs = (7/12) * 100% = 58.33%.
Labor costs = (1/12) * 100% = 8.33%.
Cash expenses = (4/12) * 100% = 33.33%.
Chartically, the percentage of expenses can be represented as follows:
Percentage is the receipt of a result, expressed as a percentage, when tasks of the following nature are solved.
Consider a modern example: There was a question about the demolition of a five-story building and the residents of the house must express their opinion.
A total of 100 apartment owners live in the house. According to the voting results, 50 residents voted "FOR DEMOLITION", 30 residents voted "AGAINST9" and 20 did not deign to vote at all. The question is - will the house be demolished by the results of the vote? The publication of the voting results is always given in percentage.
Interest calculation formula: C = B / Ax100, where A is a whole, B is a countable part,
Finding percentage ratio two numbers
Rule. To find the percentage of two numbers, divide one number by the other, and multiply the result by 100.
For example, calculate the percentage of 52 of 400.
According to the rule: 52: 400 * 100 - 13 (%).
Typically, such relationships are found in tasks when the values are set, but it is necessary to determine by what percentage the second value is greater or less than the first (in the question of the task: by how many percent overfulfilled the task; by how many percent have completed the work; by how many percent has decreased or increased the price, etc.) etc.).
Percentage problem solutions rarely involve only one action. Most often, the solution of such problems consists of 2-3 actions.
1. The plant was supposed to produce 1,200 items in a month, and produced 2,300 items. By what percentage did the plant exceed the plan?
1,200 items are the plant plan, or 100% of the plan.
1) How many products did the plant produce in excess of the plan?
2 300 - 1 200 = 1 100 (ed.)
2) What percentage of the plan will be overplanned items?
1 100 from 1 200 => 1 100: 1 200 * 100 = 91.7 (%).
1) What percentage is the actual output of products in comparison with the planned?
2,300 from 1,200 => 2,300: 1,200 * 100 = 191.7 (%).
2) By what percentage is the plan overfulfilled?
2. The wheat yield in the farm for the previous year was 42 kg / ha and was included in the plan for the next year. The next year, the yield dropped to 39 kg / ha. By what percentage was the next year's plan fulfilled?
42 kg / ha is a farm plan for this year, or 100% of the plan.
1) How much the yield has decreased in comparison
2) How much, in percent, is the plan not completed?
3 of 42 => 3: 42 * 100 = 7.1 (%).
3) What percentage of this year's plan has been fulfilled?
1) How many percent is the yield of this goal in comparison with the plan?
2 300 - 1 200 = 1 100 (ed.)
1 100 from 1 200 =>
2 300 from 1 200 =>
3 of 42 => 3: 42 * 100 = 7.1 (%).
Percentage of two numbers
The percentage (or ratio) of two numbers is the ratio of one number to another multiplied by 100%.
The percentage of two numbers can be written using the following formula:
For example, there are two numbers: 750 and 1100.
The percentage of 750 to 1100 is
750 is 68.18% of 1100.
The percentage of 1100 to 750 is
The number 1100 is 146.67% of 750.
The vehicle manufacturing plant's quota is 250 vehicles per month. The plant assembled 315 vehicles in a month. Question: by what percentage did the plant exceed the plan?
Percentage of 315 to 250 = 315: 250 * 100 = 126%.
The plan was fulfilled by 126%. The plan was overfulfilled by 126% - 100% = 26%.
The company's profit for 2011 was $ 126 million, in 2012 the profit was $ 89 million. Question: by what percentage did profit fall in 2012?
The percentage of 89 million to 126 million = 89: 126 * 100 = 70.63%
Profit fell by 100% - 70.63% = 29.37%
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Finding the percentage of two numbers
Rule. To find the percentage of two numbers, divide one number by the other, and multiply the result by 100.
For example, calculate the percentage of 52 of 400.
According to the rule: 52: 400 * 100 - 13 (%).
Typically, such relationships are found in tasks when the values are set, but it is necessary to determine by what percentage the second value is greater or less than the first (in the question of the task: by how many percent overfulfilled the task; by how many percent have completed the work; by how many percent has decreased or increased the price, etc.) etc.).
Percentage problem solutions rarely involve only one action. Most often, the solution of such problems consists of 2-3 actions.
1. The plant was supposed to produce 1,200 items in a month, and produced 2,300 items. By what percentage did the plant exceed the plan?
1,200 items are the plant plan, or 100% of the plan.
1) How many products did the plant produce in excess of the plan?
2 300 - 1 200 = 1 100 (ed.)
2) What percentage of the plan will be overplanned items?
1 100 from 1 200 => 1 100: 1 200 * 100 = 91.7 (%).
1) What percentage is the actual output of products in comparison with the planned?
2,300 from 1,200 => 2,300: 1,200 * 100 = 191.7 (%).
2) By what percentage is the plan overfulfilled?
2. The wheat yield in the farm for the previous year was 42 kg / ha and was included in the plan for the next year. The next year, the yield dropped to 39 kg / ha. By what percentage was the next year's plan fulfilled?
42 kg / ha is a farm plan for this year, or 100% of the plan.
1) How much the yield has decreased in comparison
2) How much, in percent, is the plan not completed?
3 of 42 => 3: 42 * 100 = 7.1 (%).
3) What percentage of this year's plan has been fulfilled?
1) How many percent is the yield of this goal in comparison with the plan?
What is percentage? The formula for calculating the percentage?
Percentage (ratio) - what is it?
Percentage is the ratio of one number to another, expressed as a percentage. If you need to find out how many percent of the number A is the number B, then you need to divide the number B by the number A and multiply by 100 percent. The formula looks like this B: A x 100%. And for clarity, examples: how many percent of 50 is the number 250. 250: 50 X 100% = 500%.
And vice versa: what percentage of 250 is 50? 50: 250 x 100% = 20%
This is a comparative characteristic of two or more numbers (quantities), which shows
1) What part is one number from another number or from a whole.
2) How many percent will one number be more (less) than other numbers.
There are 2 types of percentages:
1) Percentage of two numbers.
2) The percentage of several elements of one whole.
Below we will consider the calculation methodology.
Percentage of two numbers
This is the ratio of one number to another as a percentage.
Let 2 numbers be given: N and M.
The percentage between them can be calculated using the following formula:
N / M * 100% (the ratio of the first number to the second).
M / N * 100% (the ratio of the second number to the first).
The ratio of the number N to the number M in% = (500/600) * 100% = 83.3%.
The ratio of the number M to the number N in% = (600/500) * 100% = 120%.
Percentage of elements of one whole
This type of ratio shows the structure of the constituent elements of any integer value, it is more clearly displayed in the form of a pie chart.
For example, the percentage of the organization's expenses for a certain period.
Here, the integer (N) is the total cost. Let's say they will be equal to 12 million rubles.
Parts from the whole (N1, N2, N3.) Are separate types of expenses. Let's say material costs are equal to 7 million rubles, labor costs are equal to 1 million rubles, cash costs are equal to 4 million rubles.
The percentage for each element is found by the formula:
It shows how much of the whole (the amount of expenses) is each component (expense item).
Material costs = (7/12) * 100% = 58.33%.
Labor costs = (1/12) * 100% = 8.33%.
Cash expenses = (4/12) * 100% = 33.33%.
