An anonymous number A 56% less than a number in, which is 2.2 times less than the number of C. What is the percentage of the number with relative to the number e? Nmitra a \u003d b - 0,56 ⋅ b \u003d b ⋅ (1 - 0.56) \u003d 0.44 ⋅ bb \u003d A: 0.44 C \u003d 2.2 ⋅ B \u003d 2.2 ⋅ A: 0,44 \u003d 5 ⋅ AC 5 times more AC per 400% more A anonymous help. In 2001, revenues increased compared with 2000 by 2 percent, although planned 2 times. How much percent is undervalued the plan? Nmitra a - 2000 year b - 2001 b \u003d a + 0.02a \u003d a ⋅ (1 + 0.02) \u003d 1.02 ⋅ A b \u003d 2 ⋅ A (plan) 2 - 100% 1.02 - x% x \u003d 1.02 ⋅ 100: 2 \u003d 51% (plan) 100 - 51 \u003d 49% (no plan) anonymous help answer the question. Watermelon contains 99% humidity, but after drying (put on the sun for several days) the humidity is 98%. How much will the weight of the watermelon change after drying? If you calculate mathematical means, it turns out that I have a watermelon completely. For example: when weighing 20 kg, water is 99% of the mass, that is, the dry weight is 1% \u003d 0.2 kg. Here the watermelon loses fluid, and consists of 98%, therefore, the dry weight is 2%. But the dry weight cannot change due to water loss, so it is as before 0.2 kg. 2% \u003d 0.2 \u003d\u003e 100% \u003d 10 kg. Anonymous Tell me, please, how to calculate the percentage itself in the range of 2 values? Say, what percentage in the number 37 in the range of values \u200b\u200b22-63? I need a formula for the application, previously solved such tasks in a couple of minutes, and now the brain is oral). Check. Nmitra I have this way: percent \u003d (number - z0) ⋅ 100: (z1-z0) z0 - the initial value of the z1 range is the final value of the range for example, x \u003d (37-22) ⋅ 100: (63-22) \u003d 1500 : 41 \u003d 37% for example below converges
| 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 35 | 50% | 10 | 45 |
| 16 | 23% | 4,6 | 20,6 |
| 18 | 26% | 5,2 | 23,2 |
| 1 | 1% | 0,2 | 1,2 |
| 70 | 100% | 20 | 90 |
| 35 | 50% | 10 | 45 | 67,5 |
| 16 | 23% | 4,6 | 20,6 | 30,9 |
| 18 | 26% | 5,2 | 23,2 | 34,8 |
| 1 | 1% | 0,2 | 1,2 | 1,8 |
| 70 | 100% | 20 | 90 | 135 |
Rule. To find the percentage of two numbers, you need one number to divide to another, and the result is multiplied by 100.
For example, calculate how many percent is the number 52 from the number 400.
According to Rule: 52: 400 * 100 - 13 (%).
Typically, such relationships are found in tasks, when the values \u200b\u200bare specified, and you need to determine how much percent the second value is greater or less (in the question of the problem: how much percent exceeded the task; how many percentaged work; how much percentage decreased or the price and T . d.).
Solving tasks for the percentage of two numbers rarely assume only one action. A cup of such tasks consists of 2-3 actions.
1. The plant was supposed to produce 1,200 products for a month, and produced 2,300 products. How much percent of the plant exceeded the plan?
1,200 products are a plant plan, or 100% plan.
1) How many products made a plant over plan?
2 300 - 1 200 \u003d 1 100 (ed.)
2) How many percent of the plan will be superplanted products?
1 100 from 1 200 \u003d\u003e 1 100: 1 200 * 100 \u003d 91.7 (%).
1) How many percent is the actual issue of products compared to the planned?
2 300 from 1 200 \u003d\u003e 2 300: 1 200 * 100 \u003d 191.7 (%).
2) How much percent is exceeded the plan?
2. Wheat yields in the economy for the previous year amounted to 42 c / ha and was listed next year. Next year, the yield decreased to 39 centners / ha. How many percentage was the next year plan?
42 c / ha is a farm plan for this year, or 100% plan.
1) how much reduced yields compared
2) How much, percentage plan is not valued?
3 from 42 \u003d\u003e 3: 42 * 100 \u003d 7.1 (%).
3) how much percentage is the plan of this year?
1) How many percent is the yield of this goal compared to 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 recorded as follows:
For example, there are two numbers: 750 and 1100.
The percentage of 750 to 1100 is equal
The number 750 is 68.18% of 1100.
The percentage of 1100 K 750 is equal
The number 1100 is 146.67% of 750.
The norm of the plant for the production of cars is 250 cars per month. The plant collected 315 cars for the month. Question: How much percent of the plant exceeded the plan?
Percentage of 315 K 250 \u003d 315: 250 * 100 \u003d 126%.
The plan is made by 126%. The plan is exceeded by 126% - 100% \u003d 26%.
The company's profit for 2011 amounted to $ 126 million, in 2012 the profit was $ 89 million. Question: How much percent has fallen profits in 2012?
Percentage of 89 million k 126 million \u003d 89: 126 * 100 \u003d 70.63%
Profit fell 100% - 70.63% \u003d 29.37%
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The ratio (in mathematics) is the relationship between two or more numbers of one kind. The ratios compare absolute values \u200b\u200bor parts of the whole. The ratios are calculated and recorded in different ways, but the basic principles are the same for all relations.
Steps
Part 1
Definition of relations-
Definition of ratios. The ratio is the relationship between two (or more) values \u200b\u200bof the same kind. For example, if 2 cups of flour and 1 cup of sugar are needed for cooking cake, then the ratio of flour to sugar is 2 to 1.
- Relations can also be used in cases where two values \u200b\u200bare not related to each other (as in the example with a cake). For example, if 5 girls and 10 boys learn in the class, the ratio of girls to boys is 5 to 10. These values \u200b\u200b(the number of boys and the number of girls) do not depend on each other, that is, their values \u200b\u200bwill change if someone leaves the class Or the class will come a new student. The ratios simply compare the values \u200b\u200bof the values.
-
pay attention to different methods Representations of relations. Relationships can be represented by words or with mathematical symbols.
- Very often, the ratios are expressed with words (as shown above). Especially such a form of representation of relations is used in everyday life, far from science.
- Also, the relationship can be expressed through a colon. When comparing two numbers in the ratio, you will use one colon (for example, 7:13); When comparing three or more values, put the colon between each pair of numbers (for example, 10: 2: 23). In our example with the class you can express the ratio of girls and boys like this: 5 girls: 10 boys. Or so: 5:10.
- More frequent ratios are expressed by inclined feature. In the example of the class, it can be recorded as follows: 5/10. Nevertheless, this is not a fraction and is read by this ratio not as a fraction; Moreover, remember that in the ratio, the numbers do not represent a part of the whole.
Part 2
Using relations-
Simplify the ratio. The ratio can be simplified (similar to fractions), dividing each member (number) of the ratio by. However, do not miss the initial values \u200b\u200bof the ratio.
- In our example in class 5 girls and 10 boys; The ratio is 5:10. The greatest common divisor of the ratio members is 5 (as it is 5, and 10 are divided into 5). Divide each number of ratio by 5 and get a ratio of 1 girl to 2 boys (or 1: 2). However, when simplifying the ratio, remember source values. In our example in class not 3 student, and 15. The simplified ratio compares the number of boys and the number of girls. That is, each girl accounts for 2 boys, but in the class not 2 boys and 1 girl.
- Some ratios are not simplified. For example, a ratio of 3:56 is not simplified, since these numbers have no common divisors (3 - a simple number, and 56 is not divided into 3).
-
Use multiplication or division to increase or reduce the ratio. Tasks are common in which it is necessary to increase or decrease the two values \u200b\u200bproportional to each other. If you are given a ratio and you need to find the corresponding more or less relationship, multiply or divide the original ratio to some given number.
- For example, a baker needs to triple the amount of ingredients, data in the recipe. If, according to the recipe, the ratio of flour to sugar is 2 to 1 (2: 1), then the baker will multiply each member of the ratio of 3 and receives a ratio of 6: 3 (6 cups of flour to 3 sugar cups).
- On the other hand, if the baker must be taken to lay the number of ingredients, data in the recipe, then the baker will divide each member of the 2 ratio and receives a ratio of 1: ½ (1 cup of flour to 1/2 cup of sugar).
-
Search for an unknown value when two equivalent ratios are given. This is a task in which it is necessary to find an unknown variable in one ratio using a second ratio, which is equivalent to the first. To solve such tasks, use. Write down each ratio in the form of an ordinary fraction, put the equality sign between them and multiply their members crosswise.
- For example, a group of students in which 2 boys and 5 girls are given. What will be the number of boys if the number of girls increases to 20 (proportion is saved)? First, write down two ratios - 2 boys: 5 girls and h. Boys: 20 girls. Now write these ratios in the form of fractions: 2/5 and x / 20. Multiply the members of the crosses crosswise and get 5x \u003d 40; Consequently, x \u003d 40/5 \u003d 8.
Part 3.
Common mistakes-
Avoid addition and subtracts in text tasks to the ratio. Many text tasks look like this: "In the recipe it is necessary to use 4 potato tuber and 5 carrot roots. If you want to add 8 potato tubers, how much does carrots need, so that the ratio remains unchanged? " When solving such tasks, students often make an error, adding the same amount of ingredients to the initial number. However, to save the ratio, you need to use multiplication. Here are examples of the right and improper decision:
- Invalid: "8 - 4 \u003d 4 - so we added 4 potatoes tuber. So, you need to take 5 carrots roots and add 4 more ... Stop! Relations are not so calculated. It is worth trying again. "
- True: "8 ÷ 4 \u003d 2 means, we multiplied the amount of potatoes at 2., respectively, 5 carrot roots should also be multiplied by 2. 5 x 2 \u003d 10 - to the recipe you need to add 10 carrot roots."
-
Convert members to the same measurement units. Some text tasks are specifically complicated by adding different units of measurement. Convert them before calculating the ratio. Here is an example of the task and solutions:
- The dragon has 500 grams of gold and 10 kilograms of silver. What is the ratio of gold to silver in the dragon treasury?
- Grams and kilograms are different units of measurement, they need to be converted. 1 kilogram \u003d 1000 grams, respectively, 10 kilograms \u003d 10 kilograms x 1000 grams / 1 kilogram \u003d 10 x 1000 grams \u003d 10,000 grams.
- The dragon in the treasury is 500 grams of gold and 10,000 grams of silver.
- The ratio of gold to silver is: 500 grams of gold / 10,000 grams of silver \u003d 5/100 \u003d 1/20.
-
Record units of measurement after each value. In text tasks, it is much easier to recognize the error if you write units of measure after each value. Remember that values \u200b\u200bwith one and the same units of measurement in the numerator and denominator are reduced. Reducing the expression, you will get the right answer.
- Example: 6 boxes are given, there are 9 balls in each third box. How many balls?
- Invalid: 6 boxes x 3 boxes / 9 balls \u003d ... Stop, nothing can be cut. The answer will be like this: "Boxes x boxes / balls." It does not make sense.
- True: 6 Boxes X 9 Balls / 3 Boxes \u003d 6 Boxes * 3 Balls / 1 Box \u003d 6 Boxes * 3 Balls / 1 Box \u003d 6 * 3 Balls / 1 \u003d 18 Balls.
Using ratios. Relations are used both in science and in everyday life For comparison of values. The simplest relations are associated with only two numbers, but there are ratios that compare three or more values. In any situation in which more than one value is present, you can write the ratio. Combining some values, relations can, for example, suggest how to increase the amount of ingredients in the recipe or substances in the chemical reaction.
Private two numbers call relation These numbers.
Thus, with the help of letters, the ratio of numbers a and b is recorded, and, and the previous member, B is a subsequent member. (Reminder: fractional feature means a sign of division).
Percentage.
Rule. To find the percentage of two numbers, you need one number to divide to another, and the result is multiplied by 100.
For example, calculate how many percent is the number 52 from the number 400.
According to Rule: 52: 400 × 100 - 13 (%).
Typically, such relationships are found in tasks, when the values \u200b\u200bare specified, and you need to determine how much percent the second value is greater or less (in the question of the problem: how much percent exceeded the task; how many percentaged work; how much percentage decreased or the price and T . d.).
Solving tasks for the percentage of two numbers rarely assume only one action. A cup of such tasks consists of 2-3 actions.
Examples
Task 1.
The plant was supposed to produce 1,200 products for a month, and manufactured 2,300 products. How much percent of the plant exceeded the plan?
1st option
Decision:
1,200 products are a plant plan, or 100% plan.
1) How many products made a plant over plan?
2 300 - 1 200 \u003d 1 100 (ed.)
2) How many percent of the plan will be superplanted products?
1,100 from 1 200 \u003d\u003e 1 100: 1 200 × 100 \u003d 91.7 (%).
2nd option
Decision:
1) How many percent is the actual issue of products compared to the planned?
2 300 from 1 200 \u003d\u003e 2 300: 1 200 × 100 \u003d 191.7 (%).
2) How much percent is exceeded the plan?
191,7 - 100 = 91,7 (%)
Answer: 91.7%.
Task 2.
We must plow the field of the field in 500 hectares. 150 hectares plowed on the first day. How many percent is a plowed plot from the entire site?
Decision
To answer the question of the task, it is necessary to find the attitude (private) plowed part of the site to the entire area of \u200b\u200bthe site and express its relationship as a percentage:
150/500 = 3/10 = 0,3 = 30 %
Thus, we found a percentage, that is, how many percent one number (150) is from another number (500).
Task 3.
The worker made per shift 45 parts instead of 36 by plan. How many percent actual production is from the planned?
Decision
To answer the question of the task, it is necessary to find the ratio (private) number 45 to 36 and express it as a percentage:
45: 36 = 1,25 = 125 %.
Task 4.
In soy seeds contain 20% oil. How many oil is contained in 700 kg of soy?
Decision.
The task requires to find the specified part (20%) from the known value (700 kg). Such tasks can be solved by the way to bring to one. The basic value of the value is 700 kg. We can take it for a conditional unit. And the conditional unit is 100%. Since proportional dependence Direct brief conditional conditions can be written as follows:
We will prepare the proportion and find an unknown member of the proportion:
Answer: 140kg.
Finding a number by its percentage.
Task 1.
The raw cotton obtains 24% fiber. How much do you need to take raw cotton to get 480 kg of fiber?
Decision
480 kg of fibers are 24% of some mass of raw cotton, which we will take for x kg. We assume that X kg is 100%. Now briefly the condition of the task can be written as follows:
Answer: 2000kg \u003d 2T.
This task can be solved otherwise.
If, in the condition of this problem, instead of 24%, to write an equal number 0.24 equal to it, then we obtain the task of finding a number according to its known part (fracted). And such tasks are solved by division. From here it follows another solution:
1) 24% \u003d 0.24; 2) 480: 0.24 \u003d 2000 (kg) \u003d 2 (T).
To find a number according to its interest, it is necessary to express interest in the form of a fraction and solve the task to find the number on this fraction.
Questions to the abstract
In the garden, 5 bushes of yellow roses are growing. This is 25% of all roses in the garden. How many rose bushes in the garden?
Give the attitude towards natural numbers:
To get to the recreation center, the tourist drove 80km, which is 40% of the total path. What distance left to drive to get to the base?
2 300 - 1 200 \u003d 1 100 (ed.)
1,100 from 1 200 \u003d\u003e
2 300 from 1 200 \u003d\u003e
3 from 42 \u003d\u003e 3: 42 * 100 \u003d 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 recorded as follows:
For example, there are two numbers: 750 and 1100.
The percentage of 750 to 1100 is equal
The number 750 is 68.18% of 1100.
The percentage of 1100 K 750 is equal
The number 1100 is 146.67% of 750.
The norm of the plant for the production of cars is 250 cars per month. The plant collected 315 cars for the month. Question: How much percent of the plant exceeded the plan?
Percentage of 315 K 250 \u003d 315: 250 * 100 \u003d 126%.
The plan is made by 126%. The plan is exceeded by 126% - 100% \u003d 26%.
The company's profit for 2011 amounted to $ 126 million, in 2012 the profit was $ 89 million. Question: How much percent has fallen profits in 2012?
Percentage of 89 million k 126 million \u003d 89: 126 * 100 \u003d 70.63%
Profit fell 100% - 70.63% \u003d 29.37%
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With full or partial copying of the articles of the site, the source reference is required.
Finding the percentage of two numbers
Rule. To find the percentage of two numbers, you need one number to divide to another, and the result is multiplied by 100.
For example, calculate how many percent is the number 52 from the number 400.
According to Rule: 52: 400 * 100 - 13 (%).
Typically, such relationships are found in tasks, when the values \u200b\u200bare specified, and you need to determine how much percent the second value is greater or less (in the question of the problem: how much percent exceeded the task; how many percentaged work; how much percentage decreased or the price and T . d.).
Solving tasks for the percentage of two numbers rarely assume only one action. A cup of such tasks consists of 2-3 actions.
1. The plant was supposed to produce 1,200 products for a month, and produced 2,300 products. How much percent of the plant exceeded the plan?
1,200 products are a plant plan, or 100% plan.
1) How many products made a plant over plan?
2 300 - 1 200 \u003d 1 100 (ed.)
2) How many percent of the plan will be superplanted products?
1 100 from 1 200 \u003d\u003e 1 100: 1 200 * 100 \u003d 91.7 (%).
1) How many percent is the actual issue of products compared to the planned?
2 300 from 1 200 \u003d\u003e 2 300: 1 200 * 100 \u003d 191.7 (%).
2) How much percent is exceeded the plan?
2. Wheat yields in the economy for the previous year amounted to 42 c / ha and was listed next year. Next year, the yield decreased to 39 centners / ha. How many percentage was the next year plan?
42 c / ha is a farm plan for this year, or 100% plan.
1) how much reduced yields compared
2) How much, percentage plan is not valued?
3 from 42 \u003d\u003e 3: 42 * 100 \u003d 7.1 (%).
3) how much percentage is the plan of this year?
1) How many percent is the yield of this goal compared to the plan?
What is a percentage? Formula of calculation percent relationship?
Interest ratio (attitude) - what is it?
An interest ratio 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 the number in divided by the number A and multiply by 100 percent. The formula looks like this: a x 100%. And for clarity, examples: how many percent of 50 is the number 250. 250: 50 x 100% \u003d 500%.
And vice versa: How many percent of 250 is 50? 50: 250 x 100% \u003d 20%
This comparative characteristics two or more numbers (values) that shows
1) What part is one number from another number or from the whole.
2) How much percent one number will be more (less) than other numbers.
You can select 2 types of interest ratios:
1) the percentage ratio of two numbers.
2) the percentage ratio of several elements of one whole.
Below, consider the method of calculation.
The percentage ratio of two numbers
This is the ratio of one number to another in percent.
Let 2 numbers: N and M.
The percentage of them can be calculated according to 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% \u003d (500/600) * 100% \u003d 83.3%.
The ratio of the number M to the number n in% \u003d (600/500) * 100% \u003d 120%.
The percentage of elements of one whole
This type of ratio shows the structure of compound elements of any whole value, it is clearly displayed in the form of a circular chart.
For example, the percentage ratio of the organization's expenses for a certain period.
Here, the whole (N) is cumulative expenses. Suppose they will be equal to 12 million rubles.
Parts from the whole (N1, N2, N3.) Are separate types of expenses. Suppose material costs 7 million rubles are equal, labor costs are equal to 1 million rubles, cash flows are equal to 4 million rubles.
The percentage for each element is by the formula:
It shows what part of the whole (amount of expenses) is each composite element (the cost of expenses).
Material expenses \u003d (7/12) * 100% \u003d 58.33%.
Labor expenses \u003d (1/1 12) * 100% \u003d 8.33%.
Cash spending \u003d (4/12) * 100% \u003d 33.33%.
