Advice 1: How to solve problems with percent

Often tormented in mathematics lessons a question: "Why me?" can find the answer when the boss promised next month wage will increase by 15%. Today, the ability to solve problems on interest is a vital necessity.
How to solve problems with percent
You will need
  • 1) Paper 2) Pen 3) Calculator
According to the Ozhegov Sergei Ivanovich, a percentage called the hundredth (part) from the whole and represent the symbol %. Hundredth can be written as:

1% = 1/100 = 0,01

The role of the whole, i.e. 100% can be anything: any number, bunch of grapes, a barrel of honey or pension.

1) Find 18% of the pension is equal to 6 122 R.

6 R. 122*18% = 6 122 R.*18/100 = 6 122 R.*0,18 = 1101,96 R.

2) Pour a barrel of honey for 8 cans. 3 banks give to guests. What percentage of honey from the barrel you gave? And how many have remained?

3/8 or 0.375 of the barrel you gave. Translate into a percentage by multiplying by 100. You gave 37.5% of the honey that you had. Left 5/8 = 0,625*100% = 62,5%.
All task interest easily solved with a proportion.

Find 82% of the number 506.


506 – 100%

X – 82%, where X is an unknown that must be found.

506/X = 100%/82%, or from 506*82% = X*100%

X = 506*82%/100% = 414,92

The percentage (%) as unit of measurement decreased.
From a mathematical point of view there are three main types of task to the percent. The remaining tasks are produced on the basis of these types. Learn how to solve these problems.
The first type

Find the percentage from a given number.

The average salary in your organization is 20 thousand rubles next year promise an increase of 20%. How to grow expected salary next year?

20 thousand rubles – 100%

X – 20%

X = 20 $ *20%/100% = 4 thousand.

The expected average salary to grow by 4 thousand rubles and will be in the amount of 24 thousand.
The second type

Find the number by the percentage.

40% of tomatoes in the box, which amounted to 5 kg, were green. How many pounds of tomatoes lying in the drawer?

5 kg – 40%

X kg – 100%

X = 5kg*100%/40% = 12.5 kg
The third type

Find the percentage of one number by the other.

In the morning Peter usually drinks 1 Cup of tea, and in the evening – 4. How many percent of the evening the volume of cups of tea he drinks in the morning?

4 cups – 100%

1 Cup – X%

X = 1 Cup*100%/4 cups = 25%
1) Carefully choose the value that will indicate 100%. 2)If over 100% you mentioned, for example, the number 200, then 99% - there will always be a number less than 200 and 101% - more. 3)After you have solved a problem, always analyze the response - this will help to avoid mistakes.
Useful advice
Write the terms on paper - so the task becomes clearer and clearer.

Advice 2 : How to solve the task from the exam in algebra

Unified State Examination is centrally conducted in the Russian Federation exam in secondary schools (the schools). 2011 exam paper in mathematics contains 12 items (B1-B12), and 6 more advanced tasks (S1-S6). Unified State Exam in algebra need to pass, as it is mandatory for all graduates.
How to solve the task from the exam in algebra
You will need
  • Leaf, pen, ruler.
Consider the task (B1). Example: Ballpoint pen costs 40 RUB. What is the largest number of such pens can be bought for 300 rubles after the increase in the price of pen is 10 %? For a start, find out how much cost is ball point pen after the price increase. For 40 divide by 100, multiply by 10 and add 40. New price handles - 44 RUB And now 300 divide by 44. Answer: 6.

Reference (B2). This job you can easily decide on a schedule, just be very careful.

Job (B3). Example: Find the root of the equation 7 to the extent of (u - 2) is equal to 49. First, imagine 49 as 7 in the second degree. Now you have the equation: y - 2 = 2. Deciding it, you will get the answer: 4.
The Job (Q4). Example: In triangle ABC, the angle is 90 degrees, angle A is 30 degrees, AB = the square root of 3. Find the ACE.. Draw on a piece of this triangle, so it will be easier to present it. So, the cosine of angle A = AC/AB. Here you can Express as: AC = the cosine of A multiplied by AB. The cosine of 30 degrees = square root of 3/2. Response: 1,5.
Job (B5). This task you can easily decide, just be careful and read correctly.
Job (B6). To solve this problem, you will need to remember formulas, areas, volumes of various shapes. If you know them, you will get the correct answer.
Job (V7). This is an example with logarithms. To solve it, remember all the properties of logarithms.
Reference (B8). This task will resolve it with graphics.
Reference (B9). Share this job to you, as in the reference (B6), you will need the formulae of areas and volumes.
Reference (B10). Example: the Height at which is located a stone thrown from the ground vertically upward, changing the law h(t) = 2 + 14t - 5 t squared (meters). How many seconds the stone will have a height of 10 meters?. Write down the equation: 2 + 14t - 5t squared = 10. And decide it. You get roots: 2 and 0.8. 2 - 0,8 = 1,2. Answer: 1,2.
Job (Q11). Find the greatest or least value of a function on an interval. First, find the derivative of this function, equate it to zero, find the roots, check that they belong to segment and substitute them in the function itself. So you will find the value of the function.
Job (B12). Here can be a challenge to work together, movement, concentration. Learn to solve such problems.
Part of the problem With more complex. To learn how to solve them, you need to go to the tutor or to resolve them in collaboration with your teacher in algebra.
Useful advice
When solving examination papers be very careful. If you can not get any job, move on to the next. If time remains, return to outstanding assignments. And then you will succeed.
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