**Definition:** the Percentage ( % ) is called a hundredth part of the whole.

of the number .

## The most common task interest

- To find the percentage of a given number
- Find a number given another number and its value in percentage from the initial number
- Find a number given a percent
- To find the percentage of one number from another.
- Find percentage of two numbers
- To find compound interest.
- By what percentage one number is greater than (less than) another number

## Finding percent

The ratios and formulas that are needed to solve the task with interest, are taken out of proportion

**all {X}**

**part {Y}the Y part in **

which can be written as proportions

## Finding percentage of a number

of the number .

the number 35 is: .

**Examples** on finding percentage of a number:

1) the number 35 is: .

2) Milk contains fat. How much fat in 54 kg of milk?

(kg) – fat.

3) the Investor has put in Bank 60000 UAH. at 8% per annum. How much money is in the account after two years?

(UAH).

## Finding the number for a given value of its percent

If any numbers are equal , then all the number is :

of the number .

**Example: ** to Find the number for a given value of its percent

from of some number a is: . Find the number and

**The task** of finding the number for a given value of its percent

The alloy contains copper. What is the mass of the alloy, of copper if it is 2.8 kg?

(kg) – the weight of the entire alloy.

### Finding percentages of two numbers

To find what percent is a number and the number in need and to share the in's and multiply by 100%

The number is

of the number .

### The relationship between decimal fractions and percentages

Desyatnikovo to turn a fraction into a percentage, multiply it by 100.

To convert a percentage to a decimal number you need to divide percent by 100.

**Examples convert the decimal into a percentage**

Example: to Convert a decimal into a percentage: 5; 1; 0,5; 0,05; 0,005

.

.

.

.

.

**Examples convert the percent to a decimal**

Example: to Convert a percent to a decimal 600%; 100%; 60%; 8%; 0,7%

.

.

.

.

.

Task: Calculate the percentage content of copper in the alloy with a mass of 10 kg, if of copper in it – 5.2 kg?

– the percentage of copper in the alloy.

### By what percentage one number is greater than another number

If the numbers A and B such that A>B and need to know what percentage a number a is greater than B, we can use the following formula:

### What percentage is one number less than another number

If the numbers A and B such that and it is necessary to know the percentage A number less than the number B, we can use the following formula:

**Example 1:** Find how many percent the number 60 is greater than the number 30.

Solution:

,

Reply: the number 60 is greater than the number 30 to 50%

Example 2: Find the percentage a number less than the number of 40 80.

**Solution:**

,

Answer: the number 40 is less than the number 80 50%

Example 3: a kilogram of strawberry costs 20 hryvnia, a kilogram of raspberry is 40 hryvnia. The percentage kilogram of strawberries cheaper kilogram of raspberries?

Solution:

,

Answer: kilogram of strawberries cheaper pounds raspberry 50%

- an increase of 100 % means a doubling of the
- a decrease of 50% means halving
- a reduction of 60% means a decrease in 2,5 times
- a decrease of 100% means zeroing the initial value

## Compound interest (interest)

If the specified number is growing by without seizure increase, in this case we speak of **compound interest**.

### Compound interest

To follow the change of the given number when you calculate **compound interest** by entering whether the magnification (reduction) .

### The formula for calculating compound interest

,

where A is future value, present value, p is the interest rate per payment period, n - number of calculation periods