Interest, the percentage of the number

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

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Examples convert the percent to a decimal

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

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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:

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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:

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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%

  1. an increase of 100 % means a doubling of the
  2. a decrease of 50% means halving
  3. a reduction of 60% means a decrease in 2,5 times
  4. 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

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