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Number System in Algebra

Number systemis a set of numbers that are placed together by using some operations addition, subtraction, multiplication, and division. There are different types of numbers that are placed in a number system they are natural numbers, integers, rational numbers, algebraic numbers, real numbers, and complex numbers.

A fraction is a number that represents a part from a whole, in short it is represents a part from whole. A fraction generally contains numerator and denominator they are separated by a / and all these together known as a fraction. It is represented as shown below.

Fraction = part / whole -or- numerator / denominator

Example:

2/3, 4/6, 7/19, 200/893 etc.

Here is an example of adding fractions.

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Decimal is a number that are represented using (.) these values present in between any two consecutive real numbers such as 0 to 1 or 1 to 2 or 1556 to 1557.

Example:

0.1, 0.003, 2.87, 2344.87, 103.00002 etc.

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The ratio between two quantities represents how many times the first quantity is present in the second quantity.

Example:

This home work help problem explain the ratios concpet much better

There are 300 students in a school out of this only 100 are girls and remaining are boys. Find the ratio between boys and girls.

Total number of students = 300

Total number of girls = 100

Total number of boys = 300 – 100 = 200

The ratio between boys and girls is 200/100 = 2/1 = 2 : 1

Proportions are also related to ratios and represented with a symbol (?), this is of two types two types they are direct and inverse.

In direct proportion change in one quantity effects the change in another quantity i.e. the increase in one quantity effects the increase in another quantity similarly decrease in one quantity decrease other quantity.

In inverse proportion the change in one quantity affects the other quantity in reverse i.e. the increase in one quantity effects the decrease in another quantity, similarly decrease in one quantity increase other quantity.

Example:

If A ? B then it means that A and B are directly proportional, i.e. increase in A also increases B and vice versa.

If A ? 1/B then it means that A and B are inversely proportion, i.e. increase in A decreases B and vice versa.

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Percents

A percentage gives out the value as a fraction of 100; it is denoted by the symbol (%).

Example:

50 percentage of 60 =?

50% x 60 = 50/100 x 60 = 1/ 2 x 60 = 30.

There are 300 students in a school out this only 150 are boys, Find the percentage of boys.

Total number of students = 300

Total number of boys = 150

Percentage of boys = 150/300 x 100 = 1/ 2 x 100 = 50%

There are 50% of boys.