## Introduction to Fundamentals Concepts in Mathematics

Fundamentals basically mean the simplest and the most important part of something which is more in detail and complicated. It generally refers to some basic principles, ideas and theories which are the important elements of something. So here, fundamentals of mathematics imply some basic theories, principles and some most important ideas which are very important before studying detailed mathematics. There are many basic fundamentals which a Class 7 student needs to know before going into the topic in detail. Here we will be discussing some of those Fundamentals.

### Integers

Those numbers which cannot be a fraction but can be positive, negative or a zero are termed as integers. All the whole numbers are integers.

Numbers which are greater than zero and represented by a positive sign are positive integers. eg: +10.

Numbers which are less than zero and represented by a negative sign are negative integers. eg: -8.

### Rational Numbers

Any number which can be expressed as a fraction of two integers where the denominator is never equal to zero is a rational number. Eg: 8/9, 2 (can be written as 2/1), 0 (can be written as 0/47, 0/8..).

### Fractions

A fraction generally denotes some part of a whole. It can be represented as p/q where p is known as the numerator and q is known as the denominator. The denominator is never zero.

For example,

If we cut an apple in two equal pieces then each part is one half of the whole which is denoted by ½.

If there are 8 students in a class and 5 of them are girls. So the fraction of boys will be ⅜ and the fraction of girls will be ⅝.

### Exponent

An exponent is known as the power of the number. It tells us how many times the number is multiplied by itself.

For example, (p)^{q}, where q is known as the power or exponent of p and p is the base. Below are some laws of exponent:

Product law states that:

(p)^{q} * (p)^{r} = (p)^{q + r}

Quotient law states that:

(p)^{q} /(p)^{r} = (p)^{q - r}

Power law states that :

(p

^{q})^{r}= (p)^{qr}(p)

^{q}* (s)^{q}= (ps)^{q}(p)

^{q}/(s)^{q}= (p/s)^{q}(p)

^{0}= 1

### Ratio and Proportion

Ratio is basically a fraction which tells us the number of times one number contains the other. It can be written as p:q or p/q.

For example, if there are a total of 10 students in a class and 7 are girls and 3 are boys.

The ratio of girls to boys is 7:3.

The ratio of boys to girls is 3:7.

The ratio of girls to total students is 7:10.

The ratio of boys to total students is 3:10.

When the two ratios are made equal, it is known as a proportion. Is can be termed as an equation which needs to be solved.

### Percent and Percentage

Percent is basically formed by two words - per and cent. Which means one part out of a hundred. It can be said as a number which is denoted in a fraction of one hundred. The sign which is used to tell that the number is a percentage is %. For example, if you want to denote a fraction by percentage, multiply the fraction by 100 and then denote it by the sign %.

8/20 = 8/20 * 100 = 40%

### Profit and Loss

Whenever we buy something we pay some money for that, now if we sell the same thing again, we may be either in profit or in loss which will depend on the cost price and the selling price of the product.

Cost Price: The price at which any product is purchased is the cost price of the product.

Selling Price: The price at which the product is sold is known as the selling price of the product.

Profit: When the selling price is more than the cost price, we are in profit which is equal to -

(selling price) - (cost price)

Loss: When the selling price is less than the cost price of the product we are in loss which is equal to -

(cost price) - (selling price)

Q1. What do we Mean by Linear Equations?

Answer: A simple algebraic equation in which every term is either constant or a single variable or a product of the two.

For example: px + q =0 where p and q are constants and x is a variable:

8x + 9 = 0

x - 9 = 5

**Rule:**

If the same number is added, subtracted, multiplied, or divided to both sides of the linear equation, the equation remains the same.

Q2.What do You Understand by the Pythagoras Theorem.

Answer: A mathematician named Pythagoras gave an interesting formula which was known as:

Pythagoras Theorem according to which:

For a right-angled triangle, the sum of squares of sides forming the right angle is equal to the sum of the square of the hypotenuse which is opposite to the right angle.

If P is the hypotenuse opposite to the right angle and Q and R are the sides forming the right angle then:

(Q)^{2} = (P)^{2} + (R)^{2}