# Learn Math

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# Math topics:

## What is profit and loss?

The amount of money you pay for something is: cost price.

The amount of money you get for sell something is: selling price.

Selling price is greater than the cost price: you get a profit.

Profit = selling price – Cost price

Selling price is less than the cost price: It gives loss.

Loss = Cost price – Selling price

How to find Ratio?

Ratio: to compare two quantities by division.

The quotient of that division is called a ‘ratio’.

The colon ‘:’ is used to express a ratio.

The ratio of 7 to 9 is written as ‘7:9’

The ratio of 7 to 9  is read as ‘7  is to 9’.

The ratio  is written as ‘a:b’ and is read as ‘a is to b’.

Let us understand this better by example:

In a cricket match, Max scored 80 and Sam scored 40 runs.

Let us see how many times Max’s score is that of Sam’s.

Just divide Max’s score by Sam’s

Max’s score/  Sam’s score=   80/40 =  2/1= 2:1

Thus,we find here that,  Max’s score is 2 times Sam’s score. More

Volume of the cylinder

How to calculate the volume of a cylinder?

Volume of cylinder = area of base × height

Example: The radius of the base of a cylinder is given 28 cm and its height is 20 cm.

Find the volume of this cylinder.

Here,

Height h = 20 cm

= 22/7× 28× 28× 20

= 22 × 4 × 28× 20

= 49280 cu cm

Example:

The height of a cylindrical tank is 1 m

and its diameter is 84 cm.

How many liters of water can it hold?

(1000 cu cm = 1 liter)

Here, r = 84/2= 42 cm

H = 1 m = 100 cm

Volume of tank   = ?

= 22/7× 42 × 42 × 100

= 22 × 6 × 42 × 100

= 554400 cu cm

1000 cu cm = 1 liter

554400 cu cm = 554400 /1000 liters= 554.400 liters

Evaluate each expression

A)   Rule 1: x1= x.

Example:

(1/2)4 x (5/2)-2

you see that when base raised to the positive power value;

x= x.

So that,

(1/2)4 = ½ × ½ × ½ × ½

(5/2)-2= 2/5 × 2/5(reciprocal of the number)

So that,

(1/2)4 x (5/2)-2
= ½ × ½ × ½ × ½ × 2/5 × 2/5

Multiply numerators and multiply denominators

= 1/100

B)   Rule 2:- When base raised to the negative power value; x-1 = 1/ x1

Any number with an exponent of 0 (except 0) automatically equals 1

Example:-

(7/12)0 ×4-1

(7/12)0 = 1 and

4-1= 1/4

Therefore,

(7/12)0 ×4-1

= 1 × 1/4

=   1/4  (Multiply numerators and multiply denominators)

1. John G. Gellner, FRIC, C.Sci., C.Chem. says: