## Tuesday, 12 February 2019

### What is an Equation?

An equation says that two things are equal. It will have an equals sign "=" like this:
x+2=6
That equations says: what is on the left (x + 2) is equal to what is on the right (6)

So an equation is like a statement "this equals that"

### What is a Formula?

A formula is a special type of equation that shows the relationship between different variables.

A variable is a symbol like x or V that stands in for a number we don't know yet.

Ex. The formula for finding the volume of a box is:
V = lwh

V stands for volume, l for length, w for width, and h for height.

### Cuboid

When l=10, w=4, and h=5, then:

V = 10 × 4 × 5 = 200

A formula will have more than one variable.

These are all equations, but only some are formulas:

x = 2y - 7    Formula (relating x and y)
a2 + b2 = c2    Formula (relating a, b and c)
x/2 + 7 = 0    Not a Formula (just an equation)

### Without the Equals

Sometimes a formula is written without the "=":

Ex. The formula for the volume of a box is:
lwh

But in a way the "=" is still there, because we can write V = lwh if we want to.

### Subject of a Formula

The "subject" of a formula is the single variable (usually on the left of the "=") that everything else is equal to.

Ex. in the formula
s = ut + ½ at2

"s" is the subject of the formula

### Changing the Subject

A very powerful thing that Algebra can do is to "rearrange" a formula so that another variable is the subject.

Ex. Rearrange the volume of a box formula (V = lwh) so that the width is the subject
divide both sides by h:    V/h = lw
divide both sides by l:    V/(hl) = w
swap sides:    w = V/(hl)
So now when we want a box with a volume of 12, a length of 2, and a height of 2, we can calculate its width:

w =    V/(hl)
=    12 / (2 × 2)
=    12 / 4
=    3

### Profit and Loss

#### Profit/loss = Sales price - Cost price

In case of profit
25% of  Cost Price (1/4 of CP) = 20% of Selling Price (1/5 of SP)
Similarly, 1/3 of CP  = 1/2 of SP

In case of loss
25% of  Selling Price (1/4 of SP) = 20% of Cost Price (1/5 of CP) Profit and Loss

### Estimation

#### That's the most important technique. This is not a secret that every successful candidate is using this technique during exams.

Example - 112 × 92
Simply 112 × 9 = 1008

You need to do all the calculations in your brain. Don't use paper. You need to divide complex calculations into parts and solve it in your brain without paper. That's how toppers do complex calculations during exams.

Right now it will be difficult for you to use this method but with practice, you will be able to do any complicated calculation within seconds.
ilarly, 1/3 of SP  = 1/2 of CP

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