Equations and Formulae

Difference between equations and formulae

An equation contains unknown quantities; for example,

3x + 2 = 11.

This equation can be solved to determine x.

A formula links one quantity to one or more other quantities; for example,

C = 2πr

The formula can be used to determine C for any given value or r

Ask Questions on Algebra

Ask any questions you may have on algebra

Please post your questions and I'll reply asap.

Factorising

Factorising

Factorising (put in brackets) can be said to be the 'opposite of expanding brackets'.

To factorise an expression live 3w+12 you find out the highest factor the terms have in common.
In this case it is 3. That means 3 needs to be outside the bracket.
Then you find out what you multiply by 3 to get 3w and what you multiply by 3 to get 12.

3 x w = 3w and 3 x 4 = 13 since 3 is the highest factor both terms have in common.

so factorising 3x+12 gives 3(w+4).

Examples:

Factorise the following expressions

1) 4y + 12
The highest common factor is 4, so 4 has to be outside the bracket.
4 x y = 4y and 4 x 3 = 12

so 4y + 12 = 4(y + 3)

2) 30b + 42
The highest common factor is 6, so 6 has to be outside the bracket.
6 x 5b = 30b and 6 x 7 = 42

so 30b + 42 = 6(5b + 7)

3) 6v + 15w
The highest common factor is 3, so 3 has to be outside the bracket.
3 x 2v = 6v and 3 x 5w = 15w

s0 6v + 15w = 3(2v + 3w)

Expanding Brackets

Expanding or multipying out brackets.

To expand a bracket such as 3(x +2) you multiply every term in the bracket by 3 making it 3x + 6.

Examples

Expand these brackets:

1) 4(y + 3) = 4y + 12
2) 6 (5b + 7) = 30b + 42
3) 3 (2v + 5w) = 6v + 15w

Spot the mistake

Spot the mistake:

3(x + 5) = 3x + 5

4(xy + y) = 4x + 4y

7(w - 4) = 7w + 28

6(a + 2) = 6a + 12

6a + 7a + 2b = 15ab

Solving Simple Linear Equations

A lot of students seem to find it difficult to solve equations. The act of solving equations is all about doing the same thing to both sides of the equation and making sure you end up with the letters on one side and the numbers on the other side of the equation.

For Example:

Find the value of y in these equations:

y + 3 = 10
Subtract 3 from both sides
y = 7

y – 3 = 10
Add 3 to both sides
y = 13

3) 4y + 5 = 21
Subtract 5 from both sides
4y = 16
Divide both sides by 4
y = 4

In the first equation we subtracted 3 because it was + 3. So the general rule is to use the inverse operation.

Importance of Algebra

I would be making thousands of pounds if I got a penny every time one of my students asks ‘Miss when will I ever use Algebra in my life?’ or every time an adult says ‘I hated maths in school especially Algebra’.

It’s amazing that people don't believe algebra is used very often, but we use it every day in different applications, sometimes without even knowing it! One fascinating thing about algebra is that a mastery of algebra helps in problem solving and thinking in an abstract way.

Some importance of algebra:

A typical example of when algebra is used in everyday life is when you have a certain amount of money say £15 and you want to buy an item that cost £3 each you would have to solve the equation 3x = 15 to find out how many of the items you can buy with £15.

Algebra is used in calculations involving simple formulas for example the formula used in converting °Celsius temperature into °Fahrenheit.

Banks use algebra to work out interest rates.

Algebraic reasoning and formulas are used in spreadsheet calculations. Spreadsheets are used by almost all businesses.

Shops use algebra to predict the demand of a particular product.

Builders use algebraic calculations during constructions to figure out measurements, angles etc.

Almost every maths problem which involves money, time, distance, area, perimeter or volume of something, comparing prices, rent and similar situations are solved using algebra.

The list goes on... Algebra is a very important branch of mathematics and is often referred to as the language of mathematics!

Please feel free to comment.