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Multiplying and dividing negative numbers

When a positive number is multiplied by a negative number the answer is negative.

When two negative numbers are multiplied together the answer is positive.

For division, the rules are the same as multiplication

A minus and a plus make a minus.

Adding and subtracting negative numbers

For adding and subtracting with negative numbers a number line is very useful.

-1 - 4 = -5

Start at -1 then go left 4 places. To get the answer.

This always applies when subtracting negative numbers. It is possible to replace two signs next to each other by one sign as follows.

+ + = +

- - = +

- + = -

+ - = -

When two signs next to each other have been replaced by one sign in this way, the calculation is completed using the number line.

Substituting numbers into a formula

y= 5 (x - 4) Find y when x = 7 m = 8 + 3n + nc

y = 5 (7 - 4) Find m when n = 5 and c = 7

y = 5 * 3 m = 8 + (3 *5) + (5 *7)

y= 15 m = 58

negative numbers can be subsituited into formulas

m = 6- n y= 3x + w

Find m when n = -2 Find y when x= 4 and w = -8

m= 6- (-2) y= (3*4) + (-8)

m= 6+2 y= 12-8

m= 8 y = 4

Equations are like weighing scales which are balanced. the scales remain balanced if the same weight is added or taken away from both sides. Whatever you do to one side you have to do to the other side.

Rules for solving equations

Equations can be solved in the same way as the weighing scale problems were solved.

the main rule is Do the same thing to both sides.

If you need to you may:

add the same thing to both sides

subtract the same thing from both sides

multiply both sides by the same thing

divide both sides by the same thing

Mixed equations

11 = 3 + 2n

-3 -3

8= 2n

divide 2 both sides

4= n

Multiply out Single Brackets

The number outside the brackets multiplies each number inside the brackets.

eg . Multiply out 3 (a + b)

3 ( a+b) = 3* a + 3 * b

= 3a + 3b

Expand the bracket is another way to say multiply out the bracket

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