When you are dealing with equations, you have to imagine that you have an old fashioned weigh scale, with say, 6 apples in each pan. If you divide the number of apples in the left pan by 2, you will have 3 apples in the left pan and still 6 in the right pan. The left pan will shoot up into the air, and the right pan will hit the table. To balance it again, you have to do exactly the same to the right pan as you did to the left, ie. you must also divide the number of apples there by 2.
| 6 apples = 6 apples | 6 apples ÷ 2 ≠ 6 apples | 6 apples ÷ 2 = 6 apples ÷ 2 |
This holds true for all operations. If you add 2 apples to the left pan, you must also add 2 to the right, if you subtract 2 or multiply by 3 on the left hand side, you must do EXACTLY the same to the other side, or the scale won't balance.
THIS IS YOUR PRIME DIRECTIVE.
WHATEVER YOU DO TO ONE SIDE OF AN EQUATION IN MATH, YOU MUST DO EXACTLY THE SAME TO THE OTHER SIDE,OR IT WON'T BALANCE.
Lets look at the examples
ADDITION
The x has 2 added to it
x + 2 = 6
The number that we want to disappear is the 2 on the left hand side. If we subtract 2 from both sides, look what happens:
x + 2 - 2 = 6 - 2
x = 4
SUBTRACTION
The x has 2 subtracted from it
x - 2 = 6
The number that we want to disappear is the 2 on the left hand side again. If we add 2 to both sides, look what happens:
x - 2 + 2 = 6 + 2
x = 8
Notice that we have done the opposite operation. When 2 was added to x, we subtracted 2 to eliminate the 2, and when 2 was subtracted from x we added 2 to eliminate the 2.
MULTIPLICATION
The x is multiplied by 10.
10x = 20
If we divide both sides by 10, the 10 cancels out, because 10 divided by 10 is 1.
Cancelling the 10's
Answer:
x = 2
Again we have done the opposite operation. Since the x was multiplied by 10, we divided by 10 to eliminate it.
DIVISION
The x is divided by 6
If we multiply (the dot means multiply) both sides by 6, the 6's cancel because 6 divided by 6 is 1.
Cancelling the 6's
Answer:
x = 24
Again we have done the opposite operation. Since the x was divided by 6, we multiplied by 6 to eliminate it.
If you have both multiplication/division and addition/subtraction in the same question, you do the addition/subtraction first, and then the division/multiplication. If there are brackets as well, you do those last.
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