Doing the Opposite

Opposites:
• The opposite of addition is subtraction.
• The opposite of subtraction is addition.
• The opposite of multiplication is division.
• The opposite of division is multiplication.
• There are other opposites (square root/square, etc...), but those are for another time.

Examples:



For x - 1 = 3, The 1 is being subtracted from the x, so addition must be used.

x - 1 = 3

  + 1   + 1     Add a 1 to each side to get rid of the 1 from the left side of the equation.




For 3x = 15, The 3 and the x are being multiplied with each other, so division must be used.

3x = 15

--   --
3     3         Divide both sides by 3 to get ride of the 3 from the left side of the equation.




For x + 5 = 9, The 5 is being added to the x, so subtraction must be used.

x + 5 = 9

  - 5   - 5	Subtract 5 from each side to get rid of the 5 on the left hand side of the equation.




For x/2 = 4, The x is being divided by 2, so multiplication must be used.

x/2 = 4

*2    *2        Multiply both sides by 2 to get rid of it from the left hand side of the equation.




Return to the Equation Solving page.

Go to the Practice page.

Go to the Order of Operations page.

Return to the  page.

Other Links

Get Math Homework Help from the Discovery School web page.

Go to the Math Forum at Swarthmore College.

Go to the SCORE Math page by the Kings County Office of Education.

See the California Mathematics Academic Standards for K - 12.