Equation
Tips for Equation
Addition and Subtraction
Three things are important to remember
1. Changing the order of the addends (numbers you're adding) doesn't change their sum (what they equal when added together). Example:
a + (b + c) = (a + b) + c
2. Any number plus 0 (zero) equals itself. Example:
a + 0 = a
3. If two sides of an equation are equal, you can add or subtract the same amount to both sides, and they will still be equal. Example:
a = b
a + c = b + c
a - c = b - c
Here are two examples:
1. Solve: x + 79 = 194
Solution:
x + 79 = 194
x + 79 - 79 = 194 - 79
x = 115
You need to get the variable by itself. To
undo adding 79, subtract 79 from both sides.
2. Solve: x - 56 = 604
Solution:
x - 56 = 604
x - 56 + 56 = 604 + 56
x = 660
You need to isolate the variable.
To undo subtracting 56, add 56 to both sides.
Multiplication and Division
Six things are important to remember
1. Order of operations:
The operations inside parentheses () and brackets [] are done first.
Then any operations involving exponents (which you will learn about later).
Then do all multiplying and dividing from left to right.
Finally, do all addition and subtraction from left to right.
2. Multiplication can be written three different ways:
9 * x
9x
9(x)
3. A fraction bar is also a division symbol.
4. Changing the order of multipliers (numbers you're multiplying together) doesn't change their product (total when the numbers are multiplied together). Example:
ab = ba
5. Zero times any number is zero and 1 times any number is the number. Examples:
x(0) = 0
(0)x = 0
x(1)= x
1 * x = x
6. If two sides of an equation are equal, you can multiply or divide each side by the same quantity (number or equation) and it will still be equal. Examples:
a = b, c <> 0
ac = bc
(a / c) = (b / c)
Here are two examples:
1. Solve: 6x = 36
Solution:
6x = 36
(6x) / 6 = 36 / 6
x = 6
You need to get the variable by itself. To undo
multiplying by 6, divide by 6 on both sides.
2. Solve: x / 5 = 10
Solution:
x / 5 = 10
5(x / 5) = 10(5)
x = 50
You need to isolate the variable.
To undo dividing by 5, multiply both sides by 5
|
