User:Jackieguyach
PREALGEBRA
WHOLE NUMBERS Addition and Subtraction Addition is to find the sum or total of numbers. Subtraction is to find the difference between two or more numbers. EXAMPLE:
387 97578 7,345 295 +65492 6,222 --- ------ ----- 682 163070 13567
INTEGERS Integers are the positive and negative numbers. Numbers to the left of 0 are negative, and numbers to the right of 0 are positive.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 <----------------------------------------------------->
Multiply and Divide Integers When you multiply and divide integers, if the number as the same sign the answer is always positive. When you have a positive and a negative sign, the answer is negative. If you have a odd number of negative signs your answer will be negative. EXAMPLE: Multiply
-4(3) = -12 (-2)(-2) = 4 4(-3) = -12 (3)(2) = 6
Divide
-27 % 9 = -3 (-27) % 9 = -3 (-27) % (-9) = 3 27 % 9 = 3
ORDER OF OPERATIONS The order of operations must be completed in order to get the right answer. -Do everything in parentheses first. -Simplify. -Multiply and divide, Left to right. -Add and subtract, left to right. EXAMPLE:
2-(8-10) % 2 parentheses first 2-(-2) % 2 Simplify 2+4 % 2 Multiply & divide 2+2 Add 4
FRACTIONS Dividing Fractions When dividing Fractions the first step is to flip the second number. Second, make the problem multiplication. EXAMPLE:
4 8 = 4 15 = 2 * 2 * 3 * 5 = 3 = 1.5 - % - - * -- ------------- - 5 15 5 8 5 * 2 * 2 * 2 2
Adding Fractions In order to add fractions you must have the same denominator. Second, you add the top numbers together and keep the denominator. EXAMPLE:
5 + 7 = 5 + 7 = 12 = 3 - - ----- -- - 16 16 16 16 4
Subtracting Fractions The same with subtracting, you must have the same denominator on the bottom befor you can subtract. After you have the denominator, then you subtract the top numbers. EXAMPLE:
5 - 3 = 5 - 3 = 2 = 1 - - ----- - - 8 8 8 8 4
DECIMALS Addition of decimals When you add decimals you must allign the decimals. Then you add the problem. EXAMPLE:
35.8 45.32 185.72 6.76 74.32 + 8.23 ------ ----- 263.62 60.31
Multiplication of decimals To multiply decimals you must line up the numbers, multiply, then count the spaces behind all decimals. EXAMPLE:
0.000073 745.333
0.052 x 45.8
146 -------
X 365 34136.2514
---------
0.00003796
POLYNOMIALS Monomial is a polynomial with one term. EXAMPLE. 4x^ Binomial is a polynominal with two terms. EXAMPLE: 7x^ = 4x Trinomial is a polynomial with three terms. EXAMPLE: 3x + 5y^ - 6x^ When adding polynomials you can add horizontal or vertical. First you must add the coefficients with like terms. Then arrange like terms in order.
SCIENTIFIC NOTATION When writing numbers in scientific notation, write out the numbers in decimal notation then times by 10. EXAMPLE:
2,370,000 = 2.37 x 10 to the six power 934,800,000 = 9.348 x 10 to the eight power
PROPERTY OF EQUATIONS Addition To find the sum of addition property you must subtract the same number from each side. EXAMPLE:
X + 8 = 4 y + 3 = 2
X + 8 - 8 = 4 - 8 y + 3 - 3 = 2 - 3
X + 0 = - 4 y + 0 = -1`
X = - 4 y = - 1
Multiplication When you multiply properties of equations, multiply each side. EXAMPLE:
48 = -12y = -4y = -4 -- ---- -12 -12
PROPORTIONS A true proportion is when two ratios are equal on both sides. Use the criscross method. EXAMPLE:
15 = 9 3 * 90 = 270 -- - 15 * 18 = 270 3 18
This is a true proportion If your proportion has two different answers the proportion is not true. EXAMPLE:
2 = 13 2 * 304 = 608 - -- 13 * 47 = 611 47 304
This is not a true proportion