# Pre-Algebra Summary Calculator

Fractions
OperationComments
Adding FractionsDenominators Must match
Subtracting FractionsDenominators Must match
Multiplying FractionsMultiply the top numerators to get the answer numerator and the bottom denominators to get the answer denominator.
Dividing FractionsMultiply the top fraction by the reciprocal of the bottom fraction. a/b ÷ c/d = a/b x d/c
Mixed Numbers to Fractions:
 a & b/c = (c * a) b

Fractions to Mixed Numbersc/b where c is greater than b is INT(c/b) & (c - b)/b

Order of Operations: 40(3 + 5) - 92
Follow the PEDMAS Rule: Parentheses, Exponents, Division, Multiplication, Addition, Subtraction

Exponents:
xn = x multipled by itself n times
53 = 5 x 5 x 5 = 125

Square Roots
Check to see if a number is a square, i.e., √81 = 92 = 9 x 9
For numbers that do not have a square, i.e., √40, we find the highest square in it's factors.40 = 20 x 2, 10 x 4, 8 x 5, and we know that √4 = 2, so we have 2√10

Prime Factorization and Prime Power Decomposition
Prime Factorization: Factor a number into a product of primes, i.e., 40 = 2 x 2 x 2 x 5
Prime Power Decomposition: Combine common prime numbers from the Prime factorization, i.e., 40 = 23 x 5
Proportions:
 a b
 =
 c d

You can cross multiply to get a x d = b x c

Like Terms