Pre-Algebra Summary Calculator

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Fractions

Operation	Comments
Adding Fractions	Denominators Must match
Subtracting Fractions	Denominators Must match
Multiplying Fractions	Multiply the top numerators to get the answer numerator and the bottom denominators to get the answer denominator.
Dividing Fractions	Multiply 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 Numbers	c/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

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