Equations / Concepts Flashcards
If two different fractions are being multiplied, you can make one fraction by…
(a/b) * (c/d) =
Dividing a multiple of the numerators by a multiple of the denominators
(ac)/(bd)
if a/b = c/d then
ad = bc
If two different fractions are being divided, you can multiply by…
(a/b) / (c/d) =
Swapping the numerator and denominator of the second fraction
(a/b) * (d/c)
Then simplify: (ad) / (bc)
If two fractions are being added with the same denominator, you can make one fraction by…
a/c + b/c =
Adding the numerators and dividing by the common denominator
(a+b)/c
Or (ac+bc)/cc
If two different fractions are being added, you can make one fraction by…
a/b + c/d =
Multiplying the numerator of one by the denominator of the other, adding those values, and dividing by a multiple of the two denominators
(ad + bc) / (bd)
Simplify by…
(ac) / (bc) =
Removing the common multiplier
a / b
How do you factorize?
Divide by the lowest prime number until you get to 1
How do you find LCD by factorizing?
Multiply the highest power of each prime factors that occur in factorizing the two denominators
Then multiply the numerator and denominator of each fraction by the amount that would make the denominator equal the LCD
a^0 =
1
a^-n =
1/a^n
To multiply two powers of the same number…
a^m * a^n =
Add the exponents
a^m+^n
To divide two powers of the same number…
a^m / a^n =
Subtract the exponents
a^m-^n
To raise a power to a new power…
(a^m)^n =
Multiply the exponents
a^m^n
To raise a product to a power…
(ab)^n =
Raise each factor to the power
a^n * b^n
To raise a quotient to a power…
(a/b)^n =
Raise both numerator and denominator to the power
a^n / b^n
