Rational Number Operations Rules
Addition: To combine or put together.
N: (+) + (+) or (-) + (-) => Add the numbers, keep the sign.
(+) + (-) or (-) + (+) => Subtract the numbers, take the sign of
the dominant number.
F: Make common denominators (Find GCM, use multiple to
create equivalent fractions).
Add the numerators, keep the denominators.
Simplify if possible.
D: Line up place values.
Add normally & bring down the decimal point.
Multiplication: Groups of numbers or to add repeatedly.
N: (+) x (+) or (-) x (-) => Multiply. Answer is positive (+).
(+) x (-) or (-) x (+) => Multiply. Answer is negative (-).
F: If there are whole or mixed numbers, convert to improper
fractions.
Simplify by cancelling common factors.
Multiply across.
Simplify if possible.
D: Multiply as if they are whole numbers.
Count the number of decimal places in the two factors.
The product contains the total number of decimal places in
the two factors.
Subtraction: To remove, take apart, or find the difference.
N: (+) - (+) or (-) - (-) => Subtract the numbers. If the first
number is dominant, keep the sign. If the second number
is dominant, use the opposite sign.
(+) - (-) or (-) - (+) => Add the numbers, keep the sign of the
first number.
If using the traditional subtraction set-up, always put the
DOMINANT number on top.
F: Make common denominators (Find GCM, use multiple to
create equivalent fractions).
Subtract the numerators, keep the denominators.
Simplify if possible.
D: Line up place values.
Subtract normally & bring down the decimal point.
Division: Split into groups of numbers or fair sharing.
N: (+) ÷ (+) or (-) ÷ (-) => Multiply. Answer is positive (+).
(+) ÷ (-) or (-) ÷ (+) => Multiply. Answer is negative (-).
F: If there are whole or mixed numbers, convert to improper
fractions.
Change ÷ to × and use the reciprocal (flip) of the second
fraction. (aka “Keep, Switch, Flip”)
Simplify by cancelling common factors.
Multiply across.
Simplify if possible.
D: Move the decimal in the divisor (second number) until it is a
whole number.
Move the decimal in the dividend (first number) the same
number of places.
Divide normally.