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Fractions Operations at a Glance

Addition, Same Denominators:

PROCESS: To add or subtract fractions, you
must have the SAME DENOMINATORS. If the
denominators are already the same, simply add (or
subtract) the numerators & keep the denominator
the same in the answer. Don’t forget to reduce
your answer to lowest terms . For example:

Addition, Different Denominators :

PROCESS: To add fractions, with different
denominators, you must first CHANGE them to the
SAME denominators. Do this by multiplying one or
both
fractions by the SAME NUMBERS, to increase its
value. Then simply add the numerators and any
whole numbers separately . Don’t forget to reduce
your answer to lowest terms . For example:

Subtraction, Different Denominators:

To subtract fractions with different denominators,
first use multiplication to create equivalent
fractions with the SAME denominators. Then
subtract the numerators first . Subtract any whole
numbers second. Keep the denominator he same
and simplify the answer.

Subtraction with Borrowing

Sometimes when subtracting you may find you don’t
have enough value in the top fraction’s numerator to
do the subtraction. When this happens we borrow
from the whole number, adding the borrowed whole
number to the existing fraction to increase its value.


whole number, it is written as fraction with the same
numerator/same denominator (one whole). This
whole is then ADDED to the existing fraction to
combine the two into a new , improper fraction, which
we then use for subtracting.

Multiplication of Fractions:

When multiplying fractions, IT DOES NOT MATTER whether the denominators are the same or different!
However, you cannot multiply mixed numbers – you must change them to improper fractions. Also, you can
sometimes use the process called cancellation before multiplying. Using cancellation can save you from having
to simplify your answer. To use cancellation, before multiplying, FACTOR all numbers to prime & rewrite the
problem. Now cancel any “ common factors ” shared in ANY numerator with ANY denominator. Multiply any
remaining factors to finish and simply your final answer.

Division of Fractions :

To divide fractions you must first change any whole or mixed numbers to improper fractions. Then invert (or
flip) EVERY fraction that directly follows a division sign . You should then factor each numerator & denominator to
prime so you can cancel common factors. Multiply any factors that remain and simplify your answer.

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