Operations with rational numbers

Any number that can be made by dividing one integer by another. The word comes from "ratio".
This means that rational numbers include positive and negative numbers, whole numbers, fractions and decimals.

Two fractions that stand for the same number

Mixed Numbers Improper Fractions

The sum of a whole number and a fraction

& These are examples of mixed numbers

A fraction with a numerator greater then the denominator
NUMERATOR denominator

These are examples of improper fractions
&

Adding Fractions Subtracting Fractions Multiplying Fractions Dividing Fractions

Adding fractions requires a common denominator To find the common denominator between fractions simply multiply the denominators and this is the common denominator. this number may be large so try and find a number that all denominators will divide into evenly.

However this number may be large so try and find a number that all denominators will divide into evenly.
Adding fractions requires a common denominator To find the common denominator between fractions simply multiply the denominators and this is the common denominator.

We need to find a C.D. in order to add these fractions.
If we multiply the denominators
that is a big number…but both 6 and 12 divide evenly (without a remainder) into 12.
The first fraction already has a denominator of 12 so we leave it alone but what do we have to multiple the second denominator by in order to change it to 12?
If you said 2…you are right!

If you multiply the denominator by 2 you MUST multiply the numerator by two also!
Remember: whatever you do to the bottom you must do to the top.
Once you have common denominators…add the numerator and KEEP the Common Denominator.

Same rule…you have to get a common denominator before you subtract the numerators!

Multiplying fractions is easy Multiple the numerators Multiple the denominators

Dividing fractions requires one more step Keep the first fraction the same Change the multiple to divide And FLIP the second fraction

When the fraction is “flipped” it is called the INVERSE

Operations with rational numbers

by Kelly Scallion

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