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.

a

b

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

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= =

=

= =

= =

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

denominatorTo 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 denominatorsthat 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!

2 4

12 6

12 6 72

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.

2 4

12 62 4 2

12 6 22 8

12 1210

12

Same rule…you have to get a common denominator before you

subtract the numerators!

3 2

4 53 5 2 4

4 5 5 415 8

20 2015 8

207

20

Multiplying fractions is easy

Multiple the numeratorsMultiple the denominators

1 2

3 51 2

3 52

15

Dividing fractions requires one more step

Keep the first fraction the sameChange the multiple to divide And FLIP the second fraction

2 6

5 72 7

5 62 7

5 614

30

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