Rational Numbers

Summary

Definition of 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

What is an equivalent fraction?

Vs.Mixed

NumbersImproper Fractions

What is a mixed number?

The sum of a whole number and a fraction

&

These are examples of mixed numbers

What is an improper fraction

A fraction with a numerator greater then the denominator

NUMERATOR denominator

These are examples of improper fractions

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Changing an improper fraction to a mixed number

= =

Notice how the denominator stays the same when converting to an improper fraction to a mixed number

=

Changing a mixed number into an improper fraction

= =

Notice how the denominators stay the same when converting from a mixed number to an improper fraction

= =

Fractions are FUNNY!

Were here to show you the rules!

Adding Fractions

Subtracting Fractions

Multiplying Fractions

Dividing Fractions

Adding 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.

Adding Fractions• 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.

Example

• 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!

2 4

12 6

12 6 72

Example continued…• 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

Subtracting Fractions

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

subtract the numerators!

Example of Subtraction

3 2

4 53 5 2 4

4 5 5 415 8

20 2015 8

207

20

Multiplying Fractions

Multiplying fractions is easy

Multiple the numeratorsMultiple the denominators

Example of Multiplying

1 2

3 51 2

3 52

15

Dividing Fractions

Dividing fractions requires one more step

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

Example of Dividing 2 6

5 72 7

5 62 7

5 614

30

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