dad's guide to fractions

8/7/2019 Dad's guide to fractions

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Dads Guide to Fractions

Fractions Overview:

A fraction is used to describe a piece of something or a part of a whole unit.

X Numerator = How many parts you have

Y Denominator = The size of the parts or how many parts it takes to make one whole unit.

The bottom number or denominator specifies the size of each part of 1 whole unit.

The top number specifies how many parts you have.

In the fraction 1/5 have one part and it takes 5 parts to make a whole.

To convert a fraction to a decimal, divide the top number by the bottom number.

Example 1/5 = .2

.2

5 1.0

10

Fractions can be equal but have different size parts.

Example

1/2, 2/4, 3/6 (NOTE is in simplest form)

You can convert a fraction to a different size part or denominator by multiply the top and bottom number by the

same factor.

Example:

1/2 x 2/2 = 2/4

This works because X/X or 2/2 or 5/5 or 10/10 all equal one. When you multiply something by one it stays the

same. This is the identity property of multiplications. This is true because you have all the parts 10/10 you

have all ten parts and it takes ten parts to make one whole unit.

Any whole number can be converted to a fraction by writing the number over 1. Example 10 = 10/1


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Adding and Subtracting Fractions:

Step One

When adding or subtracting fractions ALWAYS convert the fractions to a common denominator. You

can not add or subtract different size parts!!!!!

EXAMPLE:

1/5 + 1/3 = X Convert to a common denominator of 15.

Example:

1 x 3 = 3

5 x 3 = 15

1 x 5 = 53 x 5 = 15

Remember we have not changed either number, because 3/3 and 5/5 are both different ways of writing the

number ONE. One times a number is the same number!

Step Two

Since the denominator just describes the size of the part we do not add or subtract the bottom numbers. Once

we have a common denominator all we have to worry about is the number of parts or numerator.

Example:

3 + 5 = 8

15 15 15

The final step would be to put the fraction in simplest form!


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Multiplying Fractions

You do NOT need to find a common denominator when multiplying or dividing fractions!

Example:

2/3 x 6/8 = x

Step One

Cross Simplify!!!!! This make things a lot easier!

2 63 8

Look at the diagonal pairs of numbers and reduce them by common factors. 2 and 8 can both be divided by 2.3 and 6 can both be divided by 3.

Step Two

Multiply the numerator times the numerator and denominator times the denominator.

In the simplified problem above this would be easy:

1 x 2 = 21 x 4 = 4

Lets do a second example:

3 x 1 = 3

5 x 4 = 20

Step 3 Simplify!

In the first example we would need to simplify 2/4 to 1/2.


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Dividing Fractions

You do NOT need to find a common denominator when multiplying or dividing fractions!

If you know how to multiply fractions dividing is EASY!

First we need to know what a reciprocal fraction is. A reciprocal fraction is where the numerator and

denominator get switched. Another way to say it is you flip the fraction upside down.

Examples

3/4 reciprocal is 4/3, 3/5 reciprocal is 5/3, 7/3 reciprocal is 3/7

(Interesting Note: A fraction times its reciprocal is always 1)

Step One

When dividing fractions you actually multiply the two fractions but you use the reciprocal of the fraction you

are dividing by.

Example:

2/3 -- 4/5 = X Flip the number you are dividing by in this example the reciprocal of 4/5 is 5/4 so you

now have a multiplication problem that looks like this

2/3 x 5/4 = X

Step Two

Cross Simplify!!!!! This make things a lot easier!

2 53 4

Look at the diagonal pairs of numbers and reduce them by common factors. 2 and 4 can both be divided by 2.

3 and 5 do not have any common factors so they can not be simplified.

Step Two

Multiply the numerator times the numerator and denominator times the denominator.


5/5

In the simplified problem above this would be easy:

1 x 5 = 53 x 2 = 6

Step 3 Simplify!

The answer above is 5/6. It is in simplest form.

Fractions in Equations

When a variable is being multiplied by a fraction you will multiple both sides by the reciprocal to simplify.

Example:

2/3Z = 12

3/2 x 2/3Z = 12 x 3/2

Z=18

A fraction times its reciprocal is always ONE.

Another way of looking at this is we are multiplying both sides by 2/3. The opposite of multiplication isdivision. When dividing fractions we multiply by the reciprocal!!!

If you have a fraction that has a numerator of 1 like 1/3, if you are multiplying the variable by 1/3 (1/3Z) this isthe same thing as dividing the number by the denominator in this case Z/3. See below

1/3Z = 1 x Z = Z3 x 1 = 3

dad's guide to fractions

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