# Fraction Unit

## Adding Fractions - The Clock Model

Using the clock model, you can turn fractions into minutes, add them together, and put them back into fractions. The clock model is often found the easiest way to add fractions.

Bench Marks
1/2 = 30 minutes

1/3 = 20 minutes

1/4 = 15 minutes

1/6 = 10 minutes

1/12 = 5 minutes

These are the most common fractions to use, and are also the simplest fractions to remember because they're all unit fractions!

Examples of adding fractions using the clock model;

1.) 1/2 + 1/3 = 30 minutes + 20 minutes = 50 minutes = 50/60 or 5/6

2.) 2/3 + 1/4 = 40 minutes + 15 minutes = 55 minutes = 55/60 or 11/12

You can also use or even draw a model of a clock to divide into whatever the desired denominator is, for example, you can take your clock and split it into a half and you can see that by the numbers that it is 30 minutes. How easy is that?!

## Adding Fractions - Lowest Common Multiples

Adding fractions using lowest common multiples is very easy. If you have two fractions that have two different denominators, just list all the multiples of each number and then find the lowest one. Then multiply the denominator by whatever number you need to, to get to the lowest multiple. Make sure that you do this to both fractions and don't forget that whatever you do to the bottom, you must do to the top. Then, add the numerators from each fraction and the denominators and voila!, you have your answer.

## Adding Fractions- The Money Model

Adding fractions using the money model is simple. You just have to turn the fractions that you are adding into cents and then add them together. After that, just turn your answer back into a fraction and you have your answer.

Bench Marks

1/4= 25 cents

1/2= 50 cents

1/5= 20 cents

1/10= 10 cents

1 whole= \$1

Examples

1/2 + 1/10= 50 cents + 10 cents= 60 cents= 60/100 or 3/5

1 + 2/5= 100 cents or one dollar + 40 cents= 140 cents or \$1.40=1 40/100 or 1 2/5

## Equivalent Fractions

Equivalent fractions are just fractions that are the same, even though they have different numerators and denominators.

## Multiplying Fractions

Multiplying is the easiest to do out of dividing, subtracting, multiplying, and adding. All you have to do is multiply the numerator by the numerator and then multiply the denominator by the denominator. If you are multiplying mixed numbers, just turn it into a improper fraction and do the exact same thing.

Examples

2/4 x 5/6= 10/24 or 5/12

3/5 x 1/3= 3/15 or 1/5

## Dividing Fractions

Dividing fractions; it may sound very hard because dividing actual numbers comes later in the grades, but it's the exact opposite when it comes to fractions. When you are dividing fractions, you just have to switch the numerator and denominator of the second fraction and then multiply the fraction. If you are dealing with fractions and whole numbers, just turn the whole number into a fraction by putting the denominator as 1. After that, all you have to do is do the same thing as above. Although, if it is a unit fraction, you can just divide the whole number by the denominator of the fraction, and you have your answer.

Examples

4 ÷ 1/4= 1

1/3 ÷ 2/6= 1/3 x 6/2= 6/6 or 1 whole

2 ÷ 1/6= 3

2/5 ÷ 1/2= 2/5 x 2/1= 4/5

## Subtracting Fractions

Subtracting Fractions is basically the same as adding fractions, but, you are subtracting. Just list all the multiples of each fraction's denominator and choose one that shows up in both lists. It could be the lowest or the highest. Then multiply the denominator by whatever number you need to, to get the lowest or highest multiple. Make sure that you do this to both fractions. Don't forget, whatever you do to the bottom, you must do to the top.

If both fractions already have the same denominator, just subtract the numerators and keep the denominator the same.

Examples

Lowest common multiple is 15~ 4/5 - 2/3= 4x3/5x3- 2x5/3x5= 12/15 -10/15= 2/15

3/5 - 4/10= 3x2/5x2 - 4/10= 6/10 - 4/10= 2/10 or 1/5

## Reducing Fractions

Reducing fractions is just taking a fraction and making it smaller. You make it smaller by dividing the numerator and the denominator by a number that you can divide both by.

Examples

30/60= 15/30= 3/6= 1/2

20/60= 10/30= 5/15= 1/3

15/25= 3/5

24/32= 12/16=6/8=3/4