## Adding Fractions

Adding fractions is a very important skill to learn when dealing with complex equation solving. You will encounter fraction addition when dealing with more difficult algebra and geometry. So let’s take a look at a few methods to solve problems that involve simple addition of fractions.

### Vocabulary

- Numerator – This is the top number of a fraction
- Denominator – This is the bottom number of a fraction
- Factor – Number that divides evenly into another number without remainder
- Common Denominator – When denominators of two or more fractions is the same

### Strategy: What to look for…

When you are looking to add fraction, you first need to determine how complex the problem is and then formulate a plan on which steps are necessary and which can be skipped. The most important thing to remember with adding fraction is that you need to ensure that you are adding fractions with COMMON DENOMINATORS.

### Same Denominator

**2/3 + 1/3 =?**

Since they already have common denominators, you can simply add the numerators. This is how the above is solved:

2/3 + 1/3 = 3/3 (or 1)

### Differing Denominator

**2/3 + 1/6 =?**

When the denominator (bottom number) is different from the denominator on the second fraction you will need to find a common factor between the two numbers. Let’s take a look at the denominator and possible factors:

- 2/3 – Denominator is 3
- 1/6 – Denominator is 6
- Factors of 3 & 6 – 0,1,3,6

In this example we have a few choices, but it is best to choose the largest common denominator. By choosing the largest common denominator, you decrease the chance that you will need to further reduce the fraction after getting a solution.

Once you have determined the largest common denominator, you will need to convert any fraction without that denominator. Below I have selected ‘6’ as the largest common denominator:

2/3 – You need to multiply this my 2/2 to bring the denominator to 6

2/3 * 2/2 = 4/6

1/6 – You need to multiply this by 1/1 to bring denominator to 6.

1/6 * 1/1= 1/6

Now that you have the same denominator, you just add the numerators (top number):

4/6 + 1/6 = 5/6

### More examples of adding fractions

**3/8 + 4/24 =?**

Common factors: 0, 1, 2, 4,8,24 (24 is best choice)

3/8 * 3/3 = 9/24

4/24 * 1/1 = 3/24

9/24 + 3/24 = 12/24 (can reduce further to 1/2)

**10/5 + 5/10 =?**

Common factors: 0, 1,2,5,10 (10 best choice)

10/5 * 2/2 = 20/10

5/10 * 1/1 = 5/10

20/10 + 5/10 = 25/10 (can further reduce to 2 5/10 or 2 1/2)

### ADDING FRACTIONS RECAP

- Determine common denominator
- Convert all fractions to same denominator
- Add numerators
- Reduce fractions if possible

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