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Basic Steps of Adding Fractions

We have to start somewhere, so let's start with adding fractions. The most important thing about adding fractions is that they need to be "like" fractions. That means you need to make sure that both addends (numbers being added) have common denominators. 5/6 + 6/7 may look hard, but when they have the common denominator of 42 it is an easy addition problem. Let's get started.

Adding Fractions with the Same Denominators

We'll start with easy ones. In class, you will be given addends with the same denominator. All you have to do is add up the numerators (numbers on top) and then simplify your answer. Let's try some.

1/13 + 6/13 = ?
• Create common denominators. They are already the same at 13, so we do nothing.
• Add the numerators from the two addends. 1 + 6 = 7
• Write the sum of the numerators above the common denominator. 7/13.
•Simplify the fraction. 7/13 cannot be simplified. You are done.
Answer: 1/13 + 6/13 = 7/13

5/9 + 1/9 = ?
• Create common denominators: The denominators are the same. Do nothing.
• Add numerators: 5 + 1 = 6
• Write the sum of the numerators above the common denominator: 6/9.
• Simplify: 6 and 9 have a common factor of 3. When you divide the numerator and denominator by 3 you get 2/3.
Answer: 5/9 + 1/9 = 6/9 = 2/3

Creating Common Denominators

Let's get more advanced. What about adding unlike fractions? You don't have common denominators. We've looked at creating equivalent fractions in our earlier pages. You will use that process here.

1/7 + 1/3 = ?
•Create common denominators: We have 7 and 3. They have no common factors, so let's just multiply to create two new equivalent fractions. Remember how we multiplied by equivalents of 1? It went like this...
1/7 = 1/7 * 1 = 1/7 * 3/3 = (1*3)/(7*3) = 3/21
1/3 = 1/3 * 1 = 1/3 * 7/7 = (1*7)/(3*7) = 7/21
You now have the common denominator 21. You can now rewrite the problem as 3/21 + 7/21 = ?
• Add numerators: 3 + 7 = 10
• Write the sum of the numerators above the common denominator: 10/21
• Simplify: 10/21 cannot be simplified. You are done.
Answer: 1/7 + 1/3 = 10/21

Adding Mixed Numbers

You've got common denominators and unlike fractions under control now. Let's look at an example with mixed numbers before we go. Our first example will look at mixed numbers that have common denominators.

2 2/9 + 4 3/9 = ?
• Check for common denominators: They are like fractions with a denominator of 9. Do nothing.
• Add the numerators from each fraction: 2 + 3 = 5
• Write the sum of the numerators above the common denominator: 5/9
• Add the whole numbers: 2 + 4 = 6
• Write out the mixed number: 6 5/9
• Simplify: 5/9 can't be simplified. You are done.
Answer: 2 2/9 + 4 3/9 = 6 5/9

What happens if you wind up with an improper fraction in your answer? You need to simplify that improper fraction and then add the whole numbers. We'll use an example like the last one. We just made the first addend a bit bigger.

2 7/9 + 4 3/9 = ?
• Check for common denominators: They are like fractions with a denominator of 9. Do nothing.
• Add the numerators from each fraction: 7 + 3 = 10
• Write the sum of the numerators above the common denominator: 10/9
• Add the whole numbers: 2 + 4 = 6
• Write out the new mixed number: 6 10/9
• Simplify: This example has an improper fraction that you have to simplify. You need to use division to create a new fraction. 10 ÷ 9 = 1r1. The new mixed number will be 1 1/9. You will need to add that new whole number to your original 6. The entire process goes like this...
6 10/9 = 6 + 10/9 = 6 + 1 1/9 = 6 + 1 + 1/9 = 7 1/9
Answer: 2 7/9 + 4 3/9 = 7 1/9

Let's put it all together with an example that has unlike fractions. You're going to need to make common denominators with this one and simplify an improper fraction.

2 5/8 + 5 3/4 = ?
Common denominators: Start with the fractions. We've got 4 and 8. They have a common factor of four so we only need to fix the 3/4 fraction.
3/4 = 3/4 * 1 = 3/4 * 2/2 = (3*2)/(4*2) = 6/8
Add the numerators: 5 + 6 = 11
Rewrite fraction: Sum of the numerators above the common denominator: 11/8
Add whole numbers: 2 + 5 = 7
New mixed number is 7 11/8
Simplify: We've got an improper fraction. Start dividing... 11 ÷ 8 = 1r3. Your new mixed number is 1 3/8. Add the new mixed number to the original 7.
7 11/8 = 7 + 11/8 = 7 + 1 3/8 = 7 + 1 + 3/8 = 8 3/8
Answer: 2 5/8 + 5 3/4 = 8 3/8

Now it's up to you to practice. If you want to keep going, continue on to subtract fractions. It's very close to addition, so you will do fine.

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