Get ready to become an expert at adding fractions & mixed numbers!

Adding with the same denominator. Adding fractions that have the same denominator is simple. You add the numerators and write the sum over the common denominator. If your answer is an improper fraction, re-write it as a mixed number.

3 5 4 5 + 2 5 7 5 = 1 Example: Solve on your own. Click for the answer!

Adding fractions with different denominators. Adding fractions with different denominators is impossible. In order for fractions to be added, they must have the same number of parts. The denominator represents the number of parts. Therefore, you must find a common denominator.

Why? You have two pies. One cut in 4 slices and the other cut in three slices. You at 1/4 of one pie and 1/3 of the other pie. How much pie did you eat all together? A common denominator is necessary so that each piece of pie is the same size and can be added with the others. What is a common denominator for 3 and 4? + = 12

What are the steps? To add fractions: Find a common denominator if there isn’t one already. Convert each of your fractions into an equivalent fraction using the common denominator. Add the numerators. Write the sum as the numerator in your answer. The denominator will be your common denominator. If your answer is an improper fraction, convert to a mixed number. Simplify if necessary.

What is the least common denominator? 3 5 4 7 Click for the answer! + 35

How do you re-write the fractions using the common denominator? 3 5 x 7 21 35 Click for the answer! = x 7 4 7 35 20 x 5 = + x 5

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 3 5 4 7 + 21 35 20 35 41 35 6 35 + = = 1

What is the least common denominator? 7 8 1 3 Click for the answer! + 24

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 7 8 1 3 + 21 24 8 24 29 24 5 24 = + = 1

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 5 6 3 4 + 10 12 9 12 19 12 7 12 + = = 1

When you add multi-digit numbers, do you add from: Right to left? Left to right?

Right to Left! For example: 485 123 You add 5+3 first! +

When we add mixed numbers, we do the same thing!

Add the fractions before the whole numbers Right to Left! Add the fractions before the whole numbers For example: 4 ¼ 1 ¼ 5 You add ¼ + ¼ first! + 2 4

But Why?

Click to move through the problem visually. We add the fractions before the whole numbers in order to make as many “wholes” as possible. 1 4 5 6 Example: Click to move through the problem visually. 1 2 + 1 4 3 12 = 5 6 10 12 + + 1 12 1

We add the fractions before the whole numbers in order to make as many “wholes” as possible. 1 4 5 6 Example: Click to move through the problem visually. 1 2 + You already figured out that + is 1 1 12 Next, add the whole numbers 1 + 2 = 3 1 1 4 5 6 1 12 1 12 1 12 3 + 1 = 4

What are the steps? To add mixed numbers: Find a common denominator if there isn’t one already. Convert each of your fractions into an equivalent fraction using the common denominator. Add the numerators. Write the sum as the numerator in your answer. The denominator will be your common denominator. If your answer is an improper fraction, convert to a mixed number. Simplify if necessary. Add the whole numbers. Combine with the fraction sum if necessary.

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 1 5 7 8 2 + 4 2 + 4 = 6 8 40 35 40 43 40 3 40 + = = 1 3 40 3 40 6 + 1 = 7

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 5 6 2 3 5 + 3 5 + 3 = 8 5 6 4 6 9 6 1 2 + = = 1 1 2 1 2 8 +1 = 9

Solve: Rewrite using the least common denominator, then solve on your own. Click for the answer! 3 4 1 3 1 + 1 1 + 1 = 2 9 12 4 12 13 12 1 12 + = = 1 1 12 1 12 2 + 1 = 3