# Adding and subtracting unlike fractions

This fifth grade lesson teaches how to add and subtract unlike fractions (fractions with different denominators). First, we use visual models to learn that the fractions need converted into like fractions, using equivalent fractions. Students do several exercises using visual models, and try to look for a pattern in the common denominators. The next lesson concentrates on how we find the common denominator.

The video below outlines a lesson plan for teaching adding unlike fractions (which I consider to be the most difficult topic in fraction arithmetic). In the video, I first go through exercises that have a visual model and the common denominator is given. Then, we work exercises without a visual model where the common denominator is still given. Lastly, we study the rule about finding the common denominator. I also have another lesson that concentrates on the common denominator.

Cover the page below the black line. Then try to figure out the addition problems below.

 + = 1 3 + 1 2 = What fraction  would this be?

 + = 1 3 + 1 4 = What fraction  would this be?

 + 1 3 + 1 2 ↓ ↓ + = 2 6 + 3 6 = 5 6
 + 1 3 + 1 4 ↓ ↓ + = 4 12 + 3 12 = 7 12
Did you solve the problems above?

The solution is this:

We convert the fractions so that they
become like fractions (the same
denominator), using equivalent fractions.

Then we can add or subtract.

1. Write the fractions shown by the pie images. Convert them into equivalent fractions with the same
denominator
(like fractions), and then add them. Color in the missing parts.

 a. + 1 2 + 1 4 ↓ ↓ + = + =
 b. + + ↓ ↓ + = + =
 c. + + ↓ ↓ + = + =

2. Convert the fractions to like fractions first, and then add or subtract. In the bottom problems (d-f), you
need to figure out what kind of pieces to use, but the top problems (a-c) will help you do that!

 a. + 1 2 + 1 6 ↓ ↓ + = + 1 6 =
 b. + 1 8 + 1 4 ↓ ↓ + = 1 8 + =
 c. + 1 6 + 1 4 ↓ ↓ + = + =
 d. 5 6 − 1 2 ↓ ↓ 5 6 − =
 e. 5 8 − 1 4 ↓ ↓ − =
 f. 5 6 − 1 4 ↓ ↓ − =

 g. + 1 2 + 1 8 ↓ ↓ + = + =
 h. + 3 10 + 1 5 ↓ ↓ + = + =
 i. + 2 5 + 1 2 ↓ ↓ + = + =
 j. 1 2 + 3 8 ↓ ↓ − =
 k. 9 10 − 2 5 ↓ ↓ − =
 l. 4 5 − 1 2 ↓ ↓ − =

3. Split the parts only in the first fraction so that both fractions will have the same kind of parts. Add.

 a. 8 + 5 8 =
 b. + 3 4 =
 c. + 5 6 =

Now split the parts in both fractions so that they will have the same kind of parts. Add.

 d. 10 + 10 =
 e. 15 + =
 f. + =

4. Fill in the table based on the problems above. What kind of parts did the two fractions have at first?
What kind of parts did you use in the final addition?

 Types of parts: Converted to: a. 2nd parts and 8th parts 8th  parts b. 2nd parts and 4th parts _____ parts c. 3rd parts and 6th parts _____ parts

 Types of parts: Converted to: d. 2nd parts and 5th parts _____ parts e. 3rd parts and 5th parts _____ parts f. 3rd parts and 2nd parts _____ parts

5. Now think: How can you know into what kind of parts to convert the fractions that you are adding?
Can you see any patterns or rules in the table above?

6. Challenge: If you think you know what kind of parts to convert these fractions into, then try these
problems. Do not worry if you do not know how to do them—we will study this in the next lesson.

 a. 1 2 + 2 3 ↓ ↓ + =
 b. 2 3 − 2 5 ↓ ↓ − =
 c. 1 3 + 3 4 ↓ ↓ + =

This lesson is taken from my book Math Mammoth Fractions 1.

#### Math Mammoth Fractions 1

A self-teaching worktext for 5th grade that teaches fractions and their operations with visual models. The book covers fractions, mixed numbers, adding and subtracting like fractions, adding and subtracting mixed numbers, adding and subtracting unlike fractions, and comparing fractions.