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 Adding and subtracting unlike fractions
a free lesson with a video

The video below (also available at my Youtube channel) 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, students should be given exercises without a visual model but the common denominator is still given. Lastly, we study the rule about finding the common denominator. I also have another video that concentrates solely on that.

The lesson below also explains the same ideas. It is taken from Math Mammoth Fractions 1 book.

Cover the page below the black line. Then, try to figure out additions below. Manipulatives may help.

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

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

Did you solve the problems above? Study the pictures below for solutions. Discuss with your teacher. 

+ 1 3 + 1 2     ↓   ↓     + = 2 6 + 3 6 = 5 6

+ 1 3 + 1 4     ↓   ↓     + = 4 12 + 3 12 = 7 12

1. Write the fractions. Convert them into equivalent fractions. Add. Color parts where needed.

+       +           ↓   ↓       + = a.     +     =

Let's write the addition all on the same line now (horizontally).   + = + =   3 10 + 2 5 = 3 10 + 4 10 =      10

2. Change to equivalent fractions first, and then add. Each box below has TWO problems. In the bottom problem, you need to figure out what kind of pieces to use, but the top problem will help!

a. + = + =   1 2 + 1 6 =      6 + 1 6   = + = + =     + = + =
c. + = + =     +   =   +   = + = + =     + = + =

3. Look at the problems above in exercise (2). What kind of parts did the fractions have? What kind of parts did you use in the final addition? Fill in the table.

4.  Split the parts     so that both     fractions will have     the same kind of parts.     Write an addition sentence.

These pictures change into...   ...these.   Example:          1 4  +  3 8   2 8  +  3 8  =  5 8

a.     +     =
d.     +     =

5. Fill in the table based on the problems above in exercise (4).

6. 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?
 

7. If you think you know what kind of parts to convert the fractions to, try these problems. Don't worry if you don't know how to do them - we will study this more in the next lesson.

Next lesson: Adding unlike fractions 2: finding the common denominator

The ideas in this fraction lesson are taken from Math Mammoth Fractions 1 book.

Math Mammoth Fractions 1 $4.50 A self-teaching printable worktext that teaches fractions and their operations with visual models. You don't need to just memorize fraction rules blindly - learn and understand! The book covers fractions, mixed numbers, equivalent fractions, adding and subtracting like fractions and unlike fractions, adding and subtracting mixed numbers, comparing fractions, and finding a fractional part of a group.