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Simplifying fractions
Free lesson with a video

In the video below (also available at my Youtube channel), I first show the simplification process using visual models and an arrow notation to help students understand the concept. Simplifying fractions is like joining or merging fractional pieces together, such as in 4/12, we merge each 4 pieces so we get 1/3.

I show how we can simplify a fraction in several steps, instead in one step. If you simplify in one step, you need to use the greatest common factor of the numerator and denominator, but this is not necessary if you simplify in several steps.

Sometimes you cannot simplify. Lastly we explore if the given fractions are already in their lowest terms.

Remember? You know how to convert fractions into other equivalent fractions. =   × 2    3 4   =   6 8 Each slice has been split two ways. ÷ 2   =   × 3    1 3   =   3 9 Each slice has been split three ways. ÷ 3 We can also reverse the process.  Then it is called SIMPLIFYING: =   ÷ 2    6 8   =   3 4 Each two slices are joined together. ÷ 2   =   ÷ 3    3 9   =   1 3 Each three slices are joined together. ÷ 3 Notice: Both the the numerator and the denominator change into smaller numbers, but the value of the fraction does not. In other words, you get the SAME AMOUNT of pie either way. The fraction is now written in a simpler form. We also say that the fraction is written in lower terms, because the new numerator and denominator are smaller numbers than the originals.  Both the numerator and the denominator are divided by the same number. This number shows how many slices are joined together.

1. Write down the simplification process. Show the arrows and the division the same as in the example.

a.  Each ______ parts were joined together. =   ÷        =    ÷

b.  [available in the book]

2. Write the simplifying process. You can also write the arrows and the divisions to help you.

a. Each _______ slices     were joined together. = ÷ 3 3 6  =      ÷ 3
	f. [available in the book]	g. [available in the book]	h. Each _______ slices     were joined together. =

3. Draw a picture and simplify the fractions.

4. Simplify the fractions. Draw pie pictures of the process.

=   ÷     a.  2 8  =   ÷			=   ÷     d.  4 8  =   ÷
e.  [available in the book]			h.  [available in the book]

5. Simplify, or write the fractions in lowest terms.

÷     a.  12 20  =   ÷

[available in the book]

e. [available in the book]

6. Some of the following fractions are such that you CANNOT simplify them. Cross them out. 
    Simplify the ones that you can.

7. Simplify. Place the letter from each problem under the correct answer, and thus solve the riddle.

WHY ARE TEDDY BEARS NEVER HUNGRY?

The ideas in this fraction lesson are taken from the Math Mammoth Fractions 2 book. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Math Mammoth Fractions 2 A self-teaching worktext that teaches fractions using visual models, a sequel to Math Mammoth Fractions 1. The book covers simplifying fractions, multiplication and division of fractions and mixed numbers, converting fractions to decimals, and ratios. Available as an affordable download ($5.00), and also as a printed copy. => Learn more and see the free samples! See more topical Math Mammoth books

Next lesson: Multiplying fractions by whole numbers