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May 2012

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Comparing fractions
Free lesson with a video

In the video below (also available at my Youtube channel), I explain several methods for comparing fractions. When comparing two fractions, there are three methods that sometimes work:
- If the denominators are the same, compare the amount of pieces
- If the numerators are the same, think of the size of the parts.
- Sometimes you can easily compare to 1/2

If none of those "work", you can always convert the two fractions so they have the same denominator, and then compare.

Sometimes it is easy to know which fraction is greater. With like fractions, all you do is check which fraction has more "slices", and that fraction is greater. 7 9 > 2 9

3 9 < 3 8 If both fractions have the same number of pieces, then the one with larger pieces is greater.

Sometimes one fraction is clearly less than 1/2, and the other is clearly more than 1/2. Here, 4/7 is more than 1/2, and 5/12 is less than 1/2. 4 7 > 5 12

6 5 > 9 10 Sometimes one fraction is clearly less than 1 whole pie, and the other is clearly more than 1. Here, 6/5 is more than 1, and 9/10 is less than 1.

2 5 > 1 4 Sometimes you can imagine the pie pictures in your mind, and "see" that one fraction is more than the other. For example, it's easy to see that 2/5 is more than 1/4.

1. These are like fractions. Compare them, and write > or < .

2. These have the same amount of pieces. Compare them, and write > or < .

a. 1 8 1 10	c. 2 11   2 5	e.  (available in the book)
	d. 5 14   5 9	f.  (available in the book)

3. Compare to one half. Write <, >, or = .

a. 4 9 1 2	b. 1 2 4 7
e. 1 2   3 4	f. (available in the book)

4. Compare to one.

a. 8 7 3 3

b. 4 4 9 11

5. Compare by imagining the pies in your mind.

a. 3 4 5 6

b. 1 3 2 8

6. The number lines are divided into halves, thirds, and fifths. Put the given fractions in order by using the number lines.

7. For each pair of fractions, find one that is in between them. Any such fraction will do!
     Hint: You can visualize pies in your mind, or convert the fractions into like fractions.

Comparing unlike fractions Sometimes none of the “tricks” explained in the previous lesson work. But we do have one more up our sleeve! Convert both fractions into like fractions. Then compare. In the picture on the right, it’s hard to be sure if 3/5 is really more than 5/9. Convert both into 45th parts, and then it is easy to see that 27/45 is more than 25/45. Not by much, though!   3 5   5 9   ↓   ↓   27 45 > 25 45

1. Convert the fractions into like fractions, and then compare them.

a. 2 3 5 8   ↓ ↓	(available in the book)	c. 1 3 3 10   ↓ ↓	(available in the book)
(available in the book)	f. 3 8 4 10   ↓ ↓	g. 6 9 8 12   ↓ ↓	h. 1 5 2 9   ↓ ↓

2. Convert the fractions into like fractions and compare them.

3. A certain coat costs $40. Which is a bigger discount:
    1/4 off the normal price, or 3/10 off the normal price?

    Does your answer change if the original price
    of the coat was $60 instead? Why or why not?

4. Compare the fractions using any method.

5. Find the equivalent fraction when the denominator is 100.

a. 1 2  =    100	b. 3 10  =    100	(available in the book)	(available in the book)
(available in the book)	f. 2 10  =    100	g. 3 4  =    100	(available in the book)

6. Compare these fractions with hundredth parts. Write > or <.

a. 1 2 40 100

b. 6 10 42 100

c. 7 10 75 100

(available in the book)

(available in the book)

7. Write the three fractions in order.

8. (available in the book)

9. The number lines below are divided into eighths, tenths, and sixths.
    Use the number lines to put the given fractions in order.

The ideas in this fraction lesson are taken from the Math Mammoth Fractions 1 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 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. Available as an affordable download ($4.50), and also as a printed copy. Learn more and see the free samples! See more topical Math Mammoth books

Next lesson: Simplifying fractions