Arithmetic Grade Four

Lesson Seventy-three: Comparing Fractions

Which is greater, 2/3 or 3/4? Look at the following illustration.
1/3 1/3 1/3
1/4 1/4 1/4 1/4

From this table we can see that 3/4 is greater than 2/3. Without a table like this it isn't quite so easy, but there is a trick we can use to help us to determine which of two fractions is largest in a quick and easy manner.

Cross-Products

Just three lessons we used cross-products to figure out if two fractions were equivalent. We can also use cross-products to figure out which of two fractions is the largest. Here's an illustration:
Multiplying the 3 x 3 = 9 and the 2 x 4 = 8, we get our cross-products. You will notice that we wrote the 9 as the answer to 3x3 on the right side and the 8 for 2x4 on the left side. You should also notice the less than sign which is open towards the 9. This test tells us that 3/4 is greater than 2/3.
Here's another example: 

  
  (3x9=27)             (5x5=25)
           3         5
          ---   >   ---
           5         9
Now you get to try a few.

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