Grade 4 Fractions: Comparing Fractions

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   1/6 ___ 9/12

   1. Make the pieces the same size: write 1/6 in twelfths.
   2. Multiply the top and bottom by 2: 1 × 2 = 2 and 6 × 2 = 12, so 1/6 = 2/12.
   3. Now both are counted in twelfths: 2 is less than 9, so 2/12 < 9/12.
   4. So 1/6 < 9/12.

   Answer: <

2. Example 2

   1/2 ___ 1/10

   1. Both fractions have 1 piece, but the pieces are different sizes.
   2. More equal parts means smaller pieces: 1/2 is bigger than 1/10, so 1/2 is greater than 1/10.
   3. So 1/2 > 1/10.

   Answer: >

3. Example 3

   3/4 ___ 5/6

   1. The denominators are different, so rename both with a common denominator, 12.
   2. Multiply the top and bottom by 3: 3 × 3 = 9 and 4 × 3 = 12, so 3/4 = 9/12.
   3. Multiply the top and bottom by 2: 5 × 2 = 10 and 6 × 2 = 12, so 5/6 = 10/12.
   4. Now compare the numerators: 9 is less than 10, so 9/12 < 10/12.
   5. So 3/4 < 5/6.

   Answer: <