- 1). Find the fractions on a fraction chart to compare denominators up to 12. Find the lengths of the given fractions on the chart. The fractions that are closer to the left side of the chart are smaller in value because they are closer to zero. The fractions that are closer to the right side of the chart are greater in value because they are closer to one whole. If the fractions line up evenly on the chart, they are equal in value.
- 2). Divide the numerator by the denominator, using a calculator, to find the decimals that are equal to the fractions. The fraction bar represents division as an operation. For example, the fraction one fourth is actually one divided by four, which is equal to .25 as a decimal. The fraction one half, is actually one divided by two, which is equal to .50. When comparing the two decimals, .25 is less than .50. This also means that the fraction one fourth is less than the fraction one half.
- 3). Cross multiply to compare the value of two different fractions. Multiply the denominators of the fractions by the numerators of the other fractions. Place the multiple, or answer, above the numerator. The numerator with the higher multiple is the fraction with the greater value. For example, when comparing one third to two fifths, multiply 3 x 2 and 5 x 1. Place the multiple or 3 x 2 (6), above the two fifths, and place the multiple or 5 x 1 (5) above the one third. Since the 6 is greater than the 5, the fraction two fifths is greater than the fraction one third.
- 4). Use benchmarks, such as one half to compare fractions with even denominators. All of the fractions that are equal to one half have a numerator that is half of the value of the denominator. To use the one half benchmark, decide if the fractions are greater than, less than or equal to one half. When comparing two sixths to five eighths, compare them to one half. The fraction two sixths is less than one half because it is less than three sixths, which is equal to one half. The fraction five eighths is greater than one half because it is greater than four eighths, which is equal to one half. This shows that two sixths is less than five eighths.