How to Compare Fractions

Fractions designate values less than one.

Fractions provide the means to express values less than one. Fractions can also express ratios, percentages, estimates and measurements. A fraction consists of a numerator and a denominator, with the numerator on the top and the denominator on the bottom. Comparing fractions is simple when the denominators are the same; the larger fraction has the larger numerator. However, when the denominators are different, compare the fractions by cross-multiplying.

Things You'll Need

• pen or pencil
• paper

Instructions

1. Multiply the numerator of the first fraction by the denominator of the second fraction. For instance, when comparing 3/5 and 4/9, multiply 3 by 9, which equals 27.

2. Multiply the numerator of the second fraction by the denominator of the first fraction. For the example above, that would mean multiplying 4 by 5, which equals 20.

3. Compare the cross-products to determine which fraction has the greater value. In the example above, the first cross-product is 27 and the second cross-product is 20. Since the first cross-product is larger, the first fraction has the higher value. If the cross-products are equal, the fractions are equivalent, which means they share the same value.

Tips & Warnings

• This technique works for comparing ratios as well. Simply create a fraction out of the ratio, placing the number to the left of the colon on top (i.e., 2-to-3 becomes 2/3).

• Remember that the result of the multiplication belongs to the fraction whose numerator was used.

References

• NDT Resource Center: Fractions
• Syracuse University: Comparing Fractions

Resources

• Syracuse University: Operations in Fractions