The two math subtests of the ASVAB often ask you to compare fractions to determine which one is the largest or smallest. If the fractions all have the same denominator, it’s easy. The fraction with the largest numerator is the largest, and the one with the smallest numerator is the smallest.
But how do you compare fractions that have different denominators? It’s up to you to determine which of the following proven methods you like the best.
Method 1: Finding a common denominator
The first method is to convert the fractions so they all have a common denominator. After conversion, the fraction with the largest numerator is the largest fraction, and the one with the smallest numerator is the smallest. This method is what you probably learned in school.
Which of the following fractions is the largest: 5/12, 3/4, 9/15, or 13/16?
First, find a common multiple for each denominator:
The multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240.
The multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 100, 104, 108, 112, 116, 122 … 240.
The multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240.
The multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240.
The lowest common denominator for all four fractions is 240.
Next, convert all the fractions so they have a denominator of 240 by dividing the new common denominator by the original denominator of the fraction and then multiplying the result by the original numerator:
Here’s how you do the second fraction.
And the third.
And finally, the last.
The largest fraction is the one with the largest numerator:195/240 or 13/16.
Method 2: The cross-product method
You may find Method 1 to be a bit time-consuming. If so, you’ll enjoy this method.
The second method is called the cross-product method. To use it, you compare the cross-products of two fractions. The first cross-product is the product of the first numerator and the second denominator. The second cross-product is the product of the second numerator and the first denominator. If the cross-products are equal, the fractions are equivalent.
If the first cross-product is larger, the first fraction is larger. If the second cross-product is larger, the second fraction is larger.
Which of the following fractions is the largest: 5/12, 3/4, 9/15 or 13/16?
Compare the first two fractions, 5/12 and 3/4: 5 × 4 = 20 and 12 × 3 = 36. The second fraction is larger.
Compare the larger fraction, 3/4 with the third fraction, 9/15: 3 × 15 = 45 and 4 × 9 = 36, so 13/16 is still the largest fraction.
Now compare 3/4 to the final fraction, 13/16: 3 × 16 = 48, and 4 × 13 = 52.
The final fraction, 13/16, is the largest.