Comparing Fractions: A Simple Method

In her will, your late Aunt Charlotte provided for you to choose the size of your inheritance. Your choices are the percentage represented by the fractions: 5/17, 11/37, 17/68.

The will dictates:

1. You must make you choice at the official reading of the will.

2. You must choose without help from another person or without foreknowledge of the possible choices.

3. The trustee of the estate may provide you pencil and paper.

You want to maximize your inheritance. Which fraction should you choose? Do you have a strategy?

Comparing numbers is seldom a problem without a calculator. But when the numbers are unfamiliar fractions and no computing device is available, often trouble looms.

In the post, Understand Equivalent Fractions, cross multiplication was used to determine if two fractions are equivalent. In this note we use cross multiplication compare the sizes of fractions. That is the larger of two fractions.

THIS example reveals the method.

Given fractions 3/7 and 8/19.

Placed them side-by- side. 3/7 8/19

1. Compute Products

The first to compute is the downward product. It is obtained by multiplying the numerator of the first fraction, (3), by the denominator of the second fraction, (19). To perform this multiplication, the action is downward. Hence the phrase "downward product". The downward product: 3 × 19 = 57.

The second product is called the upward product. It is formed by multiplying the denominator of the first fraction, (7), by the numerator of the second fraction, (8). The upward product: 7 × 8 = 56.To compute these products you must make an X pattern. This crossing names the method, cross multiplication.

The Placement of The Products

Place the downward product under the first fraction and place the upper product under the second fraction

3/7 8/19

57 56

Choose the correct sign (choose one: < , =, >) and place it between the products.

In this case put, the correct choice is " >". Because 57 is greater than 56 .Place the identical sign between the fractions. It gives the correct mathematical statement.

So 3/7 > 8/19.

Now which fraction should you choose to get your largest inheritance?

CLOSING REMARKS

Many mathematical computations use cross multiplication. An effective learning strategy is to coordinate the different ways a concept can be used. This note shows how to use cross multiplication to compare fractions.