Algebra Know-It-ALL

92 Fractions Built of Integers

Now multiply a/b by d/d, which is equal to 1. Then multiply c/d by b/b, which is also equal to 1.

(Remember, anything multiplied by 1 is equal to itself.) The above expression turns into this:

(a/b)(d/d)+ (c/d)(b/b)

Next, multiply the products of the fractions on each side of the plus sign, getting

ad /bd+cb/db

Now apply the commutative law for multiplication to the numerator cb and the denominator

db, morphing the above expression into

ad/bd+bc/bd

This produces a sum of two fractions with the common denominator bd. These two fractions

have the same numerical values as the original ones, but they are in “higher terms.”

A fraction plus another fraction

Once you’ve found a common denominator for a sum of two fractions, adding the fractions is

easy. Simply add the numerators, and put them over the common denominator. In the above

situation, then

ad /bd+bc /bd= (ad+bc)/bd

An equation such as this, which describes a general solution to a math problem, is called a

formula. This particular formula is worth “homogenizing” into your brain! If a and c are inte-

gers, and b and d are positive integers, then

a/b+c/d= (ad+bc)/(bd)

If you’d rather see it in words, the process goes like this:

• Multiply the numerator of the first fraction by the denominator of the second.


• Multiply the denominator of the first fraction by the numerator of the second.


• Add these two products together.


• Divide this sum by the product of the denominators.

Are you confused?

When you add two fractions using the above method, the result might not be in lowest terms. As a final

step in the addition of two fractions, you can reduce the result to lowest terms. But you don’t always

have to.

By now you must wonder, “Does it matter whether or not a fraction is in lowest terms?” The answer is,

“It depends.” If you want to express a fraction in the simplest or most “elegant” possible way, you should

reduce it. But you will sometimes come across situations where it’s better to put a fraction, ratio, or pro-

portion in a form other than lowest terms.