Algebra Know-It-ALL

Part One 159

Question 6-7

How can we quickly subtract a fraction p/q from a fraction m/n, where m and p are integers,
andn and q are positive integers?

Answer 6-7

The difference can be found this way:

m/n−p/q= (mq−np)/nq

Stated in words:

• 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.


• Subtract the second product from the first.


• Divide this difference by the product of the denominators.

Question 6-8

How do we multiply a fraction m/n by a fraction p/q, where m and p are integers, and n and
q are positive integers?

Answer 6-8

We multiply the numerators to get the numerator of the product, and multiply the denomina-
tors to get the denominator of the product. As a formula:

(m/n)(p/q)=mp/nq

Question 6-9

How do we divide a fraction m/n by a fraction p/q, where m and p are integers, p≠ 0, and n
andq are positive integers?

Answer 6-9

First, we invert the second fraction, making it q/p. Then we multiply the numerators to get
the numerator of the product, and multiply the denominators to get the denominator of the
product. As a formula:

(m/n)/(p/q)=mq/np

Question 6-10

What sort of fraction do we have on the left-hand side of the equation in Answer 6-9?

Answer 6-10

This is a ratio of fractions, also known as a compound fraction. It’s a good idea to simplify
expressions like this whenever we can (as the formula above shows), because compound frac-
tions can be awkward and confusing.