Algebra Know-It-ALL

158 Review Questions and Answers

Question 6-5

On the number line of Fig. 10-3, suppose a through e all represent ratios of integers. Which of

these ratios, if any, would be proper fractions if written out with numerators and denominators?

Answer 6-5

The ratios represented by c and d would be proper fractions if written out. That’s because the

absolute values of the numerators would be less than the absolute values of the denomina-

tors. In the ratios represented by a, b, and e, the absolute values of the numerators would be

larger than the absolute values of the denominators. That means they’d be improper fractions

if written out.

Question 6-6

How can we quickly add two fractions m/n and p/q, where m and p are integers, and n and q

are positive integers?

Answer 6-6

We can add these two fractions like this:

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

We can also express this 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.


• Add these two products together.


• Divide this sum by the product of the denominators.

1

2

3

1

2

• 3


• 
  


• 
  

0

a

b

c

d

e

Figure 10-3 Illustration for

Question and

Answer 6-5.