Algebra Demystified 2nd Ed

60 algebra De mystif ieD

deMYstiFied / algebra deMYstiFied / HuttenMuller / 000-0 / Chapter2

8. Number of adult tickets sold = x.
   Number of children’s tickets sold = 450 − x.
   (Or x = number of children’s tickets and 450 − x = number of adult
   tickets)


9. Retail selling price = x.
   Sale price =^1
   44

3

4

4

4

3

4

43

44

x  orxxx−=xx−=xx− =x





.

10. Length of the longest piece (in the given units) = x.
    Length of the shortest piece (in the given units) =
    51 x
    Length of the mid-length piece (in the given units) =

(^12) x

Summary

In this chapter, we learned how to:

•   Simplify fractions containing variables. Simplify a fraction whose numer-

ator and/or denominator contain variables by dividing out common fac-

tors. Treat variables as if they were prime numbers. Only factors can be

divided out (canceled), not terms.

•   Perform arithmetic on fractions that contain variables. The steps for adding,

subtracting, multiplying, and dividing fractions containing variables are

the same we used in Chapter 1 to perform these operations on fractions

consisting of whole numbers.

•   Simplify compound fractions containing variables. The steps for simplifying

compound fractions containing variables are the same as simplifying frac-

tions that don’t contain variables. Rewrite the fraction as a division prob-

lem and then as a multiplication problem.

•   Use variables to represent unknown quantities in word problems. If a word

problem has only one unknown, we use x (or some other variable) to

represent the unknown quantity. If there are multiple unknowns, we usu-

ally let x represent one of the unknowns and then represent the other

unknowns in terms of x.

After covering the distributive property, we will work with a larger family of

fractions. Later in the book, we will use what we learned about fractions with

variables in them to solve equations, inequalities, and word problems.