60 algebra De mystif ieD
deMYstiFied / algebra deMYstiFied / HuttenMuller / 000-0 / Chapter2
- 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) - Retail selling price = x.
Sale price =^1
44
3
4
4
4
3
4
43
44
x orxxx−=xx−=xx− =x
.
- 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.