1
\displaystyle \frac{3a}{(a-3)(a-4)}-\frac{2a}{(3-a)(4-a)}
Chapter 16 · Fractions
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
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From Adding Fractions: Watch the Signs, exercise 58
Products of factors in the denominators.
From Complex Fractions, exercise 16
Now with letters. Give a single fraction in lowest terms.
2
\displaystyle \frac{\frac{m^3}{n^3}+1}{m+\frac{n^2}{m}-n}
From Mixed Expressions, exercise 12
Reduce each fraction to a mixed expression: a whole part plus (or minus) a fraction. Type it like 3x - 2 + 2/(5x).
3
\dfrac{x^6+y^6}{x^2-y^2}
From Multiplying Fractions, exercise 22
Mixed and whole expressions: turn them into fractions first, as in Example 3.
4
\displaystyle \frac{x^3-8}{6xy}\cdot\left(3-\frac{4}{2-x}\right)\cdot\frac{18x^2y^2}{x^2+2x+4}
From Dividing Fractions, exercise 7
Perform the indicated operations. Work from left to right: invert each divisor, then multiply.
5
\displaystyle \frac{6}{(2x)^2}\div\frac{12}{(4x^2)^3}\cdot\left(\frac{2}{x}\right)^2
From Equivalent Fractions and the L.C.D., exercise 2
Change each set of fractions to equivalent fractions with the lowest common denominator. You may type the denominator factored, like (5x+1)/(6(x+1)).
6
\dfrac{5}{24} and \dfrac{7}{32}
From Adding and Subtracting Fractions, exercise 31
Whole expressions mixed with fractions: write the whole part over 1, as in Example 3.
7
\displaystyle R^2+\frac{R^2}{4}
From Complex Fractions, exercise 19
Now with letters. Give a single fraction in lowest terms.
8
\displaystyle \frac{1+\frac{b}{a}-\frac{20a}{b}}{\frac{b}{a}-\frac{8a}{b}-2}
From Changes of Sign in a Fraction, exercise 7
Write each fraction in three other ways. The sign in front of the fraction is shown; type the fraction that comes after it, like x/(-y) or (-x + 3)/(2x + 4).
9
\dfrac{x^2-5x+6}{x^2-7x+12}
From Reducing Fractions to Lowest Terms, exercise 9
Reduce each fraction to lowest terms. Type answers like (x + 1)/(x - 2).
10
\displaystyle \frac{a^2-1}{a^2-2a+1}