1
5\cdot 6 = 3\cdot 10
Chapter 18 · Ratio and Proportion
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 Products into Proportions; Alternation and Inversion, exercise 2
Write each as a proportion in three different ways. Type proportions like 3 : 6 = 2 : 4 or 3/6 = 2/4.
From Ratio, exercise 9
Simplify each ratio: write it as a fraction and reduce it to lowest terms. Type 3/2, or (a - 1)/a for letters.
2
(a^3 + b^3) : (a + b)
From Miscellaneous Exercises in Proportion, exercise 1
Give numbers only, or expressions where letters appear.
3
If a : b = 4 : x, and a : b = 4 : \dfrac1x, find x.
From Composition and Division, exercise 1
Write by addition: \dfrac ab = \dfrac cd becomes \dfrac{a + b}{b} = \dfrac{c + d}{d}. You may leave sums unworked, like (2 + 3)/3 = (4 + 6)/6.
4
\tfrac23 = \tfrac46
From Products into Proportions; Alternation and Inversion, exercise 28
Write by alternation (the first term : the third = the second : the fourth).
5
\dfrac43 = \dfrac xy
From Mean, Third, and Fourth Proportionals, exercise 18
Find a fourth proportional (f with a : b = c : f) to:
6
A fourth proportional to \dfrac{a - b}{2}, \dfrac{1}{a + b}, and a^2 - b^2.
From Products into Proportions; Alternation and Inversion, exercise 14
Write as a proportion. Factor each side first, if necessary.
7
xy = 3
From A Series of Equal Ratios, exercise 3
Test the truth of the rule in Exercises 1–4.
8
3 : 4 = 6 : 8 = 12 : 16. Find (sum of the antecedents) : (sum of the consequents), reduced. Is it equal to each ratio?
From Proportion, exercise 13
Find the value of x in each proportion.
9
4 : 3\tfrac13 = 3 : (x - 3)
From Dividing in a Given Ratio, exercise 16
Give numbers only.
10
Separate 40 into two parts which are in the ratio of 2 : 3.