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Ratios are used to compare quantities by division. The ratio of two quantities is the first divided by the second. A ratio is an abstract number, that is, a number without a unit of measure. Thus, the ratio of 10 ft to 5 ft is 10 ft 5 ft, which equals 2. A ratio can be expressed in the following ways: (1) using a colon, as in 3:4; (2) using to as in 3 to 4; (3) as a common fraction, as in 3; (4) as a decimal, 0.75; and (5) as a percent, 75%. 4 The quantities involved in a ratio must have the same unit. A ratio should be simplified by reducing to lowest terms and eliminating fractions. Thus to find the ratio of 1 ft to 4 in, we first change the foot to 12 in, and then take the ratio of 12 in to 4 in; the result is a ratio of 3 to 1, or 3. Also, the ratio of 21 : 1 would be restated 2 2 as 5 :1 or 5. The ratio of three or more quantities may be expressed as a continued ratio. Thus, the ratio of $2 to $3 to $5 is the continued ratio 2:3:5. This enlarged ratio is a combination of three separate ratios; these are 2:3, 3:5, and 2:5. Throughout this chapter, readers should use a calculator whenever they choose.

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Note that immediate values, like quick watch values, are not updated as you progress through the program on a step-by-step basis The Immediate window remains visible, however, showing the value of the variable or expression when the variable/expression was last typed into the Immediate window 65 STEPPING THROUGH A PROGRAM The line-by-line stepping can be initiated either from the beginning of the program or from a breakpoint There are actually three different types of stepping: Step Into, Step Over, and Step Out Each is discussed below 1 Step Into results in line-by-line stepping within the current procedure, and any subordinate procedures that are accessed by the current procedure (see Chap 7 for more information about procedures) This is the most common choice for simple programs 2.

Two of the tests depend upon whether the second from last letter is a vowel, so we define a little boolean function i svowel ( ) for testing that condition:

7.1 Ratio of two quantities with the same unit Express each of the following ratios in lowest terms: (a) 15 to 3 ; (b) $1.25 to $5; (c) 21 years to 2 2 years.

int isvowel(char c) 11

15 5 3 1.25 1 (b) 5 4 21 2 5 (c) 2 4 (a)

return (c == 'a'

7.2 Ratio of two quantities with different units Express each of the following ratios in lowest terms: (a) 2 years to 3 months; (b) 80 cents to $3.20.

u );

(a) 2 years to 3 months (b) 80 cents to $3.20 24 months to 3 months 80 cents to 320 cents 80 320 24 3 1 4 8

The test driver repeatedly reads a word, prints it, pluralizes it, and prints it again. The loop terminates when the user enters a single blank for a word: #include #include <iostream.h> <string.h>

void pluralize(char*); main0 1 char word[80]; for (;;) 1 cin.getline(word, 80); if (*word == ' ') break; tout << '\tThe singular is [" << word << "].\n"; pluralize(word); tout << "\t The plural is [" << word << "].\n"; ,

7.3 Continued ratio of three quantities Express each of the following ratios in lowest terms: (a) 1 gal to 2 qt to 2 pt; (b) 1 ton to 1lb to 8 oz.