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11/24 c) Since 12 = 2 6 = 2 2 3 and 18 = 2 9 = 2 3 3, the factor 2 appears twice in the LCD and the factor 3 appears twice in the LCD. So the LCD is 2 2 3 3 or 36: d) To perform addition with the mixed number first convert it into an improper fraction: Note that . Then add on the 2 to get , which is the same as . Page 21 Now do Exercises 67–78 Calculator Close-Up You can check these results with a graphing calculator. Note how a graphing calculator handles mixed numbers. Helpful Hint
8/5/2019 ALEKS 360 12/24 Recall the place value for decimal numbers: So 6 Fractions, Decimals, and Percents In the decimal number system, fractions with a denominator of 10, 100, 1000, and so on are written as decimal numbers. For example, Fractions with a denominator of 100 are often written as percents. Think of the percent symbol (%) as representing the denominator of 100. For example, Example 8 illustrates further how to convert from any one of the forms (fraction, decimal, percent) to the others. EXAMPLE 8 Changing forms Convert each given fraction, decimal, or percent into its other two forms. a) b) 6% c) 0.1 Solution a) So . Note that a fraction can also be converted to a decimal by dividing the denominator into the numerator with long division. b) c)
8/5/2019 ALEKS 360 13/24 Now do Exercises 79–90 Calculator Close-Up A calculator can convert fractions to decimals and decimals to fractions. The calculator shown here converts the terminating decimal 0.333333333333 into 1/3 even though 1/3 is a repeating decimal with infinitely many threes after the decimal point. Page 22 7 Applications The dimensions for lumber used in construction are usually given in fractions. For example, a two- by-four (2 × 4) stud used in framing walls is actually . by . by . A two-by-twelve (2 × 12) ﬂoor joist with a width of and height of comes in various lengths, usually 8, 10, 12, 14, and 16 feet. In Example 9 we find the height of a wall. EXAMPLE 9 Framing a two-story house In framing a two-story house, a carpenter uses a 2 × 4 shoe, a wall stud, two 2 × 4 plates, then 2 × 12 ﬂoor joists, and a plywood ﬂoor, before starting the second level. Use the dimensions in Fig. 1.24 to find the total height of the framing shown. Figure 1.24 Solution We can find the total height using multiplication and addition:
8/5/2019 ALEKS 360 14/24 The total height of the framing shown is in.