18 + 7/9
14 + 7/8
First, rewrite each fraction in terms of a common denominator. 8 and 9 don't share a common multiple until 8 * 9 = 72, so we have
7/9 = (7/9) • (8/8) = (7 • 8)/(9 • 8) = 56/72
7/8 = (7/8) • (9/9) = (7 • 9)/(8 • 9) = 63/72
Next, write each whole number in terms of fractions with the same denominator. We have
18 • 72 = 1296 ==> 18 = 1296/72
14 • 72 = 1008 ==> 14 = 1008/72
Write each mixed number as an improper fraction:
18 + 7/9 = 1296/72 + 56/72 = (1296 + 56)/72 = 1352/72
14 + 7/8 = 1008/72 + 63/72 = (1008 + 63)/72 = 1071/72
If the backpack and book together weigh 18 + 7/9 pounds, and the backpack without the book weighs 14 + 7/8 pounds, then the book alone weighs the difference, call it <em>b</em> :
<em>b</em> = (18 + 7/9) - (14 + 7/8)
<em>b</em> = 1352/72 - 1071/72
<em>b</em> = (1352 - 1071)/72
<em>b</em> = 281/72
Convert this to a mixed number. 72 • 4 = 288, so 72 • 4 - 7 = 281:
<em>b</em> = (72 • 4 - 7)/72
<em>b</em> = (72 • 4)/72 - 7/72
<em>b</em> = 4 - 7/72
<em>b</em> = (3 + 1) - 7/72
<em>b</em> = 3 + (1 - 7/72)
<em>b</em> = 3 + 65/72
