56 Chapter 1 The Set of Real Numbers b. 12.4 subtracted from 4.7 Rewrite subtraction in terms of addition. Simplify. 4.7 12.4 4.7 112.42 17.1 c. 24 decreased by the sum of 10 and 13 Simplify inside parentheses. Rewrite subtraction in terms of addition. Simplify. 24 110 132 24 132 24 132 27 d. Seven-fourths less than one-third Rewrite subtraction in terms of addition. The common denominator is 12. 7 4 1 3 a 4 12 7 4 a 17 12 b 21 12 b 1 3 Skill Practice Write an algebraic expression for each phrase and then simplify. 7. 8 less than 10 8. 7.2 subtracted from 8.2 9. 10 more than the difference of 2 and 3 10. Two-fifths decreased by four-thirds 3. Applications Involving Subtraction Using Subtraction of Real Numbers in an Application Example 4 During one of his turns on Jeopardy, Harold selected the category “Show Tunes.” He got the $200, $600, and $1000 questions correct, but he got the $400 and $800 questions incorrect. Write an expression that determines Harold’s score.Then simplify the expression to find his total winnings for that category. Solution: Add the positive numbers. Add the negative numbers. Harold won $600. 200 600 1000 400 800 200 600 1000 14002 18002 1800 112002 600 Skill Practice 11. During Harold’s first round on Jeopardy, he got the $100, $200, and $400 questions correct but he got the $300 and $500 questions incorrect. Determine Harold’s score for this round. TIP: Recall that “b subtracted from a” is translated as a b. In Example 3(b), 4.7 is written first and then 12.4. TIP: Parentheses must be used around the sum of 10 24 and 13 so that is decreased by the entire quantity 110 132. Answers 7. 10 8; 18 8. 8.2 (7.2); 1 9. (2 3) 10; 5 2 4 14 10. ;5 3 15 11. 100, Harold lost $100.
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