Translating Algebraic Expressions

  Translating Algebraic Expressions 1. Translation of "nine times the difference of 5 and y" To translate the word phrase "nine times the difference of 5 and y" into an algebraic expression, we can break it down into the following steps: Identify the operation: The word "times" indicates multiplication. Determine the quantities involved: In this case, we have "5" and "y." Identify the relationship: The word "difference" implies subtraction, so we need to subtract "y" from "5." Multiply the result by "9" to account for "nine times." Putting it all together, the algebraic expression for this word phrase is: 9 * (5 - y) 2. Translation of "six times four less than three times x" To translate the word phrase "six times four less than three times x" into an algebraic expression, we can follow these steps: Identify the operation: The word "times" indicates multiplication. Determine the quantities involved: In this case, we have "4" and "x." Identify the relationship: The phrase "four less than" implies subtraction, so we subtract "4" from the next quantity. Multiply the result by "6" to account for "six times." Combining all these elements, the algebraic expression for this word phrase is: 6 * (3x - 4) 3. Expression for the number of rock MP3s (Eric's computer) According to the given information, the number of rock MP3s is three times more than the number of classical MP3s. Let's represent the number of classical MP3s as "c." To express the number of rock MP3s, we multiply the number of classical MP3s by three and add it to "c." Therefore, the expression for the number of rock MP3s is: 3c + c Simplifying this expression, we get: 4c 4. Expression for the number of boy cousins (Marcella's cousins) Given that Marcella has 4 fewer male cousins than female cousins, let's represent the number of female cousins as "f." To express the number of male cousins, we subtract 4 from the number of female cousins. Therefore, the expression for the number of boy cousins is: f - 4 5. Expression for the number of fives (Jeannette's wallet) According to the given information, the number of fives is eight more than five times the number of tens. Let's represent the number of tens as "t." To express the number of fives, we multiply the number of tens by five, add eight to it. Therefore, the expression for the number of fives is: 5t + 8 6. Difference between "4 times the sum of x and y" and "the sum of 4 times x and y" The difference between "4 times the sum of x and y" and "the sum of 4 times x and y" lies in the order of operations. In "4 times the sum of x and y," we first find the sum of x and y, and then multiply that sum by 4. This means that we multiply 4 by the sum of x and y. On the other hand, in "the sum of 4 times x and y," we first multiply 4 by x and then add that result to y. This means that we multiply x by 4 and then add y to that product. To summarize: "4 times the sum of x and y": 4 * (x + y) "The sum of 4 times x and y": (4 * x) + y It is crucial to understand these differences to correctly interpret and solve algebraic expressions in various mathematical problems.

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