Translating verbal phrases into algebraic equations involves recognizing key words that correspond to mathematical operations and symbols. Variables often represent unknown numbers, indicated by words like "number," "quantity," or "value." Operations such as addition, subtraction, multiplication, and division are identified through keywords like "sum," "difference," "times," "of," and "divided by."
One crucial symbol to understand is the equal sign, represented by two parallel lines, which denotes that two expressions are equal. Keywords that translate to the equal sign include "equals," "is," "gives," "results in," "yields," "amounts to," "represents," and the phrase "is the same as." Recognizing these keywords helps in forming algebraic equations from sentences.
For example, the phrase "triple a number is 81" can be translated by identifying "triple" as multiplication by 3 and "a number" as a variable, commonly represented by x. The word "is" corresponds to the equal sign. Thus, the algebraic equation becomes \(3x = 81\), where \$3x\( is an expression representing three times the number, and \(81\) is the value it equals.
Another example is the sentence "the sum of a number x and 12 is the same as three times the number." Here, "sum" indicates addition, so the expression is \)x + 12\(. The phrase "is the same as" translates to the equal sign, and "three times the number" becomes \)3x\(. Combining these gives the equation \)x + 12 = 3x$. This equation states that the sum of the number and 12 equals three times the number.
Understanding how to identify and translate these keywords into variables, operations, and the equal sign allows for the effective conversion of verbal statements into algebraic equations. This skill is foundational for solving problems involving unknown quantities and relationships expressed in words.
