Question

How do you translate 3 times the difference of $x$ and $y$ into an algebraic expression?

Answer 1

Hint: We will split the given statement into parts and understand the meaning of the words used in the question. We will associate mathematical operations to these words. Then we will combine these together to form an algebraic expression. We will look at some similar examples involving other mathematical operations.

Complete step by step answer:
We have to translate a statement into an algebraic expression. The statement given is "3 times the difference of $x$ and $y$". We know that the word "times" is used when multiplying two numbers. The word "difference" is used when we have to deal with the mathematical operation of subtraction. Since we have to translate "3 times of a difference", we will first give precedence to the mathematical operation of subtraction. According to the BODMAS rule, multiplication has higher precedence than subtraction. Therefore, we will use brackets to give subtraction the higher precedence in this case. So, the difference of $x$ and $y$ can be written as $\left( x-y \right)$. Next, in the statement given, we have "3 times the difference of $x$ and $y$". So, we will multiply the difference of $x$ and $y$ by 3. Hence, we get the expression as $3\times \left( x-y \right)$.
The word "adding" or "sum" is associated with the addition operation. And for the division operation, "divide" or "distributing" is used. So, for example, consider the statement "sum of $y$ and 2 times $x$" translates to $y+2x$.

Note: It is essential to know about the words and phrases that indicate the mathematical operation. This is very useful while solving word problems. In word problems, we are given a statement and we have to translate it into equations or algebraic expressions and then solve them to obtain the solution.