Question

How do you translate “5 more than 3 times a number W” as an algebraic expression?

Answer 1

Hint: An algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc. We know that if we have ‘more than’ we need to add the operation addition. If we have ‘times’ we need to put operation multiplication.

Complete step-by-step answer:
(A variable is a symbol for a number that we don’t know yet. Generally it is represented by alphabetic letters. A number on its own is called a constant)
We have “5 more than 3 times a number W”.
‘5 more than’ meaning that \[ \Rightarrow 5 + \]
We have ‘3 times a number w’ meaning that \[ \Rightarrow 3 \times w\]
Now combining we have that,
 \[ \Rightarrow 5 + \left( {3 \times w} \right)\] is the required algebraic expression. Because we have a constant ‘5’ and a variable ‘w’ and 3 is a coefficient of ‘w’, as it is a constant value used with the variable term and it is well defined. Also we have algebraic operations addition and multiplication.
So, the correct answer is “ \[ 5 + \left( {3 \times w} \right)\] ”.

Note: Suppose let's say we need to convert “5 less than 3 times a number W” into algebraic expression. We know if we have ‘less than’ we need to put negative operation. Then we have the algebraic expression \[ \Rightarrow 5 - \left( {3 \times w} \right)\] . Let’s see some algebraic expression which are translated form words:
 \[ \bullet \] ‘a’ times ‘b’ \[ \Rightarrow a \times b\]
 \[ \bullet \] ‘a’ divided by ‘b’ \[ \Rightarrow \dfrac{a}{b}\] .