Question

How do you write the expression that represents the phrase "three times the sum of 8 and 4? \[\]

Answer 1

Hint: We recall numerical and how to write a numerical expression. We recall that the word ‘sum’ is used to represent the result of the addition and the word ‘times’ is used to represent the result of the multiplication. We use this information to write the given phrase as a numerical expression. \[\]

Complete step by step answer:
We know that a numerical expression is a mathematical expression with numbers and symbols of arithmetic operations like addition$\left( + \right)$, subtraction $\left( - \right)$, multiplication $\left( \times \right)$ and division $\left( \div \right)$. The numbers are called operands. We use brackets to prioritize operations for example square brackets$\left( {} \right)$, curly brackets $\left\{ {} \right\}$ and square brackets $\left[ {} \right]$.\[\]
We know that the symbol for an addition $\left( + \right)$ is read using the word plus and the result of the addition is called sum. So when we write$2+3=5$, it means 2 plus 3 equals 5 or the sum of 2 and 3 is 5. We similarly know that the symbols for multiplication are read using the words into or times. So when we say 3 times 4 we can write it as $3\times 4$.\[\]
We are asked in the question to write the numerical expression for the phrase "three times the sum of 8 and 4”. So we first write for the phrase sum of 8 and 4 as $8+4$. Now we understand the phrase "3 times the sum of 8 and 4” as 3 multiplied with $8+4$ which means we can write the numerical expression as
\[3\times \left( 8+4 \right)=3\left( 8+4 \right)\]

Note:
We note the BODMAS rule that when we are given a numerical expression with multiple arithmetic operations and then we have first simplified the terms with brackets and then order ( or power or exponent), division, multiplication, addition, subtraction in sequence. That is why we had to enclose $8+4$ with a round bracket to prioritize the addition before multiplication. We note that the result of the multiplication is called product and we do not need to write the multiplication symbol before the bracket. Sometimes, we might try to take 4 commons from 8 and 4 and write the final expression as $12(2+1)$. But, this is not the exact phrase given in the question. So, do not simplify it like this.