Question

Half of a number plus 7 is 13. What is the number?

Answer 1

Hint: In this question, we need to find the unknown number. Let us consider the unknown number be \[x\] and then proceed as the question says . Half a number means dividing a number by two, so the expression that shows half of a number is \[\dfrac{x}{2}\] i. e).divide a number by two)

Complete step-by-step solution:
We have already considered the unknown number which we have to find be \[x\]
Half a number \[= \dfrac{1}{2} \times x\]
= \[\dfrac{x}{2}\]
According to the question ,
Given, \[\dfrac{x}{2}\ \] plus \[7\] is \[13\]
 \[\dfrac{x}{2} + \ 7\ = \ 13\]
By moving the constants to one side,
We get,
\[\dfrac{x}{2}\ = \ 13 – 7\]
By subtracting,
We get,
\[\dfrac{x}{2}\ = \ 6\]
By cross multiplying,
We get,
\[x = \ 6 \times 2\]
\[x\ = 12\]
The number is \[12\]
Final answer :
The number is \[12\]

Note: We need to know that “one half” is the same as “a half “ . It is an irreducible fraction . It is numerically written as \[\dfrac{1}{2}\] . Similarly ”one third” is written as \[\dfrac{1}{3}\] , two-third as \[\dfrac{2}{3} \] and so on. An algebraic expression is built up with integers, constants, variables and mathematical operations ( addition, subtraction, multiplication, division etc… ) In mathematics, a symbol (letter) which doesn’t have a value is called a variable. Similarly which has a fixed value is called constant.