Question

Evaluate the expression $x$ divided by 1.2 for the given value of \[x = 1.8\]?

Answer 1

Hint: Write the expression step-by-step according to the sequence of words given in the expression. Assume the number as the variable ‘x’ and form the expression. In the end after the expression is formed we substitute the value of x and remove the decimal.
Any number divided by the other number means that we can write the divisor in the denominator of the fraction and the number or the dividend in the numerator of the fraction.

Complete step by step solution:
We have to form an expression for the statement: x divided by 1.2.
We use the definition of divided to form the expression.
Let us assume the number stated in the word phrase in the question as a variable.
Let the number be ‘x’ … (1)
Then the number x divided by 1.2 can be written in fraction form as \[\dfrac{x}{{1.2}}\] … (2)
Now we have to evaluate this expression at the value of \[x = 1.8\] i.e. we have to substitute the value of x as 1.8 in equation (2).
So, x divided by 1.2 at \[x = 1.8\] will be \[\dfrac{{1.8}}{{1.2}}\]
Now we multiply both numerator and denominator by 10 in order to remove the decimal point.
\[ \Rightarrow \dfrac{{1.8}}{{1.2}} = \dfrac{{1.8 \times 10}}{{1.2 \times 10}}\]
Shift decimal point to one place towards right in both numerator and denominator
\[ \Rightarrow \dfrac{{1.8}}{{1.2}} = \dfrac{{18}}{{12}}\]
We can write \[18 = 6 \times 3\] and \[12 = 6 \times 2\]
\[ \Rightarrow \dfrac{{1.8}}{{1.2}} = \dfrac{{6 \times 3}}{{6 \times 2}}\]
Cancel same factors from numerator and denominator i.e. 6
\[ \Rightarrow \dfrac{{1.8}}{{1.2}} = \dfrac{3}{2}\]
We can write 3 divided by 2 as 1.5
\[ \Rightarrow \dfrac{{1.8}}{{1.2}} = 1.5\]
\[\therefore \] The value of x divided by 1.2 for the given value of \[x = 1.8\] is 1.5

Note: Many students make the mistake of performing actual division along with the decimal places in both the numbers. Keep in mind it is always easier to first write the division as a fraction so we can cancel out common factors, as then we will have to divide numbers that have no common factor.