Question

Express \[2.36 + 0.23\] as a fraction in simplest form

Answer 1

Hint: We convert both the given decimal numbers in fraction form and then take LCM of both the fractions to write a single fraction. Convert the obtained fraction into simplest form by cancelling all common factors between numerator and denominator of the fraction.
* Convert a decimal number into fraction by writing the number in numerator (without decimal point) and writing \[{10^n}\] in a denominator where \[n\] is the number of places where the decimal is placed (counting from right end).
* LCM: LCM means least common multiple is the smallest number that is multiple of two or more given numbers.

Complete step-by-step solution:
We have to convert the equation \[2.36 + 0.23\] into fraction form
We convert each decimal number into fraction form separately.
Since the number of digits after the decimal place in the number 2.36 is 2, we write \[{10^2}\] in the denominator and 236 in the numerator
\[ \Rightarrow 2.36 = \dfrac{{236}}{{100}}\]..............… (1)
Since the number of digits after the decimal place in the number 0.23 is 2, we write \[{10^2}\] in the denominator and 23 in the numerator
\[ \Rightarrow 0.23 = \dfrac{{23}}{{100}}\]...............… (2)
Substitute the values from equations (1) and (2) in the equation\[2.36 + 0.23\]
\[ \Rightarrow 2.36 + 0.23 = \dfrac{{236}}{{100}} + \dfrac{{23}}{{100}}\]
Take LCM in right hand side of the equation
\[ \Rightarrow 2.36 + 0.23 = \dfrac{{236 + 23}}{{100}}\]
Add the terms in numerator in RHS of the equation
\[ \Rightarrow 2.36 + 0.23 = \dfrac{{259}}{{100}}\]..................… (3)
Now convert the fraction in simplest form. Since we know the simplest form of a fraction has no common factor between the numerator and denominator we will check if there is any common factor between the numerator and denominator in equation (3).
Fraction in equation (3) is \[\dfrac{{259}}{{100}}\], we see there is no common factor between the numerator and denominator so the simplest fraction form of \[2.36 + 0.23 = \dfrac{{259}}{{100}}\]

\[\therefore \]Value of \[2.36 + 0.23\] is \[\dfrac{{259}}{{100}}\]

Note: Students many times cancel out the common factors when converting the decimal numbers separately and then have to calculate the LCM again while again adding the fractions, students should keep in mind if we have same denominator of the two fractions we don’t need to calculate the LCM and we can directly add numerators. Also, don’t convert the final answer in decimal form if it is not required.