Question

How do you solve $40-\dfrac{4}{5}$ ?

Answer 1

Hint: Now to subtract the following numbers we will first convert 40 into fractional form by writing 1 in the denominator. Now we will make the denominators of both the fractions same by multiplying appropriate terms and hence subtract the expression using the formula $\dfrac{a}{n}-\dfrac{b}{n}=\dfrac{a-b}{n}$ .

Complete step by step solution:
We will now understand the concept of fractions.
Now a fraction is a number which denotes parts of the whole.
Hence suppose we want to write 1 out of 2 then we can show this by using the number $\dfrac{1}{2}$ .
Now consider the fraction $\dfrac{1}{2}$ in this 1 is called the numerator and 2 is called the denominator of fraction.
Now if nothing is written in the denominator then the denominator is considered as 1.
Now note that the value of fraction remains unchanged if we multiply or divide the same number to numerator and denominator.
Hence we have $\dfrac{1}{2}=\dfrac{1\times 4}{2\times 4}=\dfrac{1\div 4}{2\div 4}$ .
Now let us understand the operations on fraction.
Now first consider the operations addition and subtraction.
To add and subtract fractions the denominator of the terms must be the same.
Hence we have $\dfrac{a}{n}+\dfrac{b}{n}=\dfrac{a+b}{n}$ and $\dfrac{a}{n}-\dfrac{b}{n}=\dfrac{a-b}{n}$ .
Now to multiply or divide the fraction we multiply the numerator by numerator and denominator by denominator.
Hence we have $\dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a\times c}{b\times d}$ and $\dfrac{a}{b}\div \dfrac{c}{d}=\dfrac{a\div c}{b\div d}$
Now consider the given expression $40-\dfrac{4}{5}$.
Here we have nothing to the denominator to 40. Hence we say the denominator is 1.
Now we get the expression as $\dfrac{40}{1}-\dfrac{4}{5}$
Now to subtract the two terms the denominators must be same. Now since the denominators are different we must make them the same.
Now how can we make the denominator the same. Remember the value of fraction does not change after multiplying the denominator and numerator by same number hence $\dfrac{40}{1}=\dfrac{40\times 5}{1\times 5}=\dfrac{200}{5}$
Hence using this in the expression we get,
$\begin{align}
  & \Rightarrow \dfrac{200}{5}-\dfrac{4}{5}=\dfrac{200-4}{5} \\
 & \Rightarrow \dfrac{200}{5}-\dfrac{4}{5}=\dfrac{196}{5} \\
\end{align}$
Hence the value of the given expression is $\dfrac{196}{5}$ .

 Note:
Now note that while adding or subtracting the fractions we will often have to make the denominators the same. Now there is an easy rule to make the denominators the same. First take the LCM of the denominators. Now convert each denominator to its LCM by multiplying the appropriate term. Hence we get the denominators of both the fractions the same.