Question

How do you write 3.5 as an improper fraction?

Answer 1

Hint: We will split the given decimal number into two parts. One part is the whole number and the other part is the digits after the decimal point. We will write the whole number as it is. Then we will convert the digits after the decimal point into a fraction. Then we will write the mixed fraction as a combination of the whole number and the fraction. We will convert this mixed fraction into an improper fraction.

Complete answer:
The given number is 3.5. The whole number in this is 3. There is only one digit after the decimal point. So, the place value of this digit is one-tenth. That means, it is equivalent to the fraction ${\displaystyle \frac{5}{10}}$. This fraction can be further simplified by dividing the numerator and the denominator by 5. We get ${\displaystyle \frac{5}{10}}={\displaystyle \frac{1}{2}}$. So, the mixed fraction that represents the given decimal number is $3.5=3{\displaystyle \frac{1}{2}}$. Now, we have to convert this mixed fraction into an improper fraction. For this, we will multiply the whole number by the denominator and then add it to the numerator. So, we have the following,
$3{\displaystyle \frac{1}{2}}={\displaystyle \frac{3\times 2+1}{2}}$
Simplifying the above fraction, we get
$\begin{array}{rl}& 3{\displaystyle \frac{1}{2}}={\displaystyle \frac{6+1}{2}}\\ & \therefore 3{\displaystyle \frac{1}{2}}={\displaystyle \frac{7}{2}}\end{array}$
So, the improper fraction that represents the decimal number 3.5 is ${\displaystyle \frac{7}{2}}$.

Note: Improper fraction is defined as the fraction in which the numerator is greater than or equal to the denominator. Mixed fraction is defined as the combination of a whole number and a fraction. We should be familiar with the concept of place value for the digits that occur after a decimal number.