Question

How do you write $ 3\dfrac{1}{2} $ as a percent?

Answer 1

Hint: Here the given expression is in the form of the mixed fraction. Mixed fraction is the combination of a whole number and the fraction. Here we will convert it into the fraction and then percentage.

Complete step-by-step solution:
Take the given expression: $ 3\dfrac{1}{2} $
Convert the above mixed fraction in the form of the simple fraction which is expressed as the ratio of the numbers expressed as the numerator upon the denominator.
For that multiply the denominator with the whole number and then add with the numerator.
 $ 3\dfrac{1}{2} = \dfrac{{6 + 1}}{2} $
Simplify the above expression.
 $ 3\dfrac{1}{2} = \dfrac{7}{2} $
Divide the above expression on the right hand side of the equation.
 $ 3\dfrac{1}{2} = 3.5 $
Percentage is the number or ratio expressed as a fraction of hundred. Here it is three and half times so here we will multiply with hundred to get the equivalent value in percentage.
 $ 3\dfrac{1}{2} = 3.5 \times 100\% $
Simplify the above equation finding the product on the right hand side of the equation.
 $ 3\dfrac{1}{2} = 350\% $
This is the required solution.

Note: Fractions are the part of the whole. Generally, it represents any number of equal parts and it describes the part from a certain size and it is the number expressed in the form of numerator upon the denominator. Know the difference between the fraction and the percentage and apply accordingly. If you want to avoid division, you can convert the fraction in the equivalent form by making the denominator in tens, hundreds and then directly shifting or placing the decimal which depends on the number of zeros in the denominator.