Question

How do you change $3\dfrac{4}{7}$ to an improper fraction?

Answer 1

Hint: Here In these types of problems, the student must focus at the point that if we have the mixed fraction $a\dfrac{b}{c}$ then it can be written as the fraction $\dfrac{{ac + b}}{c}$ and $\dfrac{{ac + b}}{c}$ is known as the improper fraction as numerator is greater than the denominator.

Complete step-by-step answer:
Here we are given the mixed fraction and we need to convert the mixed fraction into the improper fraction. When the numerator in the fraction is greater than or equal to the denominator then we call that fraction as the improper fraction. For example: $\dfrac{{25}}{4},\dfrac{7}{4}$ are improper fractions while $\dfrac{4}{7}$ is proper fraction as numerator is less than the denominator.
So here we are given the mixed fraction which comprises of the integer and the proper fraction in the form of $a\dfrac{b}{c}$ where $a$ is the integer and $\dfrac{b}{c}$ is the proper fraction.
So here we must know that when we are given the mixed fraction of the form $a\dfrac{b}{c}$ we can convert it into an improper fraction where it will give us $\dfrac{{ac + b}}{c}$
Now we can compare $a\dfrac{b}{c}$ with the mixed fraction we are given that is $3\dfrac{4}{7}$ we get that:
$
  a = 3 \\
  b = 4 \\
  c = 7 \\
 $
We know that the improper fraction will be of the form $\dfrac{{ac + b}}{c}$ for the mixed fraction $a\dfrac{b}{c}$
Hence we can substitute the value of $a,b,c$ in the form of improper fraction $\dfrac{{ac + b}}{c}$
So we get:
Improper fraction$ = \dfrac{{ac + b}}{c} = \dfrac{{(3)(7) + 4}}{7}$
So on solving we get:
Improper fraction$ = \dfrac{{21 + 4}}{7} = \dfrac{{25}}{7}$

Note: Here to solve such a problem, students must keep in mind all the definitions of types of fractions like proper, improper and mixed and the way to convert mixed into improper and vice versa. We must know that the improper fraction will be of the form $\dfrac{{ac + b}}{c}$ for the mixed fraction $a\dfrac{b}{c}$.