Question

Convert $4\dfrac{5}{6}$ into an improper fraction.

Answer 1

Hint: To convert a mixed fraction of the form $Q\dfrac{R}{d}$ to an improper fraction, we have to multiply Q by d and add the result with R. Then we have to divide by the d. That is, $Q\dfrac{R}{d}=\dfrac{Q\times d+R}{d}$ . Mixed fractions will have numerators equal to or greater than the denominator.

Complete step by step answer:
We have to convert $4\dfrac{5}{6}$ into an improper fraction. Let us recollect what mixed fractions and improper fractions are. We know that a mixed fraction is a fraction that is represented with its quotient and remainder. If Q is the quotient, R is the remainder and d is the divisor, then we can represent a mixed fraction as $Q\dfrac{R}{d}$ . We know that an improper fraction is a fraction in which the numerator is equal to or greater than the denominator.
To convert a mixed fraction of the form $Q\dfrac{R}{d}$ to an improper fraction, we have to multiply Q by d and add the result with R. Then we have to divide by the d.
$\Rightarrow Q\dfrac{R}{d}=\dfrac{Q\times d+R}{d}$
Let us convert $4\dfrac{5}{6}$ into an improper fraction.
$\Rightarrow 4\dfrac{5}{6}=\dfrac{4\times 6+5}{6}$
Let us simplify the above result.
$\begin{align}
  & \Rightarrow 4\dfrac{5}{6}=\dfrac{24+5}{6} \\
 & \Rightarrow 4\dfrac{5}{6}=\dfrac{29}{6} \\
\end{align}$
Hence, the improper fraction of $4\dfrac{5}{6}$ is $\dfrac{29}{6}$ .

Note: students have a chance of making a mistake when converting a mixed fraction to an improper fraction by performing $\dfrac{Q+R\times d}{d}$ . When doing the operation $\dfrac{Q\times d+R}{d}$ , students have a chance of making a mistake by multiplying Q with the sum of R and d. They must always follow the BODMAS rule. Students must never get confused with proper fractions and improper fractions. In proper fractions, the numerator will be less than the denominator.