Fractions Formula
Fractions formula help in conveniently performing the numerous operations on fractions. Compared to normal integral numbers the basic arithmetic operations for fractions, follow different rules. Fractions formulas help us to carry out basic operations with fractions easily. The basic arithmetic operation of addition or subtraction requires the denominators of the fractions to be equal. And for the division of one fraction with another fraction, the division is transformed to multiplication, by inverting the dividend fraction.
What Are Fractions Formula?
Formula 1
A mixed fraction has a whole number and a fraction associated with it. The mixed fraction is converted into an improper fraction by multiplying the denominator with the whole number and adding it to the numerator, to form the numerator of the improper fraction.
\[ A\dfrac{b}{c} = \dfrac{Ac + b}{c} \]
Formula 2
The addition of like fractions is possible by the simple addition of numerators and having the same denominator for the answer. The denominator of the given fractions are equal to the denominator of the final answer.
\[ \frac{a}{b} +\frac{c}{b} = \frac{a + c}{b} \]
Formula 3
For the addition of unlike fractions, each of the fractions is multiplied with suitable constants to make the denominators of the two fractions equal. The aim is to get the denominators of the fractions as equal, before performing the addition process.
\[ \frac{a}{b} +\frac{c}{d} =\frac{a .d}{b. d} +\frac{c . b}{d . b} = \frac{ad + bc}{bd} \]
Formula 4
Multiplication of fraction is possible by multiplying the numerators and then the denominators of both the fractions and then writing it as a single fraction.Futhe this product is simplified and reduced to get the final answer.
\[ \frac{a}{b} \times\frac{c}{d} = \frac{ac}{bd} \]
Formula 5
Division of fractions is transformed into multiplication of fractions by first inverting the fraction in the denominator, and then multiplying it with the numerator fraction.
\[\dfrac{(a/b)}{(c/d)} = \frac{a}{b} \times \frac{d}{c}\]
Let us check a few examples to understand how to perform calculations using fractions formulas.
Solved Examples on Fractions Formula

Example 1: Find the sum of the fractions \(\frac{4}{11} \) and \( \frac{5}{8} \) using fractions formula.
Solution:
\(\begin{align} \frac{4}{11} + \frac{5}{8} &=\frac{4 \times 8}{11 \times 8} + \frac{5 \times 11}{8 \times 11} \\ &= \frac{32}{88} + \frac{55}{88} \\ &= \frac{32 + 55}{88} \\ &= \frac{87}{88} \end{align} \)
Answer: Therefore the sum of the fractions is \(\frac{87}{88}\). 
Example 2: Find the value of \(\frac{24}{36} \div \frac{96}{288} \).
Solution:
\( \begin{align} \frac{24}{36} \div \frac{96}{288} & = \dfrac{\frac{24}{36}}{ \frac{96}{288} } \\ &= \frac{24}{36} \times \frac{288}{96} \\ &= \frac{24}{36} \times \frac{36 \times 8}{24 \times 4} \\ &= 2\end{align} \)
Answer: Hence the final value is 2 using the fractions formula.