Fraction calculator

Example of Few questions where you can use this Fraction calculator
Question 1
Find the addition of the fractions $\frac {1}{5}$ and $\frac {1}{6}$ ?
Solution
Method -1
Addition of fraction works using the formula
$\frac {a}{b} + \frac {c}{d}= \frac {ad + bc}{bd}$
Therefore
$\frac {1}{5} + \frac {1}{6} = \frac {1 \times 6 + 1 \times 5}{5 \times 6} = \frac {11}{30}$
There is no common factor between numerator and denominator. So this is the answer.
Method -2
(a)We can find the L.C.M of the denominators and then convert them into like fractions.
L.C.M of denominators 5 and 6 is 30.So converting into like fractions
$\frac {1}{5}= \frac {6}{30}$
$\frac {1}{6}= \frac {5}{30}$
(b) Now like fractions can be added by just adding the Numerators.
$\frac {1}{5} + \frac {1}{6}= \frac {6}{30} + \frac {5}{30} = \frac {11}{30}$
(c) Now we can check we have any common factor between Numerator and denominator.
There is no common factor between numerator and denominator. So this is the answer.

Question 2
Find the addition of the fractions $\frac {1}{2}$ and $\frac {5}{6}$?
Solution
Addition of fraction works using the formula
$\frac {a}{b} + \frac {c}{d}= \frac {ad + bc}{bd}$
Therefore
$\frac {1}{2} + \frac {5}{6} = \frac {1 \times 6 + 5 \times 2}{2 \times 6} = \frac {16}{12}$
4 is common factor between numerator and denominator. So dividing both the numerator and denominator by 4
$\frac {1}{2} + \frac {5}{6} = \frac {1 \times 6 + 5 \times 2}{2 \times 6} = \frac {16}{12} = \frac {4}{3}$

Question 3
Subtract fraction $\frac {1}{4}$ from $\frac {1}{2}$
Solution
Method -1
Subtraction of fraction works using the formula
$\frac {a}{b} - \frac {c}{d}= \frac {ad - bc}{bd}$
Therefore
$\frac {1}{2} - \frac {1}{4} = \frac {1 \times 4 - 1 \times 2}{2 \times 4} = \frac {2}{8}$
2 is common factor between numerator and denominator. So dividing both the numerator and denominator by 2
$\frac {1}{2} - \frac {1}{4} = \frac {1 \times 4 - 1 \times 2}{2 \times 4} = \frac {1}{4}$
Method -2
(a)We can find the L.C.M of the denominators and then convert them into like fractions.
L.C.M of denominators 5 and 6 is 30.So converting into like fractions
$\frac {1}{2}= \frac {3}{6}$
$\frac {5}{6}= \frac {5}{6}$
(b) Now like fractions can be added by just adding the Numerators.
$\frac {1}{5} + \frac {1}{6}= \frac {3}{6} + \frac {5}{6} = \frac {8}{6}$
(c) Now we can check we have any common factor between Numerator and denominator.
2 is common factor between numerator and denominator. So,
$\frac {1}{5} + \frac {1}{6}= \frac {3}{6} + \frac {5}{6} = \frac {8}{6}= \frac {4}{3}$

Question 4
Multiply the fractions $\frac {6}{5}$ and $\frac {7}{8}$ ?
Solution
Multiplication of Fractions is given by
$\frac {a}{b} \times \frac {c}{d}= \frac {ac}{bd}$
Therefore
$\frac {6}{5} \times \frac {7}{8} = \frac {6 \times 7}{5 \times 8} = \frac {42}{40}$
Now 2 is the common factor between numerator and denominator. So,
$\frac {6}{5} \times \frac {7}{8} = \frac {6 \times 7}{5 \times 8} = \frac {42}{40}= \frac {21}{20}$

Question 5
Find the value of $\frac {3}{2} \div \frac {4}{5}$ ?
Solution
Division of Fractions
$\frac {a}{b} \div \frac {c}{d}= \frac {a}{b} \times \frac {d}{c}= \frac {ad}{bc}$
$\frac {3}{2} \div \frac {4}{5}= \frac {3}{2} \times \frac {5}{4}=\frac {15}{8}$
There is no common factor between numerator and denominator. So this is the answer.

Question 6
Find the value of $\frac {1}{2} \div \frac {11}{12}$ ?
Solution
Division of Fractions
$\frac {a}{b} \div \frac {c}{d}= \frac {a}{b} \times \frac {d}{c}= \frac {ad}{bc}$
$\frac {1}{2} \div \frac {11}{12}= \frac {1}{2} \times \frac {12}{11}=\frac {12}{22}$
2 is common factor between numerator and denominator. So ,
$\frac {1}{2} \div \frac {11}{12}= \frac {1}{2} \times \frac {12}{11}=\frac {12}{22}$
= \frac {6}{11}$