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Fraction and Mixed Number Calculator
This calculator helps you to determine a 'fraction' out of a given number by dividing the number in a specific manner.
Improper fractions are those in which the numerator is greater than the denominator and a mixed fraction is a mixture of a whole and a proper fraction. To convert improper fractions to mixed fractions, we need to divide the numerator by the denominator. Then, we write it in the mixed number form by placing the quotient as the whole number, the remainder as the numerator and the divisor as the denominator. Let us go through the following example to understand this better.
A mixed number $A\frac ab$ or sometimes called a \underline{mixed fraction} represents the sum of a nonzero integer number $A$ and a proper fraction $\frac ab$. The numerator $a$ and denominator $b$ of the proper fraction must be positive integers. In the notation of mixed numbers, the sum does not explicitly use operator plus. For example, two pizza and one-third of another pizza is denoted by $2\frac 13$ instead of $2+\frac 13$. Negative mixed number, for example $-2\frac 13$ represents the sum $-(2+\frac 13)$. Mixed numbers can also be written as decimals, for example, $2\frac 12=2.5$. (Source: ncalculators.com)
This method can be expressed algebraically: $$A\frac{a}{b}-B\frac{c}{d}=\frac{(A\times b+a)\times \frac{LCM(b,d)}{b}-(B\times d+c)\times \frac{LCM(b,d)}{d}}{LCM(b,d)},\quad \mbox{for}\;b,d\ne0$$ If $LCM(b,d)=b\times d$, then the previous formula becomes $$A\frac{a}{b}-B\frac{c}{d}=\frac{A\times b+a}{b}-\frac{B\times d+c}{d}=\frac{(A\times b+a)\times d-(B\times d+c)\times b}{b\times d},\quad \mbox{for}\;b,d\ne0$$ For example, let us use subtracting mixed numbers step by step calculation to find the mixed numbers difference between $5\frac 37$ and $6\frac 45$. After converting these numbers to improper fractions, we obtain $$5\frac 37-6\frac 45=\frac {5\times 7+3}{7}-\frac {6\times 5+4}{5} =\frac {38}7-\frac {34}5$$ Since $LCM(7,5)=7\times 5=35$, then $$5\frac 37-6\frac 45=\frac {38\times 5-34\times 7}{5\times 7}=\frac {-48}{35}$$ To write the result in simplest form, find the GCF of the numerator and denominator of the difference. Because $48$ and $35$ are relatively prime numbers, the final result is $-\frac{48}{35}$. To write the difference as a mixed number, use the above mentioned conversion from an improper fraction to a mixed number: $$ -\frac{48}{35}=-1\frac{13}{35}$$ The similar consideration can be applied in subtraction of algebraic expressions.