Input Data :
Mixed Fraction A = `7 1/6`
Mixed Fraction B = `2 1/3`
Objective :
Find the resultant fraction when dividing mixed number by another.
Solution :
`7 1/6\divide7 1/6 = ?`
Convert mixed numbers into equivalent frations and multiply the one improper fraction with reciprocal of another
`7 1/6 = ((7\times6)+1)/6`
= `(42 + 1)/6`
` = 43/6`
`2 1/3 = ((2\times3)+1)/3`
= `(6 + 1)/3`
` = 7/3`
Multiply one fraction by reciprocal of another fraction
`43/6\divide7/3 = 43/6\times3/7 = (43\times3)/(6\times7) `
` 43/6\divide7/3 = 129/42`
Simplify above fraction `129/42`
Common divisor of (129, 42) is 3
Divide both numerator & denominator by gcd value 3
`129/42 = frac{129\divide3}{42\divide3} = 43/14`
`7 1/6\divide2 1/3 = 43/14`
Mixed number division calculatoruses two mixed numbers, i.e. two numbers in terms of a whole numbers and proper fractions, $A\frac{a}{b}$ and $B\frac{c}{d}$ for positive integers $a,b,c$ and $d$, and calculates the quotient for $A\frac{a}{b}$ divided by $B\frac{c}{d}$. It is an online tool to find the quotient in the simplest form of two mixed numbers.
It is necessary to follow the next steps:
A mixed number $A\frac ab$ or sometimes called a mixed fraction represents the sum of a nonzero integer $A$ 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, $2\frac 12=2.5$.
Improper fractions are rational numbers where the numerator is greater than the denominator. Improper fractions can be rewritten as a mixed number in the following way:
Mixed numbers are useful in counting whole things and parts of these things together. It is used primarily in measurement. Especially of interest are mixed numbers whose denominator of the fractional part is a power of two. They are commonly used with U.S. customary units such as inches, pounds, etc. For instance, $1\; {\rm inch}=2\frac{54}{100}\; \rm{cm}$. The problem of dividing two mixed numbers can be found in almost all spheres of life. For instance, a piece of wood with the length of $15$ and $\frac 23$ inches must be divided into pieces with the length of $2$ and $\frac 15$. How many pieces will we have?
Practice Problem 1 : Divide $1\frac 47\div 3\frac 25$ and write the result in the simplest form.
Practice Problem 2 : If each cake requires $2\frac 13$ cups of sugar. How many cakes can be made from $8\frac 17$ cups of sugar?
The mixed number division calculator, formula, example calculation (work with steps), real world problems and practice problems would be very useful for grade school students of K-12 education to understand the division of two or more numbers represented as mixed numbers. Using this concept they can be able to solve complex algebraic problems and equations.