Mixed Number Division Calculator

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:

1. Enter two mixed numbers, the dividend $A\frac{a}{b}$ and the divisor $B\frac{c}{d}$ in the box. These numbers must be in terms of whole numbers and proper fractions. The numerators and denominators in the proper fractions must be positive integers.
2. Press the "GENERATE WORK" button to make the computation;
3. Mixed numbers division calculator will give the quotient of two numbers represented as mixed numbers.

Input: Two mixed numbers;
Output: A fraction in the simplest form or decimal number.

Conversion of Mixed Number to Improper Fraction Rule: The mixed number $A\frac{a}{b}$ for $a,b>0$ can be rewritten as improper fraction by the following formula $$A\frac{a}{b}=\frac{A\times b+a}{b},\quad \mbox{for}\;a,b>0$$ Mixed Numbers Division Rule: The quotient for the mixed number $A\frac{a}{b}$ divided by $B\frac{c}{d}$ is determined by the following formula \begin{align} A\frac{a}{b}\div B\frac{c}{d}&=\Big(\frac{A\times b+a}{b}\Big)\div\Big(\frac{B\times d+c}{d}\Big)\\ & = \Big(\frac{A\times b+a}{b}\Big)\times\Big(\frac{d}{B\times d+c}\Big)\\ & = \frac{(A\times b+a)\times d}{b\times ({B\times d+c})},\quad \mbox{for}\;a,b,c,d>0\end{align} Conversion of Improper Fraction to Mixed Number Rule: The improper fraction $\frac{a}{b}, a>b$ can be rewritten as mixed number by the following formula $$\frac{a}{b}=\Big[\frac a b\Big]\frac{a-\Big[\frac a b\Big]\times b}{b},\quad \mbox{for}\;b\ne0$$ where square brackets $[\; ]$ mean round down to the nearest integer.

How to Find the Quotient of Two Mixed Numbers?

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:

• Divide the numerator by the denominator;
• The whole part of the quotient is the whole number of the mixed number;
• The reminder is the new numerator of the proper fraction;
• The denominator of the proper fraction is equal to the denominator of the improper fraction.

More precisely, the improper fraction $\frac{a}{b}, a>b,$ can be rewritten as a mixed number in the following way $$\frac{a}{b}=\Big[\frac a b\Big]\frac{a-\Big[\frac a b\Big]\times b}{b},\quad \mbox{for}\;b\ne0,$$ where square brackets $[\; ]$ mean round down to the nearest integer. For example, $\frac 8 5$ is equal to $1\frac 35$.
To rewrite a mixed number to an improper fraction follow the next steps:

• Multiply the denominator of the proper fraction by the whole number in the mixed number and add it to its numerator;
• The denominator of the improper fraction is equal to the denominator of the proper fraction of the mixed number.

This means, a mixed number $A\frac{a}{b}$ for $a,b>0$ can be rewritten as improper fraction in the following way $$A\frac{a}{b}=\frac{A\times b+a}{b},\quad \mbox{for}\;a,b>0$$ For example, $$10\frac 35=\frac{10\times5+3}{5}=\frac{53}5$$ Division of two mixed numbers may be indicated by a division signs $\div$ or $:$ between two numbers. The first number is the dividend, the second number is the divisor, and the result is the quotient. In other words, to find the quotient of two mixed numbers means to find how many sets, or groups and parts of groups, can be made from another whole and parts.

To find the quotient of two mixed numbers, convert them to improper fractions then multiply the fractions. The quotient of two mixed numbers $A\frac{a}{b}$ and $B\frac{c}{d}$ can be expressed by the formula \begin{align} A\frac{a}{b}\div B\frac{c}{d}&=\Big(\frac{A\times b+a}{b}\Big)\div\Big(\frac{B\times d+c}{d}\Big)\\ & = \Big(\frac{A\times b+a}{b}\Big)\times\Big(\frac{d}{B\times d+c}\Big)\\ & = \frac{(A\times b+a)\times d}{b\times ({B\times d+c})},\quad \mbox{for}\;a,b,c,d>0\end{align} For example, let us find the quotient for $7\frac{1}{6}$ divided by $2\frac{1}{3}$. After converting these numbers to improper fractions, we obtain $$7\frac{1}{6}=\frac {7\times 6+1}{6}=\frac {43}{6}\;\mbox{and}\;2\frac{1}{3}=\frac {2\times 3+1}{3}=\frac {7}{3}$$ Further, using the fraction division rule, we get $$7\frac{1}{6}\div 2\frac{1}{3}=\frac{43}{6}\div\frac{7}{3}=\frac{43}{6}\times\frac{3}{7}=\frac{43\times3}{6\times7}=\frac{129}{42}$$ To write the quotient in simplest form, find the GCF of the numerator and denominator of the quotient. The GCF of $129$ and $42$ is $3$, so by dividing both the numerator and denominator of the quotient by $3$, we obtain $$ \frac{129\div 3}{42\div 3}=\frac{43}{14}$$ The quotient for the mixed number $7\frac{1}{6}$ divided by $2\frac{1}{3}$ is $\frac{43}{14}$. To write the quotient as a mixed number, we use the above conversion rule from an improper fraction to a mixed number: $$ \frac{43}{14}=3\frac{1}{14}$$ Dividing a mixed number by mixed number work with steps shows the complete step-by-step calculation for finding quotient for the mixed number $7\frac{1}{6}$ divided by $2\frac{1}{3}$ using the mixed numbers division rule. For any other mixed numbers, just supply two mixed numbers in terms of a whole number and proper fraction and click on the Generate Work button. The grade school students may use this Mixed Numbers Division Calculator to generate the work, verify the results of dividing two mixed numbers derived by hand, or do their homework problems efficiently.

Real World Problems Using Mixed Numbers Division

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?

Mixed number Division Practice Problems

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.