How to Divide Mixed fractions?

Last Updated : 26 Dec, 2023

Fractions are defined as numerical figure that represents a portion of a whole. A fraction is a component or sector of any amount taken from the total, which might be any number, a specified value, or an item. A fraction is also known as a piece or section of a larger quantity. It is represented by the ‘/’ sign, as in p/q.

For Example, 3/5 is a fraction in which the top part represents the numerator and the lower part represents the denominator.

Proper Fraction: The fraction in which the numerator is less than the denominator is termed a proper fraction.

For Example 4/7, 5/8, 3/5, etc

Improper fraction: The fraction in which the numerator is greater than or equal to the denominator is termed an improper fraction.

For Example 7/5, 5/5, 6/4, etc

Mixed Fraction

A mixed fraction is a form of the fraction that has both a whole number and a fractional part. A mixed fraction is one that is formed by combining a whole number and a fraction. A mixed fraction is a fraction that is expressed by its quotient and remainder.

For Example, $2{\Large\frac{3}{4}}$ is a mixed fraction and here 2 is a whole number and 3/4 is a fractional part.

$7{\Large\frac{2}{5}}$ is a mixed fraction and here 7 is a whole number and 2/5 is a fractional part.

Dividing Mixed Fraction

The division operation performed between two mixed fractions is known as dividing mixed fractions. It is similar to multiplying by the inverse of the second fraction.

There are some steps to follow for the dividing of mixed fractions :

Step 1: A mixed fraction $m{\Large\frac{n}{p}}$ is also known as m + (n/p) and vice versa.

Step 2: First convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the result to the numerator of the proper fraction while keeping the denominator.

For example: To convert mixed number $2{\Large\frac{5}{7}}$ to an improper fraction, we multiply 2 and 7 i.e, 2 × 7 = 14 and the result is added to 5 i.e., 14 + 5 = 19. Thus the improper fraction is 19/7.

Step 3: Multiply the reciprocal of the second fraction to the first fraction and rationalize the result. If an improper fraction is obtained convert it into a mixed fraction.

Step 4: To convert an improper fraction to a mixed number, divide the improper fraction’s numerator by its denominator. The quotient becomes the whole number part, the remainder becomes the proper fraction’s numerator, and the denominator remains unchanged.

For Example Convert 31/4 to a mixed number, we first divide 31 by 4 and get the quotient as 7 and the remainder as 3. Thus, the mixed number is $7{\Large\frac{3}{4}}$

Example: Divide the following Mixed fractions.

Solution:

Step 1: Convert the given mixed fractions to improper fractions. i.e.

$5{\Large\frac{3}{7}}$ = 38/7

$3{\Large\frac{4}{5}}$ = 19/5

Step 2: Then multiply the reciprocal of the second fraction with the first fraction, i.e

(38/7) × (5/19).

Step 3: Multiply The numerators and denominators of these fractions separately :

(38 × 5) / (7 × 19).

Step 4: If there is common factor ,Cancel out from the numerator and the denominator.

Step 5: BY simplification , We get 190/133 its an improper fraction , convert it into mixed fraction

$1{\Large\frac{57}{133}}$

Sample Problems

Problem 1: Divide the fraction $7{\Large\frac{1}{5}}$ by $2{\Large\frac{4}{5}}$ ?

Solution:

Step 1: Convert the given mixed fractions to improper fractions. i.e.

$7{\Large\frac{1}{5}}$ = 36/5

$2{\Large\frac{4}{5}}$ = 14/5

Step 2: Then multiply the reciprocal of the second fraction with the first fraction, i.e

(36/5) × (5/14).

Step 3: Multiply The numerators and denominators of these fractions separately :

(36 × 5) / (5 × 14).

Step 4: If there is common factor ,Cancel out from the numerator and the denominator. here cancel 5

Step 5: BY simplification , We get 36/14 its an improper fraction , convert it into mixed fraction

$2{\Large\frac{8}{14}}$

Problem 2: Divide the fraction $5{\Large\frac{9}{4}}$ by $2{\Large\frac{3}{9}}$ ?

Solution:

Step 1: Convert the given mixed fractions to improper fractions. i.e.

$5{\Large\frac{9}{4}}$ = 29/4

$2{\Large\frac{3}{9}}$ = 21/9

Step 2: Then multiply the reciprocal of the second fraction with the first fraction, i.e

(29/4) × (9/21).

Step 3: Multiply The numerators and denominators of these fractions separately :

(29 × 9) / (4 × 21).

Step 4: If there is common factor ,Cancel out from the numerator and the denominator.

Step 5: BY simplification , We get 261/189 its an improper fraction , convert it into mixed fraction

$1{\Large\frac{61}{189}}$

Problem 3: Divide the fraction $10{\Large\frac{1}{5}}$ by $2{\Large\frac{2}{4}}$ ?

Solution:

Step 1: Convert the given mixed fractions to improper fractions. i.e.

$10{\Large\frac{1}{5}}$ = 51/5

$2{\Large\frac{2}{4}}$ = 10/4

Step 2: Then multiply the reciprocal of the second fraction with the first fraction, i.e

(51/5) × (4/10).

Step 3: Multiply The numerators and denominators of these fractions separately :

(51 × 4) / (5 × 10).

Step 4: If there is common factor ,Cancel out from the numerator and the denominator.

Step 5: BY simplification , We get 204/50 its an improper fraction , convert it into mixed fraction

$4{\Large\frac{4}{50}}$

Problem 4: Divide the mixed fraction $10{\Large\frac{1}{9}}$ by $7{\Large\frac{7}{8}}$ ?

Solution:

Step 1: Convert the given mixed fractions to improper fractions. i.e.

$10{\Large\frac{1}{9}}$ = 91/9

$7{\Large\frac{7}{8}}$ = 63/8

Step 2: Then multiply the reciprocal of the second fraction with the first fraction, i.e

(91/9) × (8/63).

Step 3: Multiply The numerators and denominators of these fractions separately :

(91 × 8) / (9 × 63).

Step 4: If there is common factor ,Cancel out from the numerator and the denominator.

Step 5: BY simplification , We get 728/567 its an improper fraction , convert it into mixed fraction

$1{\Large\frac{161}{567}}$

Problem 5: Divide mixed fraction $12{\Large\frac{3}{6}}$ by $4{\Large\frac{2}{8}}$ ?

Solution:

Step 1: Convert the given mixed fractions to improper fractions. i.e.

$12{\Large\frac{3}{6}}$ = 75/6

$4{\Large\frac{2}{8}}$ = 34/8

Step 2: Then multiply the reciprocal of the second fraction with the first fraction, i.e

(75/6 ) × (8/34).

Step 3: Multiply The numerators and denominators of these fractions separately :

(75 × 8) / (6 × 34).

Step 4: If there is common factor ,Cancel out from the numerator and the denominator.

Step 5: BY simplification , We get 600/204 its an improper fraction , convert it into mixed fraction

$2{\Large\frac{194}{200}}$