How to Divide Mixed Numbers

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A mixed number is a combination of two numbers: a whole number and a proper fraction (A proper fraction is a fraction which has a denominator which is greater than the numerator, i.e., \(\frac{2}{3}\), \(\frac{4}{7}\), \(\frac{5}{6}\) , etc.). Moreover, a mixed number can be converted into a fraction and it always lies between two whole numbers.

For ex: Let's take the mixed number \(1\frac{3}{4}\). So, this mixed number comprises of two parts, a whole number which is \(1\) and a proper fraction \(\frac{3}{4}\). Now, if we convert this mixed number into an improper fraction which is \(\frac{7}{4}\) we find that it lies between the two whole numbers \(1\) and \(2\).
Some other examples of a mixed number are \(2\frac{1}{2}\), \(3\frac{1}{3}\), \(4\frac{1}{5}\), etc.

Parts of a mixed number

A mixed number consists of three distinct parts: a whole number, a numerator and a denominator. Here, the numerator and the denominator are the parts of the proper fraction.

How to Convert Improper Fractions to Mixed Fractions

First, we need to divide the numerator of the fraction by the denominator.
Next, we need to write down the quotient as the whole number of the mixed fraction.
Now, the remainder becomes the numerator and the divisor becomes the denominator of the improper part.

Ex: Let’s take the improper fraction \(\frac{5}{3}\)
Now, when we divide \(5\) by \(3\), the quotient is \(1\). Also, the remainder is \(2\) and the divisor \(3\). So, the mixed number is \(1\frac{2}{3}\).

Steps to Divide Mixed Numbers

To Divide two mixed numbers, follow these steps.

Convert the mixed numbers into improper fractions, separately.
Now Divide these improper fractions by changing the division sign into the multiplication sign. To do this, just flip the second fraction.
Write the answer in the lowest terms.

Ex: Let’s divide \(4\frac{1}{3} \div 2\frac{1}{5}\)
So, the Division becomes \( (\frac{13}{3} \div \frac{11}{5}) = \frac{13}{3} \times \frac{5}{11}= \frac{65}{33} = 1\frac{32}{33} \)

Free printable Worksheets

Exercises for Dividing Mixed Numbers

1) \( 6 {5 \over 4} \ \div \ 2 {2 \over 3} = \ \)

2) \( 4 {3 \over 4} \ \div \ 1 {4 \over 7} = \ \)

3) \( 7 {7 \over 2} \ \div \ 4 {3 \over 4} = \ \)

4) \( 10 {4 \over 3} \ \div \ 3 {5 \over 10} = \ \)

5) \( 8 {7 \over 2} \ \div \ 7 {6 \over 4} = \ \)

6) \( 10 {7 \over 2} \ \div \ 7 {7 \over 9} = \ \)

7) \( 7 {9 \over 6} \ \div \ 5 {4 \over 5} = \ \)

8) \( 5 {5 \over 3} \ \div \ 2 {8 \over 7} = \ \)

9) \( 10 {8 \over 10} \ \div \ 1 {7 \over 9} = \ \)

10) \( 10 {8 \over 3} \ \div \ 2 {1 \over 7} = \ \)

Answers

1) \( 6 {5 \over 4} \ \div \ 2 {2 \over 3} = \ \color{red}{ {(6 \times 4 + 5) \ \times \ 3 \over 4\times (2 \times 3 + 2)} = } \color{red}{ {87 \over 32} = \ } \color{red}{2{23 \over 32}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 6 {5 \over 4} = { 29 \over 4} \) and \( 2 {2 \over 3} = {8 \over 3} \)
Step 2: Apply the fractions rule for multiplication, \( { 29 \over 4} \ \div \ {8 \over 3} = \ \)\( { 29 \over 4} \ \times\ {3 \over 8} = \ \) \({87 \over 32} = \) \(2{23 \over 32}\)

2) \( 4 {3 \over 4} \ \div \ 1 {4 \over 7} = \ \color{red}{ {(4 \times 4 + 3) \ \times \ 7 \over 4\times (1 \times 7 + 4)} = } \color{red}{ {133 \over 44} = \ } \color{red}{3{1 \over 44}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 4 {3 \over 4} = { 19 \over 4} \) and \( 1 {4 \over 7} = {11 \over 7} \)
Step 2: Apply the fractions rule for multiplication, \( { 19 \over 4} \ \div \ {11 \over 7} = \ \)\( { 19 \over 4} \ \times\ {7 \over 11} = \ \) \({133 \over 44} = \) \(3{1 \over 44}\)

3) \( 7 {7 \over 2} \ \div \ 4 {3 \over 4} = \ \color{red}{{(7 \times 2 + 7) \ \times \ 4 \over 2\times (4 \times 4 + 3)} = } \color{red}{{84 \over 38} = \ } \color{red}{2{8 \over 38}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 7 {7 \over 2} = { 21 \over 2} \) and \( 4 {3 \over 4} = {19 \over 4} \)
Step 2: Apply the fractions rule for multiplication, \( { 21 \over 2} \ \div \ {19 \over 4} = \ \)\( { 21 \over 2} \ \times\ {4 \over 19} = \ \) \({84 \over 38} = \) \(2{8 \over 38}\)

4) \( 10 {4 \over 3} \ \div \ 3 {5 \over 10} = \ \ \color{red}{{(10 \times 2 + 3) \ \times \ 10 \over 2\times (3 \times 10 + 5)} = } \color{red}{{68\over 21} = \ 3{5 \over 21} }\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 10 {4 \over 3} = { 34 \over 3} \) and \( 3 {5 \over 10} = {35 \over 10} \)
Step 2: Apply the fractions rule for multiplication, \( { 34 \over 3} \ \div \ {35 \over 10} = \ \)\( { 34 \over 3} \ \times\ {10 \over 35} = \ \) \({68\over 2} = \) \(3{5 \over 21}\)

5) \( 8 {7 \over 2} \ \div \ 7 {6 \over 4} = \ \color{red}{{(8 \times 2 + 7) \ \times \ 4 \over 2\times (7 \times 4 + 6)} = } \color{red}{{92 \over 68} = \ } color{red}{1{6 \over 17}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 8 {7 \over 2} = { 23 \over 2} \) and \( 7 {6 \over 4} = {34 \over 4} \)
Step 2: Apply the fractions rule for multiplication, \( { 23 \over 2}\ \div \ {34 \over 4} = \ \) \( { 23 \over 2} \ \times\ {4 \over 34} = \ \) \({92 \over 68} = \) \(1{6 \over 17}\)

6) \( 10 {7 \over 2} \ \div \ 7 {7 \over 9} = \ \color{red}{{(10 \times 2 + 7) \ \times \ 9 \over 2\times (7 \times 9 + 7)} = } \color{red}{{243 \over 140} = \ } \color{red}{1{103 \over 140}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 10 {7 \over 2} = { 27 \over 2} \) and \( 7 {7 \over 9} = {70 \over 9} \)
Step 2: Apply the fractions rule for multiplication, \( { 23 \over 2}\ \div \ {34 \over 4} = \ \)\( { 27 \over 2} \ \times\ {9 \over 70} = \ \) \({243 \over 140} = \) \(1{103 \over 140}\)

7) \( 7 {9 \over 6} \ \div \ 5 {4 \over 5} = \ \color{red}{{(7 \times 6 + 9) \ \times \ 5 \over 6\times (5 \times 5 + 4)} = } \color{red}{{255 \over 174} = \ } \color{red}{1{27 \over 58}}\)
GCF(255,174) = 3

Solution:
Step 1: Convert mixed numbers to fractions, \( 7 {9 \over 6} = { 51 \over 6} \) and \( 5 {4 \over 5} = {29 \over 5} \)
Step 2: Apply the fractions rule for multiplication, \( {51 \over 6}\ \div \ {29 \over 5} = \ \)\( { 51 \over 6} \ \times\ {5 \over 29} = \ \) \({255 \over 174} = \) \(1{27 \over 58}\)

8) \( 5 {5 \over 3} \ \div \ 2 {8 \over 7} = \ \color{red}{{(5 \times 3 + 5) \ \times \ 7 \over 3\times (2 \times 7 + 8)} = } \color{red}{{140 \over 66} = \ } \color{red}{2{4 \over 33}}\)
GCF(140,66) = 2

Solution:
Step 1: Convert mixed numbers to fractions, \( 5 {5 \over 3} = { 20 \over 3} \) and \( 2 {8 \over 7} = {22 \over 7} \)
Step 2: Apply the fractions rule for multiplication, \( {20 \over 3}\ \div \ {22 \over 7} = \ \)\( { 20 \over 3} \ \times\ {7 \over 22} = \ \) \({140 \over 66} = \) \( 2{4 \over 33}\)

9) \( 10 {8 \over 10} \ \div \ 1 {7 \over 9} = \ \color{red}{{(10 \times 10 + 8) \ \times \ 9 \over 10\times (1 \times 9 + 7)} = } \color{red}{{ 972 \over 160} = \ } \color{red}{ 6{3 \over 40}}\)
GCF(972,160) = 6

Solution:
Step 1: Convert mixed numbers to fractions, \( 10 {8 \over 10} = { 108 \over 10} \) and \( 1 {7 \over 9} = {16 \over 9} \)
Step 2: Apply the fractions rule for multiplication, \( {108 \over 10}\ \div \ {16 \over 9} = \ \)\( { 108 \over 10} \ \times\ {9 \over 16} = \ \) \({972 \over 160} = \) \( 6{3 \over 40}\)

10) \( 10 {8 \over 3} \ \div \ 2 {1 \over 7} = \ \color{red}{{(10 \times 3 + 8) \ \times \ 7 \over 3\times (2 \times 7 + 1)} = } \color{red}{{ 266 \over 45} = \ } \color{red}{ 5{41 \over 45}}\)

Solution:
Step 1: Convert mixed numbers to fractions, \( 10 {8 \over 3} = { 38 \over 3} \) and \( 1 {7 \over 9} = {16 \over 9} \)
Step 2: Apply the fractions rule for multiplication \( {38 \over 3}\ \div \ {16 \over 9} = \ \)\( { 38 \over 3} \ \times\ {9 \over 16} = \) \({266 \over 45} = \) \( 5{41 \over 45}\)

How to Divide Mixed Numbers