How to Subtract Mixed Numbers

Read,3 minutes

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., \(\frac{3}{7}\), \(\frac{9}{11}\), \(\frac{13}{19}\) , 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 \(3\frac{1}{6}\). So, this mixed number comprises of two parts, a whole number which is \(3\) and a proper fraction \(\frac{1}{6}\). Now, if we convert this mixed number into an improper fraction which is \(\frac{19}{6}\) we find that it lies between the two whole numbers \(3\) and \(4\).
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 \(\frac{7}{2}\)
Now, when we divide \(7\) by \(2\), the quotient is \(3\). Also, the remainder is \(1\) and the divisor \(2\). So, the mixed number is \(3\frac{1}{2}\).

Steps to Subtract Mixed Numbers

To subtract two mixed numbers, follow these steps.

First, Subtract the whole parts separately and the fractional parts separately.
Next, Now simplify your answer and write it in the lowest terms.

Ex: Let’s subtract \(4\frac{1}{3} - 2\frac{1}{5}\)
So, now the subtraction is like \( (4-2) + (\frac{1}{3}-\frac{1}{5}) = 2 + \frac{5 \times 1 - 3 \times 1}{5 \times 3} = 2\frac{2}{15} \)

Free printable Worksheets

Exercises for Subtracting Mixed Numbers

1) \( 8 {6 \over 8} \ - \ 7 {2 \over 5} = \)

2) \( 5 {3 \over 4} \ - \ 4 {2 \over 3} = \)

3) \( 7 {6 \over 7} \ - \ 5 {5 \over 8} = \)

4) \( 6 {5 \over 8} \ - \ 1 {1 \over 3} = \)

5) \( 10 {3 \over 10} \ - \ 2 {3 \over 7} = \)

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

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

8) \( 6 {3 \over 4} \ - \ 3 {3 \over 6} = \)

9) \( 7 {5 \over 6} \ - \ 2 {5 \over 8} = \)

10) \( 8 {3 \over 4} \ - \ 3 {3 \over 5} = \)

Answers

1)\( 8 {6 \over 8} \ - \ 7 {2 \over 5} = \ \)\( \ \color{red}{(8 - 7)+{6 \times 5 \ - \ 2 \times 8 \over 8\times5} = } \) \(\color{red}{1{14 \over 40}}\)\(\color{red}{ = 1{7 \over 20}}\)

GCF(14,40) = 2

Solution:
Rewrite the equation with parts separated, \( 8 +{6 \over 8} -7 +{2 \over 5}\)
Solve the whole number parts \( 8 -7 = 1\) , then solve the fraction parts, \({6 \over 8} - {2 \over 5} = \)\( \ {6 \times 5 \ - \ 2 \times 8 \over 8\times5} = {14 \over 40}\) = \({14 \over 40}\) = \({7 \over 20}\)
Now, combin the whole and fraction parts, 1 + \({7 \over 20}\) = \(1{7 \over 20}\)

2)\( 5 {3 \over 4} \ - \ 4 {2 \over 3} = \ \) \( \ \color{red}{(5 - 4)+{3 \times 3 \ - \ 2 \times 4 \over 4\times3} = } \) \(\color{red}{1{1 \over 12}}\)

Solution:
Rewrite the equation with parts separated, \( 5 +{3 \over 4} - 4 +{2 \over 3}\)
Solve the whole number parts \( 5 - 4 = 1\) , then solve the fraction parts, \({3 \over 4} - {2 \over 3} = \)\( \ {3 \times 3 \ - \ 2 \times 4 \over 4\times3} = {1 \over 12}\)
Now, combin the whole and fraction parts, 1 + \({1 \over 12}\) = \(1{1 \over 12}\)

3)\( 7 {6 \over 7} \ - \ 5 {5 \over 8} = \ \)\( \ \color{red}{(7 - 5)+{6 \times 8 \ - \ 5 \times 7 \over 7\times8} = } \) \(\color{red}{2{13 \over 56}}\)

Solution:
Rewrite the equation with parts separated, \( 7 +{6 \over 7} - 5 +{5 \over 8}\)
Solve the whole number parts \( 7 - 5 = 2\) , then solve the fraction parts, \({6 \over 7} - {5 \over 8} = \)\( \ {6 \times 8 \ - \ 5 \times 7 \over 7\times8} = {13 \over 56}\)
Now, combin the whole and fraction parts, 2 + \({13 \over 56}\) = \(2{13 \over 56}\)

4)\( 6 {5 \over 8} \ - \ 1 {1 \over 3} = \ \)\( \ \color{red}{(6 - 1)+{5 \times 3 \ - \ 1 \times 8 \over 8\times3} = } \) \(\color{red}{5{7 \over 24}}\)

Solution:
Rewrite the equation with parts separated, \( 6 +{5 \over 8} - 1 +{1 \over 3}\)
Solve the whole number parts \( 6 - 1 = 5\) , then solve the fraction parts, \({5 \over 8} - {1 \over 3} = \)\( \ {5 \times 3 \ - \ 1 \times 8 \over 8\times3} = {7 \over 24}\)
Now, combin the whole and fraction parts, 5 + \({7 \over 242}\) = \(5{7 \over 24}\)

5)\( 10 {3 \over 10} \ - \ 2 {3 \over 7} = \ \)\( \ \color{red}{(10 - 2)+{3 \times 7 \ - \ 2 \times 10 \over 10\times7} = } \) \(\color{red}{8{1 \over 70}}\)

Solution:
Rewrite the equation with parts separated, \( 10 +{3 \over 10} - 2 +{3 \over 7}\)
Solve the whole number parts \( 10 - 2 = 8\) , then solve the fraction parts, \({3 \over 10} - {3 \over 7} = \)\( \ {3 \times 7 \ - \ 2 \times 10 \over 10\times7} = {1 \over 70}\)
Now, combin the whole and fraction parts, 8 + \({1 \over 70}\) = \(8{1 \over 70}\)

6)\( 6 {3 \over 5} \ - \ 5 {1 \over 2} = \ \)\( \ \color{red}{(6 - 5)+{3 \times 2 \ - \ 1 \times 5 \over 5\times2} = } \) \(\color{red}{1{1 \over 10}}\)

Solution:
Rewrite the equation with parts separated, \( 6 +{3 \over 5} - 5 +{1 \over 2}\)
Solve the whole number parts \( 6 - 5 = 1\) , then solve the fraction parts, \({3 \over 5} - {1 \over 2} = \)\( \ {3 \times 2 \ - \ 1 \times 5 \over 5\times2} = {1 \over 10}\)
Now, combin the whole and fraction parts, 1 + \({1 \over 10}\) = \(1{1 \over 10}\)

7)\( 5 {6 \over 7} \ - \ 2 {2 \over 8} = \ \)\( \ \color{red}{(5 - 2)+{6 \times 8 \ - \ 2 \times 7 \over 7\times8} = } \) \(\color{red}{3{34 \over 56}}\)\(\color{red}{ = 3{17 \over 28}}\)

GCF(34,56) = 2

Solution:
Rewrite the equation with parts separated, \( 5 +{6 \over 7} - 2 +{2 \over 8}\)
Solve the whole number parts \( 5 - 2 = 3\) , then solve the fraction parts, \({6 \over 7} - {2 \over 8} = \)\( \ {6 \times 8 \ - \ 2 \times 7 \over 7\times8} = {34 \over 56}\) = \({17 \over 28}\)
Now, combin the whole and fraction parts, 3 + \({17 \over 28}\) = \(3{17 \over 28}\)

8)\( 6 {3 \over 4} \ - \ 3 {3 \over 6} = \ \) \( \ \color{red}{(6 - 3)+{3 \times 6 \ - \ 3 \times 4 \over 4\times6} = } \) \(\color{red}{3{6 \over 24}}\) \(\color{red}{ = 3{1 \over 4}}\)

GCF(6,24) = 6

Solution:
Rewrite the equation with parts separated, \( 6 +{3 \over 4} - 3 +{3 \over 6}\)
Solve the whole number parts \( 6 - 3 = 3\) , then solve the fraction parts, \({3 \over 4} - {3 \over 6} = \)\( \ {3 \times 6 \ - \ 3 \times 4 \over 4\times6} = {6 \over 24}\) = \({1 \over 4}\)
Now, combin the whole and fraction parts, 3 + \({1 \over 4}\) = \(3{1 \over 4}\)

9)\( 7 {5 \over 6} \ - \ 2 {5 \over 8} = \ \)\( \ \color{red}{(7 - 2)+{5 \times 8 \ - \ 5 \times 6 \over 6\times8} = } \) \(\color{red}{5{10 \over 48}}\)\(\color{red}{ = 5{5 \over 24}}\)

GCF(10,48) = 2

Solution:
Rewrite the equation with parts separated, \( 7+{5 \over 6} - 2 +{5 \over 8}\)
Solve the whole number parts \( 7 - 2 = 5\) , then solve the fraction parts, \({5 \over 6} - {5 \over 8} = \)\( \ {5 \times 8 \ - \ 5 \times 6 \over 6\times8} = {10 \over 48}\) = \({5 \over 24}\)
Now, combin the whole and fraction parts, 5 + \({5 \over 24}\) = \(5{5 \over 24}\)

10)\( 8 {3 \over 4} \ - \ 3 {3 \over 5} = \ \)\( \ \color{red}{(8 - 3)+{3 \times 5 \ - \ 3 \times 4 \over 4\times5} = } \) \(\color{red}{5{3 \over 20}}\)

Solution:
Rewrite the equation with parts separated, \( 8 +{3 \over 4} - 3 +{3 \over 5}\)
Solve the whole number parts \(8 - 3 = 5\) , then solve the fraction parts, \({3 \over 4} - {3 \over 5} = \)\( \ {3 \times 5 \ - \ 3 \times 4 \over 4\times5} = {3 \over 20}\)
Now, combin the whole and fraction parts, 5 + \({3 \over 20}\) = \(5{3 \over 20}\)

How to Subtract Mixed Numbers