 ## How to Add Mixed Numbers

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

1. First, we need to divide the numerator of the fraction by the denominator.
2. Next, we need to write down the quotient as the whole number of the mixed fraction.
3. 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 Add Mixed Numbers

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

Ex: Let’s add $$4\frac{1}{3} + 2\frac{1}{5}$$
So, now the addition is like $$(4+2) + (\frac{1}{3}+\frac{1}{5}) = 6 + \frac{5 \times 1 + 3 \times 1}{5 \times 3} = 6\frac{8}{15}$$

### Exercises for Add Mixed Numbers

1) $$7 {2 \over 9} \ + \ 3 {3 \over 4} = \$$

2) $$5 {3 \over 7} \ + \ 1 {5 \over 2} = \$$

3) $$4 {6 \over 5} \ + \ 7 {2 \over 4} = \$$

4) $$2 {5 \over 4} \ + \ 5 {4 \over 3} = \$$

5) $$1 {7 \over 8} \ + \ 6 {8 \over 7} = \$$

6) $$7 {3 \over 10} \ + \ 6 {4 \over 3} = \$$

7) $$7 {10 \over 3} \ + \ 7 {5 \over 6} = \$$

8) $$7 {8 \over 6} \ + \ 2 { 3\over 8} = \$$

9) $$4 {9 \over 5} \ + \ 7 {4 \over 3} = \$$

10) $$4 {8 \over 7} \ + \ 6 {4 \over 6} = \$$

1) $$7 {2 \over 9} \ + \ 3 {3 \over 4} = \$$$$\ \color{red}{(7 + 3)+{2 \times 4 \ + \ 3 \times 9 \over 9\times4} = }$$ $$\color{red}{10{35 \over 36}}$$
Solution:
The first step is to rewrite the equation with parts separated, $$7+{2 \over 9}+3+{3 \over 4}$$
Then solve the whole number parts $$7+3=10$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${2 \over 9}+{3 \over 4}$$ = $$2 \times 4 \ + \ 3 \times 9 \over 9 \times4$$ = $$8+27 \over 36$$ = $$35 \over 36$$
At the end Combine the whole and fraction parts $$10 +{35 \over 36}$$  =  $$10{35 \over 36}$$
2) $$5 {3 \over 7} \ + \ 1 {5 \over 2} = \$$$$\ \color{red}{(5 + 1)+{3 \times 2 \ + \ 5 \times 7 \over 7\times2} = }$$ $$\color{red}{6{41 \over 14} = 8{13 \over 14}}$$
Solution:
The first step is to rewrite the equation with parts separated, $$5+{3 \over 7}+1+{5 \over 2}$$
Then solve the whole number parts $$5+1=6$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${3 \over 7} +{5 \over 2}$$ = $$3 \times 2 \ + \ 5 \times 7 \over 7 \times 2$$ = $$6 + 35 \over 14$$ = $$41 \over 14$$ = $$2{ 13\over 14}$$
At the end Combine the whole and fraction parts $$6 +2{13\over 14}$$  =  $$8{13 \over 14}$$
3) $$4 {6 \over 5} \ + \ 7 {2 \over 4} = \$$$$\ \color{red}{(4 + 7)+{6 \times 4 \ + \ 2 \times 5 \over 5\times4} = }$$ $$\color{red}{11{34 \over 20}}$$$$\color{red}{ = 11 + 1{14 \over 20}}$$$$\color{red}{ = 12{14 \over 20} = 12{ 7 \over 10}}$$
Solution:
The first step is to rewrite the equation with parts separated, $$4+{6 \over 5}+7+{2 \over 4}$$
Then solve the whole number parts $$4+7=11$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${6 \over 5} +{2 \over 4}$$ = $$6 \times 4 \ + \ 2 \times 5 \over 5 \times 4$$ = $$34\over 20$$ = $$1{14 \over 20}$$ = $$1{7 \over 10}$$
At the end Combine the whole and fraction parts $$11 +1{7 \over 10}$$  =  $$12{7 \over 10}$$
4) $$2 {5 \over 4} \ + \ 5 {4 \over 3} = \$$$$\ \color{red}{(2 + 5)+{5 \times 3 \ + \ 4 \times 4 \over 4\times3} = }$$ $$\color{red}{7{15 +16 \over 12}}$$$$\color{red}{ = 7{31 \over 12} = 7 + 2{ 7 \over 12}}$$
Solution:
The first step is to rewrite the equation with parts separated, $$2+{5 \over 4}+5+{4 \over 2}$$
Then solve the whole number parts $$2+5=7$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${5 \over 4} +{4 \over 2}$$ = $$5 \times 3 \ + \ 4 \times 4 \over 4 \times 3$$ = $$15 + 16 \over 4$$ = $$31 \over 4$$ =$$2{7 \over 12}$$
At the end Combine the whole and fraction parts $$7 +2{7 \over 12}$$ =  $$9{7 \over 12}$$
5) $$1 {7 \over 8} \ + \ 6 {8 \over 7} = \$$$$\ \color{red}{(1 + 6)+{7 \times 7 \ + \ 8 \times 8 \over 8\times7} = }$$ $$\color{red}{7{113 \over 56}}$$$$\color{red}{ = 7 + 2{1 \over 56}}$$$$\color{red}{ = 9{1 \over 56}}$$
Solution:
The first step is to rewrite the equation with parts separated, $$1+{7 \over 8}+6+{8 \over 7}$$
Then solve the whole number parts $$1+6=7$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${7 \over 8} +{8 \over 7}$$ = $$7 \times 7 \ + \ 8 \times 8 \over 8 \times 7$$ = $$113 \over 56$$ = $$2{1 \over 56}$$
At the end Combine the whole and fraction parts $$7 +2{1 \over 56}$$ = $$9{1 \over 56}$$
6) $$7 {3 \over 10} \ + \ 6 {4 \over 3} = \$$$$\ \color{red}{(7 + 6)+{3 \times 3 \ + \ 4 \times 10 \over 10\times3} = 13{ 9+40 \over 30 }}$$ $$\color{red}{= 13{49 \over 30} =13 + 1{19 \over30}= 14{19 \over 30}}$$
Solution:
The first step is to rewrite the equation with parts separated $$7+{3 \over 10}+6+{4 \over 3}$$
Then solve the whole number parts $$7+6=13$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${3 \over 10} +{4 \over 3}$$ = $$3 \times 3 \ + \ 4 \times 10 \over 10 \times 3$$ = $$9+40 \over 30$$ = $$49 \over 30$$ = $$1{ 19 \over 30}$$
At the end Combine the whole and fraction parts $$13 + 1{19 \over30}= 14{19 \over 30}$$
7) $$7 {10 \over 3} \ + \ 7 {5 \over 6} = \$$$$\ \color{red}{(7 + 7)+{10 \times 6 \ + \ 5 \times 3 \over 3\times6} = }$$ $$\color{red}{14{60 + 15 \over 18}}$$ $$\color{red}{=14 +{75 \over 18}}$$ $$\color{red}{=14 + 4{3\over 18}}$$ $$\color{red}{ =18{3 \over 18} = 18{1 \over 6}}$$
Solution:
The first step is to rewrite the equation with parts separated $$7+{10 \over 3}+7+{5 \over 6}$$
Then solve the whole number parts $$7+7=14$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${10 \over 3} +{5 \over 6}$$ = $$10 \times 6 \ + \ 5 \times 3 \over 3 \times 6$$ = $$60+ 15 \over 18$$ = $$75 \over 18$$ = $$4{3 \over 18} = 4{1 \over 6}$$
At the end Combine the whole and fraction parts $$14 + 4{1 \over6}= 18{1 \over 6}$$
8) $$7{8 \over 6} + 2{ 3\over 8} = \$$ $$\ \color{red}{(7 + 2)+{8 \times 8 \ + \ 3 \times 6 \over 6\times8} = }$$ $$\color{red}{9{82 \over 48}}$$$$\color{red}{ = 9 + {41\over 24} = 9+ 1{17\over 24}}$$$$\color{red}{ = 10{17 \over 24}}$$
Solution:
The first step is to rewrite the equation with parts separated, $$7+{8 \over 6}+2+{3 \over 8}$$
Then solve the whole number parts $$7+2=9$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${8 \over 6} +{3 \over 8}$$ = $$8 \times 8 \ + \ 3 \times 6 \over 6 \times 8$$ = $$64 + 18 \over 48$$ = $$82\over 48$$ = $$1{17 \over 24}$$
At the end Combine the whole and fraction parts $$9 +{1{17 \over 24}}$$  =  $$10{17 \over 24}$$
9) $$4 {9 \over 5} \ + \ 7 {4 \over 3} = \$$$$\ \color{red}{(4 + 7)+{9 \times 3 \ + \ 4 \times 5 \over 5\times3} = }$$ $$\color{red}{11{47 \over 15}}$$$$\color{red}{ = 11 + 3{2 \over 15}}$$$$\color{red}{ = 14{2 \over 15}}$$
Solution:
The first step is to rewrite the equation with parts separated, $$4+{9 \over 5}+7+{4 \over 3}$$
Then solve the whole number parts $$4+7=11$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${9 \over 5} +{4 \over 3}$$ = $$9 \times 3 \ + \ 4 \times 5 \over 5 \times 3$$ = $$27 + 20\over 15$$ = $$47\over 15$$ = $$3{2 \over 15}$$
At the end Combine the whole and fraction parts $$11 +{3{2 \over 15}}$$  =  $$14{2 \over 15}$$
10) $$4 {8 \over 7} \ + \ 6 {4 \over 6} = \$$$$\ \color{red}{(4 + 6)+{8 \times 6 \ + \ 4 \times 7 \over 7\times6} = }$$ $$\color{red}{10{76 \over 42}}$$$$\color{red}{ = 10 + 1{34 \over 42} = 11{76 \over 42}}$$ $$\color{red}{ = 11{17 \over 21}}$$
Solution:
The first step is to rewrite the equation with parts separated, $$4+{8 \over 7}+6+{4 \over 6}$$
Then solve the whole number parts $$4+6=10$$
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. $${8 \over 7} +{4 \over 6}$$ = $$8 \times 6 \ + \ 4 \times 7 \over 7 \times 6$$ = $$48 + 28\over 42$$ = $$76\over 42$$ = $$1{34 \over 42}$$= $$1{17 \over 21}$$
At the end Combine the whole and fraction parts $$10 +1{17 \over 24}$$  = $$11{17 \over 21}$$

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