How to Add Mixed Numbers

How to Add 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., 37, 911, 1319 , 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 316. So, this mixed number comprises of two parts, a whole number which is 3 and a proper fraction 16. Now, if we convert this mixed number into an improper fraction which is 196 we find that it lies between the two whole numbers 3 and 4.
Some other examples of a mixed number are 212, 313, 415, 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 72
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 312.

Steps to Add Mixed Numbers

To add two mixed numbers, follow these steps.

  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 413+215
So, now the addition is like (4+2)+(13+15)=6+5×1+3×15×3=6815

Free printable Worksheets

Related Topics

How to Subtract Mixed Numbers
How to Divide Mixed Numbers
How to Multiply Mixed Numbers
How to Convert Between Fractions, Decimals, and Mixed Numbers

Exercises for Add Mixed Numbers

1) 729 + 334= 

2) 537 + 152= 

3) 465 + 724= 

4) 254 + 543= 

5) 178 + 687= 

6) 7310 + 643= 

7) 7103 + 756= 

8) 786 + 238= 

9) 495 + 743= 

10) 487 + 646= 

1) 729 + 334=  (7+3)+2×4 + 3×99×4= 103536
Solution:
The first step is to rewrite the equation with parts separated, 7+29+3+34
Then solve the whole number parts 7+3=10
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 29+34 = 2×4 + 3×99×4 = 8+2736 = 3536
At the end Combine the whole and fraction parts 10+3536  =  103536
2) 537 + 152=  (5+1)+3×2 + 5×77×2= 64114=81314
Solution:
The first step is to rewrite the equation with parts separated, 5+37+1+52
Then solve the whole number parts 5+1=6
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 37+52 = 3×2 + 5×77×2 = 6+3514 = 4114 = 21314
At the end Combine the whole and fraction parts 6+21314  =  81314
3) 465 + 724=  (4+7)+6×4 + 2×55×4= 113420=11+11420=121420=12710
Solution:
The first step is to rewrite the equation with parts separated, 4+65+7+24
Then solve the whole number parts 4+7=11
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 65+24 = 6×4 + 2×55×4 = 3420 = 11420 = 1710
At the end Combine the whole and fraction parts 11+1710  =  12710
4) 254 + 543=  (2+5)+5×3 + 4×44×3= 715+1612=73112=7+2712
Solution:
The first step is to rewrite the equation with parts separated, 2+54+5+42
Then solve the whole number parts 2+5=7
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 54+42 = 5×3 + 4×44×3 = 15+164 = 314 =2712
At the end Combine the whole and fraction parts 7+27129712
5) 178 + 687=  (1+6)+7×7 + 8×88×7= 711356=7+2156=9156
Solution:
The first step is to rewrite the equation with parts separated, 1+78+6+87
Then solve the whole number parts 1+6=7
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 78+87 = 7×7 + 8×88×7 = 11356 = 2156
At the end Combine the whole and fraction parts 7+2156 = 9156
6) 7310 + 643=  (7+6)+3×3 + 4×1010×3=139+4030 =134930=13+11930=141930
Solution:
The first step is to rewrite the equation with parts separated 7+310+6+43
Then solve the whole number parts 7+6=13
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 310+43 = 3×3 + 4×1010×3 = 9+4030 = 4930 = 11930
At the end Combine the whole and fraction parts 13+11930=141930
7) 7103 + 756=  (7+7)+10×6 + 5×33×6= 1460+1518 =14+7518 =14+4318 =18318=1816
Solution:
The first step is to rewrite the equation with parts separated 7+103+7+56
Then solve the whole number parts 7+7=14
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 103+56 = 10×6 + 5×33×6 = 60+1518 = 7518 = 4318=416
At the end Combine the whole and fraction parts 14+416=1816
8) 786+238=   (7+2)+8×8 + 3×66×8= 98248=9+4124=9+11724=101724
Solution:
The first step is to rewrite the equation with parts separated, 7+86+2+38
Then solve the whole number parts 7+2=9
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 86+38 = 8×8 + 3×66×8 = 64+1848 = 8248 = 11724
At the end Combine the whole and fraction parts 9+11724  =  101724
9) 495 + 743=  (4+7)+9×3 + 4×55×3= 114715=11+3215=14215
Solution:
The first step is to rewrite the equation with parts separated, 4+95+7+43
Then solve the whole number parts 4+7=11
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 95+43 = 9×3 + 4×55×3 = 27+2015 = 4715 = 3215
At the end Combine the whole and fraction parts 11+3215  =  14215
10) 487 + 646=  (4+6)+8×6 + 4×77×6= 107642=10+13442=117642 =111721
Solution:
The first step is to rewrite the equation with parts separated, 4+87+6+46
Then solve the whole number parts 4+6=10
Now solve the fraction parts, and rewrite to solve with the equivalent fractions. 87+46 = 8×6 + 4×77×6 = 48+2842 = 7642 = 13442= 11721
At the end Combine the whole and fraction parts 10+11724  = 111721

Add Mixed Numbers Quiz