Addition and Subtraction of Mixed Numbers In this article, we will learn how to add and subtract mixed numbers easily, quickly, and effortlessly.
The solution to add and subtract mixed numbers consists of 3 steps:
The first step Convert the mixed number into an equivalent fraction, a fraction with only a numerator and denominator without whole numbers.
How do you convert a mixed number into an equivalent fraction?
Multiply the whole number by the denominator. To the result, you will add the numerator. The final result will be recorded in the new numerator.
The denominator will remain the same.
Let's look at an example Convert the mixed number 3 4 5 3 \frac {4}{5} 3 5 4 into an equivalent fraction
Solution:
Find the numerator:
We will multiply the whole number: 3 3 3 by the denominator 5 5 5 and then add the numerator 4 4 4 . We will obtain:
3 × 5 + 4 = 19 3\times 5+4=19 3 × 5 + 4 = 19
We obtained 19 19 19 and therefore this is what is written in the numerator.
The denominator will remain the same as the original: 5 5 5 .
Therefore, we will obtain that:
3 19 5 = 4 5 3 \frac {19}{5}= \frac {4}{5} 3 5 19 = 5 4
Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
The second step Find a common denominator (usually by multiplying the denominators)
Reminder:
Using the method of multiplying the denominators, we multiply the first fraction by the denominator of the second fraction and the second fraction by the denominator of the first fraction.
Remember to multiply both the numerator and the denominator.
For example Find a common denominator for the fractions : 3 4 3 \over 4 4 3 and 2 5 2 \over 5 5 2
Solution:
We multiply the fraction 3 4 3 \over 4 4 3 by 5 5 5 the denominator of the second fraction and obtain 15 20 15 \over 20 20 15
We multiply the fraction 2 5 2 \over 5 5 2 by 4 4 4 the denominator of the first fraction and obtain: 8 20 8 \over 20 20 8
The common denominator is 20 20 20 .
The third step Sum or subtract numerators only. The denominator will remain the same and will be written once in the final result.
For example 3 13 + 9 13 = 12 13 \frac {3}{13}+\frac {9}{13}=\frac {12}{13} 13 3 + 13 9 = 13 12
Solution:
When the denominator is identical, we will only add the numerators and obtain: 12 13 \frac {12}{13} 13 12
Do you know what the answer is?
Exercises on Addition and Subtraction of Mixed Numbers Now, after having learned all the steps for the solution, we will practice exercises on adding and subtracting mixed numbers:
Exercise 1 (addition and subtraction of mixed numbers) 2 3 4 + 1 2 6 = 2 \frac {3}{4}+1 \frac {2}{6}= 2 4 3 + 1 6 2 =
Solution:
Step 1 Let's convert the two mixed numbers in the exercise into equivalent fractions:
2 3 4 = 2 × 4 + 3 4 = 11 4 2 \frac {3}{4}= \frac {2 \times 4+3}{4}=\frac {11}{4} 2 4 3 = 4 2 × 4 + 3 = 4 11
1 2 6 = 6 × 1 + 2 6 = 8 6 1 \frac {2}{6}= \frac {6 \times 1+2}{6}=\frac {8}{6} 1 6 2 = 6 6 × 1 + 2 = 6 8
Let's write the exercise again:
11 4 + 8 6 = \frac{11}{4}+\frac{8}{6}= 4 11 + 6 8 =
Step 2 We find a common denominator by multiplying the denominators and we obtain:66 24 + 32 24 = \frac {66}{24}+\frac {32}{24}= 24 66 + 24 32 =
Step 3 We will only add the numerators and obtain:
66 24 + 32 24 = 98 24 \frac {66}{24}+\frac {32}{24}= \frac {98}{24} 24 66 + 24 32 = 24 98
Another exercise on adding and subtracting mixed numbers 4 1 5 − 2 4 5 = 4 \frac {1}{5}-2 \frac {4}{5}= 4 5 1 − 2 5 4 =
Solution:
Step 1 Convert the two numbers into equivalent fractions:
4 3 6 = 4 × 6 + 3 6 = 27 6 4 \frac {3}{6}= \frac {4 \times 6+3}{6}=\frac {27}{6} 4 6 3 = 6 4 × 6 + 3 = 6 27
2 1 5 = 2 × 5 + 1 5 = 11 5 2 \frac {1}{5}= \frac {2 \times 5+1}{5}=\frac {11}{5} 2 5 1 = 5 2 × 5 + 1 = 5 11
Let's write the exercise again:
27 6 − 11 5 = \frac{27}{6}-\frac{11}{5}= 6 27 − 5 11 =
Step 2 We find a common denominator by multiplying the denominators and we get:
135 30 − 66 30 = \frac{135}{30}-\frac{66}{30}= 30 135 − 30 66 =
Step 3 We will only subtract the numerators and obtain:
135 30 − 66 30 = 69 30 \frac {135}{30}-\frac {66}{30}=\frac {69}{30} 30 135 − 30 66 = 30 69
Examples and exercises with solutions for addition and subtraction of mixed numbers Exercise #1 7 5 6 + 6 2 3 + 1 3 = 7\frac{5}{6}+6\frac{2}{3}+\frac{1}{3}= 7 6 5 + 6 3 2 + 3 1 =
Video Solution Step-by-Step Solution Note that the right addition exercise between the fractions gives a result of a whole number, so we'll start with it:
6 2 3 + 1 3 = 7 6\frac{2}{3}+\frac{1}{3}=7 6 3 2 + 3 1 = 7
Now we get:
7 5 6 + 7 = 14 5 6 7\frac{5}{6}+7=14\frac{5}{6} 7 6 5 + 7 = 14 6 5
Answer Exercise #2 1 2 + 3 1 2 + 4 2 4 = \frac{1}{2}+3\frac{1}{2}+4\frac{2}{4}= 2 1 + 3 2 1 + 4 4 2 =
Video Solution Step-by-Step Solution According to the order of operations, we will solve the exercise from left to right.
Let's note that in the first addition exercise, we have an addition between two halves that will give us a whole number, so:
1 2 + 3 1 2 = 4 \frac{1}{2}+3\frac{1}{2}=4 2 1 + 3 2 1 = 4
Now we will get the exercise:
4 + 4 2 4 = 4+4\frac{2}{4}= 4 + 4 4 2 =
Let's note that we can simplify the mixed fraction:
2 4 = 1 2 \frac{2}{4}=\frac{1}{2} 4 2 = 2 1
Now the exercise we get is:
4 + 4 1 2 = 8 1 2 4+4\frac{1}{2}=8\frac{1}{2} 4 + 4 2 1 = 8 2 1
Answer Exercise #3 1 3 + 2 3 + 2 3 4 = \frac{1}{3}+\frac{2}{3}+2\frac{3}{4}= 3 1 + 3 2 + 2 4 3 =
Video Solution Step-by-Step Solution According to the rules of the order of operations in arithmetic, we solve the exercise from left to right.
Let's note that:
1 3 + 2 3 = 3 3 = 1 \frac{1}{3}+\frac{2}{3}=\frac{3}{3}=1 3 1 + 3 2 = 3 3 = 1
We should obtain the following exercise:
1 + 2 3 4 = 3 3 4 1+2\frac{3}{4}=3\frac{3}{4} 1 + 2 4 3 = 3 4 3
Answer Exercise #4 6 7 x + 8 7 x + 3 2 3 x = \frac{6}{7}x+\frac{8}{7}x+3\frac{2}{3}x= 7 6 x + 7 8 x + 3 3 2 x =
Video Solution Step-by-Step Solution Let's solve the exercise from left to right.
We will combine the left expression in the following way:
6 + 8 7 x = 14 7 x = 2 x \frac{6+8}{7}x=\frac{14}{7}x=2x 7 6 + 8 x = 7 14 x = 2 x
Now we get:
2 x + 3 2 3 x = 5 2 3 x 2x+3\frac{2}{3}x=5\frac{2}{3}x 2 x + 3 3 2 x = 5 3 2 x
Answer Exercise #5 10 1 2 − 1 2 = 10\frac{1}{2}-\frac{1}{2}= 10 2 1 − 2 1 =
Video Solution Answer Do you think you will be able to solve it?