Test yourself on addition and subtraction of mixed numbers!
\( 5\frac{2}{5}+2\frac{1}{5}= \)
Incorrect
Correct Answer:
\( 7\frac{3}{5} \)
Practice more now
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 354 into an equivalent fraction
Solution:
Find the numerator:
We will multiply the whole number: 3 by the denominator 5 and then add the numerator 4. We will obtain:
3×5+4=19
We obtained 19 and therefore this is what is written in the numerator.
The denominator will remain the same as the original: 5.
Therefore, we will obtain that:
3519=54
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Test your knowledge
Question 1
\( 6\frac{2}{6}+1\frac{2}{6}= \)
Incorrect
Correct Answer:
\( 7\frac{4}{6} \)
Question 2
\( 2\frac{1}{3}-1\frac{2}{3}= \)
Incorrect
Correct Answer:
\( \frac{2}{3} \)
Question 3
\( 10\frac{1}{2}-\frac{1}{2}= \)
Incorrect
Correct Answer:
\( 10 \)
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: 43 and 52
Solution:
We multiply the fraction 43 by 5 the denominator of the second fraction and obtain 2015
We multiply the fraction 52 by 4 the denominator of the first fraction and obtain: 208
The common denominator is 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
133+139=1312
Solution:
When the denominator is identical, we will only add the numerators and obtain: 1312
Do you know what the answer is?
Question 1
\( 2\frac{2}{5}+2\frac{2}{5}= \)
Incorrect
Correct Answer:
\( 4\frac{4}{5} \)
Question 2
\( 1\frac{2}{3}-1\frac{1}{3}= \)
Incorrect
Correct Answer:
\( \frac{1}{3} \)
Question 3
\( 13\frac{2}{3}-3\frac{1}{3}= \)
Incorrect
Correct Answer:
\( 10\frac{1}{3} \)
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)
243+162=
Solution:
Check your understanding
Question 1
\( 3\frac{1}{4}+1\frac{2}{4}= \)
Incorrect
Correct Answer:
\( 4\frac{3}{4} \)
Question 2
\( 4\frac{1}{2}-2\frac{1}{2}= \)
Incorrect
Correct Answer:
\( 2 \)
Question 3
\( 6+5\frac{2}{3}= \)
Incorrect
Correct Answer:
\( 11\frac{2}{3} \)
Step 1
Let's convert the two mixed numbers in the exercise into equivalent fractions:
243=42×4+3=411
162=66×1+2=68
Let's write the exercise again:
411+68=
Step 2
We find a common denominator by multiplying the denominators and we obtain: 2466+2432=
Step 3
We will only add the numerators and obtain:
2466+2432=2498
Another exercise on adding and subtracting mixed numbers
451−254=
Solution:
Step 1
Convert the two numbers into equivalent fractions:
463=64×6+3=627
251=52×5+1=511
Let's write the exercise again:
627−511=
Step 2
We find a common denominator by multiplying the denominators and we get:
30135−3066=
Step 3
We will only subtract the numerators and obtain:
30135−3066=3069
Examples and exercises with solutions for addition and subtraction of mixed numbers
Exercise #1
231−132=
Video Solution
Step-by-Step Solution
To solve the problem 231−132, we'll perform the following steps:
Step 1: Subtract the integer parts: 2−1=1.
Step 2: Subtract the fractional parts: 31−32.
To calculate 31−32:
Since the fractions have a common denominator, subtract only the numerators: 1−2=−1.
Therefore, 31−32=−31.
Now combine the results:
The subtraction results in 1−31.
To simplify, note 1=33.
Thus, 1−31=33−31=32.
Therefore, the solution to 231−132 is 32.
Answer
32
Exercise #2
552+251=
Video Solution
Step-by-Step Solution
To solve this problem, we'll follow these steps:
Step 1: Add the whole number parts.
Step 2: Add the fractional parts.
Step 3: Combine results and simplify if necessary.
Now, let's work through each step:
Step 1: The mixed numbers are 552 and 251. First, add the whole number parts: 5+2=7.
Step 2: Next, add the fractional parts: 52+51=53. Since the denominators are the same, just add the numerators.
Step 3: Combine these sums to form the mixed number: 7+53=753.
Therefore, the solution to the problem is 753.
Answer
753
Exercise #3
1021−21=
Video Solution
Step-by-Step Solution
Let's solve the problem step-by-step:
Step 1: Identify the parts of the mixed number 1021. It consists of the whole number 10 and the fraction 21.
Step 2: We'll subtract 21 (the fraction we are given to subtract) from the fraction part of the mixed number:
21−21=0
Step 3: After performing the subtraction, the fractional part becomes 0.
Step 4: This leaves us with the whole part of the mixed number on its own, which is 10.
Therefore, the solution to the problem is 10.
Answer
10
Exercise #4
662+162=
Video Solution
Step-by-Step Solution
To solve this problem, we will add the mixed numbers 662 and 162 by following these steps:
Step 1: Add the integer parts: 6+1=7.
Step 2: Add the fractional parts: 62+62=64.
Step 3: Combine the results to express the sum: 7+64.
Now, let's work through each step:
Step 1: Adding the whole numbers, we get 7.
Step 2: Since both fractions have a common denominator of 6, we add the numerators: 2+2=4, thus giving us the fraction 64.
Step 3: The combined sum of the whole number and the fraction is 764.
Hence, the solution to the problem is 764.
Answer
764
Exercise #5
252+252=
Video Solution
Step-by-Step Solution
To solve the problem 252+252, follow these steps:
Step 1: Add the whole numbers together. We have 2+2=4.
Step 2: Add the fractional parts together. Since both fractions have the same denominator, simply add the numerators: 52+52=54.
Step 3: Combine the results from Step 1 and Step 2. The sum of the whole numbers and fraction parts is 4+54=454.