How to Subtract Mixed Numbers?
What are Mixed Numbers?
A mixed number is a fraction containing a whole number and a fraction.
For instance, \( 5\frac{8}{11} \) is an example of a mixed number, in which 5 is a whole number and \( \frac{8}{11} \) is a fraction.
Subtraction with Mixed Numbers
There are two different methods to subtract mixed numbers.
Method 1:
Step 1: First, we subtract the whole number parts of the given mixed numbers. This will be the difference of the whole numbers.
Step 2: Now, subtract the fractional parts of the mixed numbers. We may observe two types of fractions in this step. Fractions with like denominators and fractions with unlike denominators.
Step 3: If the fractions have like denominators, we can directly subtract the numerators and further simplify the operation to get the difference of the fractional parts.
Step 4: If the fractions have unlike denominators, use equivalent fractions to make the denominators the same. In this way, we can convert the unlike fractions into like fractions. Once we get like fractions, follow the previous step to get the difference of the fractions.
Step 5: Now, merge both the results, obtained after subtracting the whole number parts and fraction parts. This will be the final result.
Method 2:
Another way to subtract two or more mixed numbers is to write each mixed number as an equivalent improper fraction. Perform the subtraction after getting the improper fractions.
For instance, consider, \( 5\frac{4}{9}~-~4\frac{2}{9} \)
The first mixed number = \( 5\frac{4}{9} \)
= \( \frac{45~+~4}{9}\) [Multiply whole number with the denominator and add numerator]
= \( \frac{49}{9} \)
And the second mixed number \( 4\frac{2}{9} \) = \( \frac{36~+~2}{9} \) [Multiply whole number with the denominator and add numerator]
= \( \frac{38}{9}\)
Now, the difference between both the numbers, \( 5\frac{4}{9}~-~4\frac{2}{9} ~=~\frac{49}{9}~-~\frac{38}{9}~=~\frac{11}{9}\)
Rapid Recall
Solved Examples
Example 1:
Find the difference between the mixed numbers: \( 5\frac{9}{100}~-~3\frac{7}{100} \)
Solution:
We have to find the value of \( 5\frac{9}{100}~-~3\frac{7}{100} \)
Subtract the whole numbers in the expression, that is 5 – 3 = 2
Since both the mixed numbers have like denominators, directly subtract the numerators and simplify if required.
Then,
\( \Rightarrow \frac{9}{100}~-~\frac{7}{100}~=~\frac{2}{100} \) [Subtract the numerator]
\(~~~~~~~~~~~~~~~~~~~~~~~=~\frac{1}{50} \) [Divide both numerator and denominator with 2]
Thus, \( 5\frac{9}{100}~-~3\frac{7}{100}~=~2\frac{1}{50} \).
Example 2:
Find the value of: \( 8\frac{11}{12}~-~5\frac{2}{3} \).
Solution:
We have to find the value of \( 8\frac{11}{12}~-~5\frac{2}{3} \)
Subtract the whole numbers in the expression, that is 8 – 5 = 3
Here, the fractions have unlike denominators. Convert them into like fractions.
That is,
\( \frac{2}{3}~=~\frac{2~\times~4}{3~\times~4} \) [Multiply numerator and denominator with 4, to make denominator 12]
= \( \frac{8}{12}\)
Now subtract,
\(\frac{11}{12}~-~\frac{2}{3}~=~\frac{11}{12}~-~\frac{8}{12}\)
\(~~~~~~~~~~~~~~~=~\frac{11~-~8}{12}\) [Subtract only numerator and keep the same denominator]
\(~~~~~~~~~~~~~~~=~\frac{3}{12}\) [Subtract]
\(~~~~~~~~~~~~~~~=~\frac{1}{4}\) [Divide both numerator and denominator with 3]
Merging both the values, we get \(3~+~\frac{1}{4}~=~3\frac{1}{4}\).
Hence, \( 8\frac{11}{12}~-~5\frac{2}{3}~=~3\frac{1}{4} \).
Example 3:
Richard has recently launched a bakery. He bought \( 5\frac{3}{2} \) pounds of butter to make cakes. If he used \( 2\frac{7}{8} \) pounds of butter to make cakes, what is the quantity of butter Richard is left with?
Solution:
It is stated that Richard has \( 5\frac{3}{2} \) pounds of butter to make cakes.
It is also mentioned out of \( 5\frac{3}{2} \) pounds of butter, he used \( 2\frac{7}{8} \) pounds and made the cakes. In order to find the amount of the remaining butter, subtract the amount of butter used from the total amount of butter.
That is,
= \( 5\frac{3}{2}~-~2\frac{7}{8} \)
Now, subtract the whole number part, 5 – 2 = 3
Since the fractions are unlike, write the equivalent fractions.
= \(\frac{3}{2}~=~\frac{3~\times~4}{2~\times~4}\) [Multiply numerator and denominator with 4, to make denominator 8]
\(~=~\frac{12}{8}\)
Now, \(\frac{3}{2}~-~\frac{7}{8}~=~\frac{12}{8}~-~\frac{7}{8}\)
\(~~~~~~~~~~~~~~~~~~~~~~~=~\frac{5}{8}\)
Now, merge both the values to get the total difference, \(3~+~\frac{5}{8}~=~3\frac{5}{8}\).
Therefore, the Richard is left with \(3\frac{5}{8}\) pounds of butter.
We can subtract two or more mixed numbers in two different ways. One way is to subtract the whole number parts and fractional parts individually. The other way is to write the mixed numbers as equivalent fractions and find the difference between them.
In the case of two or more mixed numbers having like denominators, directly subtract the whole number parts and their numerators, keeping the denominator the same and simplify in the final step.
If mixed numbers have unlike denominators, then we should write the fraction linked to one of the mixed numbers as an equivalent fraction compared to the second fraction. Subtract the mixed numbers and simplify, if required.