Subtracting Mixed Fractions is finding the difference between two mixed fractions. These mixed fractions are improper fractions that are expressed as a sum of whole numbers and a proper fraction.
Suppose 5(2/6) - 3(1/6) to subtract these mixed fractions firstly, we have to convert them into improper fractions that will be 10/6 and 3/6. Now, we subtract 3/6 from 10/6, which gives 7/6; in the mixed fraction, that will be 1(1/6).
What are Mixed Fractions?
Mixed fractions, also known as mixed numbers, are a combination of a whole number and a proper fraction. They are written in the form
fraction, in the mixed fraction
Mixed fractions are often used to represent quantities that fall between two whole numbers. They are commonly encountered in everyday measurements, such as lengths, volumes, and quantities of objects.
Operations on Mixed Fractions
Four common operations can be applied to any type of fraction, including mixed fractions i.e.,
In this article, we will discuss the subtraction of mixed fractions in detail.
How to Subtract Mixed Fractions?
To subtract a pair of mixed fractions, we first need to converted them into improper fractions, then subtract by finding a common denominator, subtracting the numerators while keeping the denominator common, and simplifying the resulting fraction if possible.
There can be two possible cases for mixed fraction under subtraction i.e., mixed fraction with
- Like Denominators: Pair of mixed fraction with same denominator
- Unlike Denominators: Pair of mixed fraction with different denominator
Let's discuss both case in detail as follows.
Subtracting Mixed Fractions with Like Denominators
To subtract mixed fractions with like denominators, we need to follow the steps mentioned below:
- Convert mixed fractions to improper fractions if they're not already in that form.
- Subtract the numerators while keeping the common denominator.
- Simplify the resulting fraction if possible.
Let's consider example of subtraction of a pair of mixed fraction with like denominators i.e., 11(12/16) and 5 (8/16).
Step 1: Convert mixed fractions to improper fractions:
5\frac{8}{16} = \frac{5 \times 16}{16} + \frac{8}{16} = \frac{80}{16} + \frac{8}{16} = \frac{88}{16} 11\frac{12}{16} = \frac{11 \times 16}{16} + \frac{12}{16} = \frac{176}{16} + \frac{12}{16} = \frac{188}{16} Step 2: Subtract the numerators while keeping the common denominator:
\frac{88}{16} - \frac{188}{16} = \frac{88 - 188}{16} = \frac{-100}{16} Step 3: Simplify the resulting fraction:
Since the numerator is negative, we can represent it as
- \frac{100}{16} a\frac{-100}{16} = -\frac{25}{4}
Which can be simplified to -6\frac{1}{4} .
Subtracting Mixed Fractions with Unlike Denominators
When subtracting mixed fractions with unlike denominators, follow these steps:
- Convert mixed fractions to improper fractions if they're not already in that form.
- Find a common denominator for the fractions.
- Perform the subtraction by subtracting the numerators while keeping the common denominator.
- Simplify the resulting fraction if possible.
Let's consider example of subtraction of a pair of mixed fraction with like denominators i.e., 7(6/9) and 3(2/5).
Step 1: Convert mixed fractions to improper fractions:
7\frac{6}{9} = \frac{7 \times 9}{9} + \frac{6}{9} = \frac{63}{9} + \frac{6}{9} = \frac{69}{9} 3\frac{2}{5} = \frac{3 \times 5}{5} + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5} Step 2: Find a common denominator:
The least common multiple (LCM) of 9 and 5 is 45.
Step 3: Perform the subtraction:
\frac{69}{9} - \frac{17}{5} = \frac{69 \times 5}{9 \times 5} - \frac{17 \times 9}{5 \times 9} = \frac{345}{45} - \frac{153}{45} = \frac{345 - 153}{45} = \frac{192}{45} Step 4: Simplify the resulting fraction:
We can simplify
\frac{192}{45} by dividing both the numerator and denominator by their greatest common divisor, which is 3.
\frac{192}{45} = \frac{64}{15} = 4\frac{4}{15}
So,7\frac{6}{9} - 3\frac{2}{5} = 4\frac{4}{15} .
Related Articles | |
|---|---|
Subtracting Mixed Fractions Examples
Example 1: Subtract 3(1/4) from 5(2/4).
Solution:
5(2/4) - 3(1/4)
= 5 - 3 + (2/4 - 1/4 )
= 2 + ( 2-1 /4)
= 2 + (1/4)
= 2 (1/4)
Example 2: Subtract 3(2/5) from 9(7/10).
Solution:
9(7/10) - 3(2/5)
= (9 - 3) + ( 7/10 - 2/5)
= 6 + ( 7/10 - 2 * 2/5* 2)
= 6 + (7/10 - 4/10)
= 6 + ( 7- 4/10)
= 6 + (3/10)
= 6(3/10)
Example 3: Subtract 5(2/3) from 8(11/12).
Solution:
8(11/12) - 5(2/3)
= (8 -5) + (11/12 - 2/3)
= 3 + ( 11/12 - 2*4/3*4)
= 3 + ( 11/12 - 8 / 12)
= 3 + ( 11 - 8/12)
= 3 + (3/12)
= 3 + (1/4) Simplify, 3/12
= 3(1/4)
Example 4: Subtract 1(3/4) from 3(1/2).
Solution:
1(3/4) - 3(1/2)
= (3 -1) + (3/4 - 1/2)
= 2 + 1/2 - 3/4
= 2 + 2/4 - 3/4
= 2 + 2-3/4
= 2 + (-1/4)
= 2 - 1/4
= 1 (3/4)
Practice Questions on Subtracting Mixed Fractions
Q1: Subtract 4(1/2) from 7(3/4).
Q2: Subtract 9(2/3) from 12(5/6).
Q3: Subtract 5(3/8) from 8(2/5).
Q4: Subtract 6(5/6) from 10(2/3).
