Subtracting Mixed Fractions

Subtracting Mixed Fractions is a subtraction operation of any two mixed fractions. Even though, These mixed fractions are improper fractions that are made up of a whole number and a proper fraction. Suppose 5(2/6) – 3(1/6). Firstly, we have to convert them into simple fractions that will be 10/6 and 3/6. Now, we subtract 3/6 from 10/6 which gives 7/6, or in the mixed fraction that will be 1(1/6).

In this article, we will learn about mixed fractions with the subtracting method;

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 [Tex]a\frac{b}{c}[/Tex] or a(b/c), where a is the whole number part, b is the numerator of the fraction part, and c is the denominator of the fraction part.

For example, in the mixed fraction [Tex]3\frac{1}{2}[/Tex] , 3 is the whole number part, 1 is the numerator of the fraction part, and 2 is the denominator of the fraction part. Together, they represent the value [Tex]3 \frac{1}{2}[/Tex], which is equal to 3 + 1/2 or 7/2.

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

There are four common operations that can be applied to any type of fraction including mixed fraction i.e.,

• Addition
• Subtraction
• Multiplication
• Division

In this article, we will discuss subtraction of mixed fraction in detail.

How to Subtract Mixed Fractions?

A pair of mixed fractions under the operation of subtraction can be converted into improper fractions, then subtracted by finding a common denominator, subtracting the numerators while keeping the common denominator, and simplifying the resulting fraction if possible.

There can be two posssible 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

When subtracting mixed fractions with like denominators, you follow these steps:

• 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 denomiators i.e., 11(12/16) and 5 (8/16).

Step 1: Convert mixed fractions to improper fractions:

• [Tex]5\frac{8}{16} = \frac{5 \times 16}{16} + \frac{8}{16} = \frac{80}{16} + \frac{8}{16} = \frac{88}{16}[/Tex]
• [Tex]11\frac{12}{16} = \frac{11 \times 16}{16} + \frac{12}{16} = \frac{176}{16} + \frac{12}{16} = \frac{188}{16}[/Tex]

Step 2: Subtract the numerators while keeping the common denominator:

• [Tex]\frac{88}{16} – \frac{188}{16} = \frac{88 – 188}{16} = \frac{-100}{16}[/Tex]

Step 3: Simplify the resulting fraction:

Since the numerator is negative, we can represent it as [Tex]- \frac{100}{16}[/Tex] a

[Tex]\frac{-100}{16} = -\frac{25}{4}[/Tex]

Which can be simplified to –[Tex]6\frac{1}{4}[/Tex].

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 denomiators i.e., 7(6/9) and 3(2/5).

Step 1: Convert mixed fractions to improper fractions:

• [Tex]7\frac{6}{9} = \frac{7 \times 9}{9} + \frac{6}{9} = \frac{63}{9} + \frac{6}{9} = \frac{69}{9}[/Tex]
• [Tex]3\frac{2}{5} = \frac{3 \times 5}{5} + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}[/Tex]

Step 2: Find a common denominator:

The least common multiple (LCM) of 9 and 5 is 45.

Step 3: Perform the subtraction:

[Tex]\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}[/Tex]

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.

[Tex]\frac{192}{45} = \frac{64}{15} = 4\frac{4}{15}[/Tex]

So, [Tex]7\frac{6}{9} – 3\frac{2}{5} = 4\frac{4}{15}[/Tex].

Conclusion

In conclusion, subtracting mixed fractions involves converting them into improper fractions, finding a common denominator, subtracting the fractions’ numerators while keeping the common denominator, and simplifying the result if needed. With practice, you’ll become more confident in handling mixed fractions and improve your overall math skills.

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).

FAQs on Subtracting Mixed Fractions

What are mixed fractions?

Mixed fractions, also known as mixed numbers, consist of a whole number and a proper fraction, such as 3(1/2)​.

How do you subtract mixed fractions?

To subtract mixed fractions, convert them to improper fractions, find a common denominator, subtract the fractions’ numerators while keeping the common denominator, and simplify the resulting fraction if necessary.

When do I need to borrow when subtracting mixed fractions?

You need to borrow from the whole number part of the minuend when the fraction part of the minuend is smaller than the fraction part of the subtrahend.

What is regrouping in subtracting mixed fractions?

Regrouping involves borrowing from the whole number part of the minuend to properly subtract the fractions when necessary, especially when the fraction part of the minuend is smaller than the fraction part of the subtrahend.

What if the denominators of the mixed fractions are different?

If the denominators are different, you need to find a common denominator before subtracting the fractions.

How do I simplify the resulting fraction after subtracting?

To simplify the resulting fraction, divide both the numerator and denominator by their greatest common divisor, if possible.