Subtraction of Mixed Numbers

Subtracting mixed numbers involves converting the mixed numbers to improper fractions or borrowing whole numbers to simplify the operation. This ensures that the subtraction is performed accurately.

Mixed numbers include: Whole Numbers: These are integers like 1, 2, etc.

Fractions: These represent parts of a whole, like 1/2, 3/4, etc.

Operators: For subtraction, the operator is the minus (-) symbol.

When subtracting mixed numbers, students should follow these rules:

Convert to improper fractions: Convert each mixed number to an improper fraction or borrow from the whole number if necessary.

Find a common denominator: Ensure both fractions have the same denominator before subtracting.

Subtract the fractions and whole numbers: Subtract the fractions and then the whole numbers separately.

Simplifying result: Simplify the resulting fraction if needed and convert back to a mixed number if necessary.

The following are the methods of subtraction of mixed numbers:

Method 1: Conversion Method

To apply the conversion method for subtraction of mixed numbers, use the following steps.

Step 1: Convert each mixed number to an improper fraction.

Step 2: Find a common denominator for the fractions.

Step 3: Subtract the fractions and simplify, if possible.

Let’s apply these steps to an example: Question: Subtract )

Step 1: Convert each mixed number to an improper fraction,

Step 2: Find a common denominator for the fractions.

Step 3: Subtract the fractions and simplify:

Answer:

Method 2: Borrowing Method

When subtracting mixed numbers using the borrowing method, we may need to borrow from the whole number if the fractional part of the minuend is smaller than the fractional part of the subtrahend. For example, Subtract 

Solution: Convert the fractional part of the minuend by borrowing from the whole number. 1 3/4 - 1 5/8 = 1 6/8 - 1 5/8 = 1/8

Therefore, upon subtracting, we get 1/8.

In mathematics, subtraction of mixed numbers has some characteristic properties. These properties are listed below:

• Subtraction is not commutative In subtraction, changing the order of the terms changes the result, i.e., A - B ≠ B - A

• Subtraction is not associative Unlike addition, we cannot regroup in subtraction. When three or more numbers are involved, changing the grouping changes the result. (A − B) − C ≠ A − (B − C)

• Subtracting zero from a number leaves the number as is Subtracting zero from any number results in the same number: A - 0 = A

• Subtraction of identical numbers results in zero Subtracting a number from itself gives zero: A - A = 0

Tips and tricks are useful for students to efficiently deal with the subtraction of mixed numbers. Some helpful tips are listed below:

Tip 1: Always pay attention to borrowing when the fractional part of the minuend is smaller than the fractional part of the subtrahend.

Tip 2: Convert mixed numbers to improper fractions for straightforward subtraction if necessary.

Tip 3: Beginners and visual learners can benefit from drawing a number line or using visual fraction models to better understand the subtraction process.

Subtraction of mixed numbers can be challenging, leading to common mistakes. However, being aware of these errors can help students avoid them.