Subtraction of Fractions with Mixed Numbers

Subtracting fractions with mixed numbers involves converting mixed numbers to improper fractions, finding a common denominator, and then subtracting the fractions.

A mixed number consists of two components:

Whole Numbers: These are the integer parts of the mixed numbers.

Fractions: These are the fractional parts of the mixed numbers.

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

When subtracting fractions with mixed numbers, students should follow these rules:

Convert to improper fractions: Convert all mixed numbers to improper fractions.

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

Subtract the fractions: Subtract the numerators while keeping the denominator the same.

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

The following are the methods for subtracting fractions with mixed numbers:

Method 1: Conversion Method

To apply the conversion method for subtraction of fractions with mixed numbers, follow these steps:

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

Step 2: Find a common denominator for the fractions.

Step 3: Subtract the numerators and keep the common denominator.

Step 4: Convert the result back to a mixed number if needed and simplify.

Example: Subtract 3 1/2 from 5 3/4

Step 1: Convert to improper fractions: 7/2 and 23/4

Step 2: Common denominator is 4: 14/4 and 23/4

Step 3: Subtract: 23/4 - 14/4 = 9/4

Step 4: Convert back: 2 1/4

Method 2: Separation Method

For the separation method, subtract the whole numbers and fractions separately:

Step 1: Subtract the whole numbers.

Step 2: Subtract the fractional parts using the common denominator.

Step 3: Combine the results and simplify if needed.

Example: Subtract 6 5/8 from 9 3/8

Step 1: Subtract whole numbers: 9 - 6 = 3

Step 2: Subtract fractions: 3/8 - 5/8 = -2/8 = -1/4

Step 3: Combine: 3 - 1/4 = 2 3/4

Subtraction of fractions with mixed numbers has some characteristic properties:

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.

Changing the grouping changes the result when three or more fractions are involved. (A − B) − C ≠ A − (B − C)

Subtracting zero from a fraction leaves the fraction unchanged

Subtracting zero from any fraction results in the same fraction: A - 0 = A.

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

Tip 1: Always convert mixed numbers to improper fractions to make calculations easier.

Tip 2: Find the least common denominator to simplify subtraction.

Tip 3: If the fractions have the same denominator, focus on the numerators; this simplifies the process.

Subtraction of fractions with mixed numbers can be challenging and often leads to common mistakes. Being aware of these errors can help students avoid them.