Subtraction of Unlike Fractions

Subtracting unlike fractions involves finding a common denominator and converting the fractions to equivalent fractions with this common denominator. Once the fractions have the same denominator, the numerators can be subtracted directly. The process involves three main components: 

Numerators: These are the top numbers of fractions. 

Denominators: These are the bottom numbers of fractions. -

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

When subtracting unlike fractions, students should follow these steps:

1. Find a common denominator: Determine the least common multiple (LCM) of the denominators.

2. Convert to equivalent fractions: Adjust the fractions so they have the same denominator.

3. Subtract the numerators: Subtract the numerators while keeping the common denominator.

4. Simplify the result: Reduce the fraction to its simplest form, if possible.

The following are the methods for subtracting unlike fractions: -

Method 1: Common Denominator Method

Step 1: Identify the least common denominator (LCD) of the fractions.

Step 2: Convert each fraction to an equivalent fraction with the LCD.

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

Example: Subtract 1/3 from 5/4

Step 1: LCD of 3 and 4 is 12.

Step 2: Convert 1/3 to 4/12 and 5/4 to 15/12.

Step 3: Subtract: 15/12 - 4/12 = 11/12.

Answer: 11/12 

Method 2: Cross Multiplication Method

This method involves using cross multiplication to find a common denominator and directly computing the difference.

Example: Subtract 2/5 from 3/7

Solution: Cross multiply: (3 * 5) - (2 * 7) = 15 - 14 = 1.

Common denominator: 5 * 7 = 35.

Result: 1/35.

Therefore, the result of the subtraction is 1/35.

In fraction subtraction, there are some characteristic properties. These properties are listed below: -

• Subtraction is not commutative: Changing the order of the fractions changes the result, i.e., A/B - C/D ≠ C/D - A/B. 

• Subtraction is not associative: Unlike addition, regrouping terms in subtraction changes the result. 

• Subtraction involves finding a common denominator: To make subtraction easier, fractions are converted to have a common denominator. 

• Subtracting zero leaves the fraction unchanged: Subtracting zero from a fraction gives the same fraction: A/B - 0 = A/B.

Tips and tricks are useful for students to efficiently handle the subtraction of unlike fractions. Some helpful tips are listed below: 

Tip 1: Always find the least common denominator to make calculations simpler. 

Tip 2: Simplify fractions whenever possible to make subtraction easier. 

Tip 3: Using visual aids like fraction strips can help beginners understand the subtraction process better.

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