Subtraction of Dissimilar Fractions

Subtracting dissimilar fractions involves finding a common denominator so the fractions can be subtracted. It requires converting each fraction to an equivalent fraction with the same denominator.

There are three components of a fraction:

Numerator: The top part of a fraction, indicating how many parts are taken.

Denominator: The bottom part of a fraction, indicating the total number of equal parts.

Fraction bar: This separates the numerator and the denominator and denotes division.

When subtracting dissimilar fractions, students should follow these steps:

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

Convert fractions: Rewrite each fraction as an equivalent fraction with the common denominator.

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

Simplify the result: If possible, simplify the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The following are methods for subtracting dissimilar fractions:

Method 1: Least Common Denominator (LCD) Method

Step 1: Find the least common denominator of the fractions.

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

Step 3: Subtract the numerators and keep the LCD as the denominator.

Step 4: Simplify the resulting fraction if possible.

Example: Subtract 3/4 from 5/6.

Step 1: LCM of 4 and 6 is 12.

Step 2: Convert: 3/4 = 9/12, 5/6 = 10/12.

Step 3: Subtract: 10/12 - 9/12 = 1/12.

Method 2: Cross-Multiplication Method

Step 1: Cross-multiply the fractions.

Step 2: Subtract the cross products and write over the product of the denominators.

Step 3: Simplify the resulting fraction if possible.

Example: Subtract 2/3 from 4/5.

Step 1: Cross-multiply: (4×3) - (2×5) = 12 - 10 = 2.

Step 2: Denominator: 3×5 = 15.

Step 3: Result: 2/15.

In fraction subtraction, some characteristic properties are observed:

1. Subtraction is not commutative In subtraction, changing the order of the fractions changes the result, i.e., A/B - C/D ≠ C/D - A/B.
2. Subtraction is not associative Unlike addition, regrouping is not possible in subtraction. For three or more fractions, changing the grouping changes the result. ((A/B) - (C/D)) - (E/F) ≠ (A/B) - ((C/D) - (E/F)).
3. Subtraction is the addition of the opposite Subtracting a fraction is the same as adding its opposite, so convert subtraction into addition by reversing the sign of the second fraction. A/B - C/D = A/B + (-C/D).
4. Subtracting zero from a fraction leaves the fraction unchanged Subtracting zero from any fraction results in the same fraction: A/B - 0 = A/B.

Useful tips for students to efficiently handle subtraction of dissimilar fractions include:

Tip 1: Always determine the least common denominator to simplify calculations.

Tip 2: Simplify fractions at every step to manage smaller numbers and reduce errors.

Tip 3: Visual learners can use fraction strips or area models to understand subtraction better.

Subtraction of dissimilar fractions can be challenging, leading to common mistakes. Awareness of these errors can help students avoid them.