Subtraction of Dissimilar Fractions

Subtracting dissimilar fractions involves finding a common denominator before performing the subtraction. This process requires converting the fractions to have like denominators and then subtracting the numerators.

The components of a fraction include:

Numerator: The top number in a fraction, representing the number of parts.

Denominator: The bottom number in a fraction, representing the total number of equal parts.

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

When subtracting dissimilar fractions, students should follow these steps:

Find a common denominator: Determine the least common multiple (LCM) of the denominators and convert fractions to equivalent fractions with this common denominator.

Subtract numerators: Once the fractions have the same denominator, subtract the numerators while keeping the denominator unchanged.

Simplify the result: If possible, reduce the fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor (GCD).

The following are the methods for subtracting dissimilar fractions:

Method 1: Finding a Common Denominator

Step 1: Identify the LCM of the denominators.

Step 2: Convert each fraction to an equivalent fraction with the LCM as the new denominator.

Step 3: Subtract the numerators and write the result over the common denominator.

Example: Subtract 3/4 from 5/6.

Step 1: LCM of 4 and 6 is 12.

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

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

Method 2: Cross-Multiplication

This method involves cross-multiplying the fractions and using the result to perform subtraction.

Example: Subtract 3/5 from 7/8.

Solution: Cross-multiply: (7*5) - (3*8) / (5*8) = (35 - 24) / 40 = 11/40.

Therefore, upon subtracting, we get 11/40.

In fraction subtraction, the following properties are observed:

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

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

• Subtraction is the addition of the opposite sign Subtracting a fraction is the same as adding its opposite, so to make calculations easier, you can convert subtraction into addition by changing the sign of the second fraction. A − B = A + (−B).

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

Here are some tips and tricks to efficiently subtract dissimilar fractions:

Tip 1: Always find the LCM of the denominators to make subtraction straightforward.

Tip 2: Simplify fractions whenever possible to make calculations easier and results clearer.

Tip 3: Use the cross-multiplication method for quick calculations, especially with simpler fractions.

Subtracting dissimilar fractions can be challenging, and common mistakes can occur. Being aware of these errors can help students avoid them.