How To Minus Fractions

Dianna Russini

3 min read

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Apr 02, 2025

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How to Minus Fractions: A Step-by-Step Guide

Subtracting fractions might seem daunting, but with a clear understanding of the process, it becomes straightforward. This guide breaks down how to minus fractions, covering everything from simple subtraction to more complex scenarios involving mixed numbers. We'll focus on using clear, step-by-step instructions and practical examples to solidify your understanding.

Understanding the Basics: Same Denominators

The easiest type of fraction subtraction involves fractions with the same denominator. The denominator represents the total number of parts in a whole, while the numerator represents how many of those parts you have.

Example: Subtract 2/5 from 4/5

1. Check the denominators: Both fractions have a denominator of 5. This is great! We can proceed directly to subtraction.

2. Subtract the numerators: Subtract the numerator of the second fraction (2) from the numerator of the first fraction (4): 4 - 2 = 2

3. Keep the denominator the same: The denominator remains 5.

4. Result: The answer is 2/5.

Subtracting Fractions with Different Denominators

When the denominators are different, we need to find a common denominator before we can subtract. This involves finding the least common multiple (LCM) of the denominators.

Example: Subtract 1/3 from 2/5

1. Find the least common denominator (LCD): The LCM of 3 and 5 is 15.

2. Convert fractions to equivalent fractions with the LCD:

   • To convert 1/3 to an equivalent fraction with a denominator of 15, multiply both the numerator and the denominator by 5: (1 x 5) / (3 x 5) = 5/15
   • To convert 2/5 to an equivalent fraction with a denominator of 15, multiply both the numerator and the denominator by 3: (2 x 3) / (5 x 3) = 6/15

3. Subtract the numerators: Subtract the numerators: 6 - 5 = 1

4. Keep the common denominator: The denominator remains 15.

5. Result: The answer is 1/15

Subtracting Mixed Numbers

Mixed numbers contain a whole number and a fraction (e.g., 2 1/2). Subtracting mixed numbers requires a slightly more involved process.

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

1. Convert mixed numbers to improper fractions:

   • 3 1/2 = (3 x 2 + 1) / 2 = 7/2
   • 1 1/4 = (1 x 4 + 1) / 4 = 5/4

2. Find the LCD: The LCD of 2 and 4 is 4.

3. Convert to equivalent fractions with the LCD:

   • 7/2 = (7 x 2) / (2 x 2) = 14/4

4. Subtract the numerators: 14 - 5 = 9

5. Keep the common denominator: The denominator remains 4.

6. Convert back to a mixed number (if necessary): 9/4 = 2 1/4

Borrowing When Subtracting Mixed Numbers

Sometimes, you'll need to "borrow" from the whole number when the fraction in the minuend (the number you're subtracting from) is smaller than the fraction in the subtrahend (the number you're subtracting).

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

1. Notice: 1/4 < 3/4. We need to borrow.

2. Borrow from the whole number: Borrow 1 from the 4, converting it to a fraction with the common denominator (4). This becomes 4/4.

3. Add the borrowed fraction: Add 4/4 to 1/4: 1/4 + 4/4 = 5/4

4. Rewrite the minuend: The minuend becomes 3 5/4.

5. Convert to improper fractions and subtract:

   • 3 5/4 = 17/4
   • 2 3/4 = 11/4
   • 17/4 - 11/4 = 6/4 = 1 2/4 = 1 1/2

Therefore, 4 1/4 - 2 3/4 = 1 1/2

This comprehensive guide provides a solid foundation for subtracting fractions. Practice these steps with various examples, and you'll quickly master this essential mathematical skill. Remember to always check your work!