Subtracting fractions calculator

Subtracting fractions is a fundamental math skill. It involves working with numerators, denominators, and sometimes finding a common denominator. This guide explains how to subtract fractions step-by-step, making it easy for anyone to understand and apply.

Steps to Subtract Fractions

Step 1: Identify the Denominators

Fractions have two parts:

• Numerator: The number above the line.
• Denominator: The number below the line.

Example: In \( \frac{3}{4} – \frac{1}{2} \), the denominators are 4 and 2.

Step 2: Check If Denominators Are the Same

If the denominators are the same, subtract the numerators directly.
Example:

\( \frac{5}{8} – \frac{3}{8} = \frac{5-3}{8} = \frac{2}{8} \)

If the denominators are different, proceed to the next step.

Step 3: Find the Least Common Denominator (LCD)

The least common denominator is the smallest number both denominators divide into.

For \( \frac{3}{4} – \frac{1}{2} \):
The denominators are 4 and 2.
The LCD is 4.

Step 4: Convert the Fractions

Adjust each fraction so they have the same denominator.

Multiply the numerator and denominator of \( \frac{1}{2} \) by 2:
\( \frac{1}{2} = \frac{2}{4} \).

Now the problem is:
\( \frac{3}{4} – \frac{2}{4} \)

Step 5: Subtract the Numerators

Keep the denominator the same. Subtract only the numerators.
\( \frac{3}{4} – \frac{2}{4} = \frac{3-2}{4} = \frac{1}{4} \)

Step 6: Simplify the Fraction (If Needed)

If the result can be reduced, divide the numerator and denominator by their greatest common factor (GCF).
Example:
\( \frac{4}{8} = \frac{1}{2} \) (divide both by 4).

Subtracting Mixed Numbers

A mixed number combines a whole number and a fraction, like \( 3 \frac{1}{2} \).

Steps to Subtract Mixed Numbers

1. Convert mixed numbers into improper fractions.
   Example: \( 3 \frac{1}{2} = \frac{7}{2} \)
2. Follow the steps for subtracting fractions.
3. If needed, convert the result back into a mixed number.

Examples

Example 1: Same Denominator

\( \frac{7}{9} – \frac{4}{9} = \frac{7-4}{9} = \frac{3}{9} = \frac{1}{3} \)

Example 2: Different Denominators

\( \frac{5}{6} – \frac{1}{4} \)

1. LCD of 6 and 4 is 12.
2. Convert fractions:
   \( \frac{5}{6} = \frac{10}{12} \)
   \( \frac{1}{4} = \frac{3}{12} \)
3. Subtract: \( \frac{10}{12} – \frac{3}{12} = \frac{7}{12} \)

Tips for Subtracting Fractions

• Always simplify your answer.
• Double-check the LCD when working with different denominators.
• Practice with simple fractions before moving to mixed numbers.

Why Learn Fraction Subtraction?

Fraction subtraction is essential for solving real-world problems, from cooking to construction. Mastering this skill builds a strong foundation for advanced math topics.

By following these steps, you can confidently subtract fractions and mixed numbers!