Adding fractions calculator

Adding fractions is a fundamental math skill. Whether you are solving homework problems or working on real-world calculations, this guide will help you understand how to add fractions step by step.

Steps to Add Fractions

1. Check the Denominators:
   Fractions have two parts: the numerator (top number) and the denominator (bottom number). To add fractions, their denominators must be the same.
2. Find a Common Denominator:
   If the denominators are different, find the least common denominator (LCD). The LCD is the smallest number that both denominators divide into evenly.
3. Convert the Fractions:
   Adjust the fractions so they have the same denominator. Multiply both the numerator and denominator of each fraction by the number needed to reach the LCD.
4. Add the Numerators:
   Once the denominators match, add the numerators. Keep the denominator the same.
5. Simplify the Result:
   If possible, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Example 1: Adding Fractions with the Same Denominator

Problem:
\[
\frac{3}{8} + \frac{2}{8}
\]

• The denominators are the same (8).
• Add the numerators:
  \[
  3 + 2 = 5
  \]
• The result is
  \[
  \frac{5}{8}
  \]
  No simplification is needed.

Example 2: Adding Fractions with Different Denominators

Problem:
\[
\frac{1}{4} + \frac{2}{3}
\]

• Find the LCD of 4 and 3, which is 12.
• Convert
  \[
  \frac{1}{4} \text{ to } \frac{3}{12}
  \]
  and
  \[
  \frac{2}{3} \text{ to } \frac{8}{12}.
  \]
• Add the numerators:
  \[
  3 + 8 = 11
  \]
• The result is
  \[
  \frac{11}{12}
  \]
  No simplification is needed.

Adding Mixed Numbers

If the fractions are part of mixed numbers (e.g.)
\[
2 \frac{1}{3} + 1 \frac{2}{5}
\]
convert the mixed numbers to improper fractions. Add the fractions using the steps above, then convert the result back to a mixed number if needed.