Adding fractions with unlike denominators

Introduction

This tutorial will guide you through the process of adding fractions with unlike denominators. Understanding how to find a common denominator and combine fractions is an essential skill in mathematics. Whether you're a student learning the basics or someone needing a refresher, this guide will provide clear, actionable steps to help you master this concept.

Step 1: Identify the Denominators

• Look at the fractions you want to add. For example, consider the fractions ( \frac{1}{3} ) and ( \frac{1}{4} ).
• Identify the denominators (the bottom numbers) of both fractions. In this case, the denominators are 3 and 4.

Step 2: Find the Least Common Denominator (LCD)

• The least common denominator is the smallest number that both denominators can divide into evenly.
• To find the LCD:
  • List the multiples of each denominator:
    • Multiples of 3: 3, 6, 9, 12, 15, ...
    • Multiples of 4: 4, 8, 12, 16, ...
  • Identify the smallest multiple common to both lists. Here, the LCD is 12.

Step 3: Convert Each Fraction to an Equivalent Fraction

• Adjust each fraction so they both have the common denominator.

• For ( \frac{1}{3} ):

  • Find what to multiply the denominator to reach the LCD: ( 3 \times 4 = 12 ).
  • Multiply both the numerator and denominator by the same number:
    • ( \frac{1 \times 4}{3 \times 4} = \frac{4}{12} ).

• For ( \frac{1}{4} ):

  • Find what to multiply the denominator to reach the LCD: ( 4 \times 3 = 12 ).
  • Multiply both the numerator and denominator by the same number:
    • ( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} ).

Step 4: Add the Equivalent Fractions

• Now that both fractions have the same denominator, you can add them:
  • ( \frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12} ).

Step 5: Simplify the Result (if necessary)

• Check if the resulting fraction can be simplified. In this case, ( \frac{7}{12} ) is already in its simplest form.

Conclusion

Adding fractions with unlike denominators involves finding a common denominator, converting each fraction, and then adding them together. Remember to always check if your final answer can be simplified. With practice, this process will become second nature. For further practice, try adding different sets of fractions using the same steps outlined above.