Subtracting Fractions with Unlike Denominators

Subtracting Fractions with Unlike Denominators

• To subtract fractions with unlike denominators, find a common denominator.
• The common denominator is a number divisible by both original denominators.
• The least common denominator (LCD) is the smallest common denominator, simplifying the process.

Finding a Common Denominator

• List the multiples of each denominator.
• Identify the smallest multiple common to both denominators. This is the LCD.
• If one denominator is a multiple of the other, the larger denominator is the LCD.

Converting Fractions to Equivalent Fractions

• To convert a fraction to an equivalent fraction with a common denominator, multiply both numerator and denominator by the same number.
• This doesn't change the fraction's value, only its representation.

Subtracting Fractions with a Common Denominator

• Once fractions share a common denominator, subtract the numerators.
• Maintain the common denominator.
• Simplify the resulting fraction by dividing both numerator and denominator by their greatest common factor (GCF), if possible.

Example

• Subtract 1/2 - 1/3
  • Find the LCD of 2 and 3. Multiples of 2: 2, 4, 6, 8... Multiples of 3: 3, 6, 9, 12... The least common multiple is 6.
  • Convert 1/2 to an equivalent fraction with a denominator of 6. Multiply both numerator and denominator by 3: (1 x 3) / (2 x 3) = 3/6
  • Convert 1/3 to an equivalent fraction with a denominator of 6. Multiply both numerator and denominator by 2: (1 x 2) / (3 x 2) = 2/6
  • Subtract the numerators: 3/6 - 2/6 = 1/6
  • The result is 1/6.

Mixed Numbers

• When subtracting mixed numbers with unlike denominators, first subtract the fractional parts. Subtract the whole numbers. Simplify the result if needed.
  • For example, 2 1/2 - 1 1/3 =...
    • Subtract the fractions: 1/2 - 1/3 = 3/6 - 2/6 = 1/6
    • Subtract the whole numbers: 2 - 1 = 1
  • Combine the results: 1 1/6

This quiz covers the steps to subtract fractions that have unlike denominators, focusing on finding a common denominator. You will learn how to determine the least common denominator and convert fractions to equivalent fractions for successful subtraction. Test your understanding of these concepts with this quiz!