Fractions and Operations Quiz

Fractions

• Definition: A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number).

Adding Fractions

1. Like Fractions:

   • Add the numerators.
   • Keep the denominator the same.
   • Example: ( \frac{2}{5} + \frac{3}{5} = \frac{2 + 3}{5} = \frac{5}{5} = 1 )

2. Unlike Fractions:

   • Find a common denominator (LCD).
   • Convert each fraction.
   • Add the numerators.
   • Example: ( \frac{1}{4} + \frac{1}{6} )
     • LCD = 12; ( \frac{1}{4} = \frac{3}{12}, \ \frac{1}{6} = \frac{2}{12} )
     • Result: ( \frac{3}{12} + \frac{2}{12} = \frac{5}{12} )

Subtracting Fractions

1. Like Fractions:

   • Subtract the numerators.
   • Keep the denominator the same.
   • Example: ( \frac{5}{8} - \frac{3}{8} = \frac{5 - 3}{8} = \frac{2}{8} = \frac{1}{4} )

2. Unlike Fractions:

   • Find a common denominator (LCD).
   • Convert each fraction.
   • Subtract the numerators.
   • Example: ( \frac{2}{3} - \frac{1}{4} )
     • LCD = 12; ( \frac{2}{3} = \frac{8}{12}, \ \frac{1}{4} = \frac{3}{12} )
     • Result: ( \frac{8}{12} - \frac{3}{12} = \frac{5}{12} )

Multiplying Fractions

• Multiply the numerators together.
• Multiply the denominators together.
• Simplify if necessary.
• Example: ( \frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10} )

Dividing Fractions

• Multiply by the reciprocal of the divisor.
• Example: ( \frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} )
• Simplify if necessary.

Fractions Overview

• A fraction denotes a part of a whole, comprising a numerator (top part) and a denominator (bottom part).

Adding Fractions

• Like Fractions:

  • Combine the numerators while keeping the denominator unchanged.
  • For example: ( \frac{2}{5} + \frac{3}{5} = \frac{5}{5} = 1 ).

• Unlike Fractions:

  • Determine the least common denominator (LCD) to convert each fraction.
  • Add the adjusted numerators.
  • For example:
    • Calculate LCD for ( \frac{1}{4} + \frac{1}{6} ), which is 12.
    • Convert: ( \frac{1}{4} = \frac{3}{12}, \ \frac{1}{6} = \frac{2}{12} ).
    • Final result: ( \frac{5}{12} ).

Subtracting Fractions

• Like Fractions:

  • Subtract the numerators, maintaining the same denominator.
  • Example: ( \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} ).

• Unlike Fractions:

  • Identify the least common denominator (LCD).
  • Transform each fraction to the common denominator before subtracting the numerators.
  • Example:
    • For ( \frac{2}{3} - \frac{1}{4} ), determine LCD as 12.
    • Convert: ( \frac{2}{3} = \frac{8}{12}, \ \frac{1}{4} = \frac{3}{12} ).
    • Resulting in ( \frac{5}{12} ).

Multiplying Fractions

• Multiply the numerators together to form the new numerator.
• Multiply the denominators to create the new denominator.
• Simplify the result if necessary.
• Example: For ( \frac{2}{5} \times \frac{3}{4} ), calculate ( \frac{6}{20} ) which simplifies to ( \frac{3}{10} ).

Dividing Fractions

• Perform division by multiplying the first fraction by the reciprocal of the second.
• Example: ( \frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} ).
• Remember to simplify the result if possible.