Multiplication of Fractions

Working with Fractions

• A fraction remains unchanged when both its numerator and denominator are multiplied by the same number.

Multiplication of Fractions

• To multiply fractions, multiply the numerators together and the denominators together.
• Mixed numbers must be converted to improper fractions before multiplication.
• Cancel common factors between the numerator and denominator prior to multiplication.

Reciprocals

• Two numbers are reciprocals if their product equals 1.
• Example: 1/3 and 3 are reciprocals since ( \frac{1}{3} \times 3 = 1 ).
• The reciprocal of a fraction is found by inverting it. For instance, the reciprocal of 3/4 is 4/3.
• Any number can be expressed as a fraction, e.g., 3 can be written as 3/1.
• The reciprocal of 3/1 is 1/3, while the reciprocal of 2.5/1 is 0.4 (or 1/2.5).

Division by a Fraction

• Dividing by a fraction entails multiplying by its reciprocal.
• Example: For ( \frac{2}{5} \div \frac{3}{7} ), convert it to ( \frac{2}{5} \times \frac{7}{3} ) to get ( \frac{14}{15} ).

Exercises on Reciprocals

• The reciprocals for specific numbers can be captured in a table format, showcasing the number alongside its reciprocal, e.g.:
  • 1 has a reciprocal of 1,
  • 2.5 has a reciprocal of 0.4,
  • 4 has a reciprocal of 0.25, etc.

Quiz on multiplying fractions, including changing mixed numbers to improper fractions and cancelling common factors.