Simplify: Divide by common factor of 3 to get 7/20
Example 2: 4/7 x 9/5
Multiply numerators: 4 x 9 = 36
Multiply denominators: 7 x 5 = 35
Result: 36/35 (No simplification needed)
Multiplying by Mixed Numbers:
Convert mixed numbers to improper fractions.
Example: Multiply 4/5 by 2 3/4
Convert 2 3/4 to improper fraction: (2 x 4) + 3 = 11/4
Multiply: 4/5 x 11/4
Result: 44/20
Simplify: Divide by common factor of 4 to get 11/5
Fractions Less Than One:
Multiplying fractions less than one results in a smaller number.
Example: 1/2 x 1/3 = 1/6
Dividing Fractions
Basic Process:
Write the division problem as a multiplication problem by flipping the second fraction (take the reciprocal).
Change the division sign to multiplication.
Example 1: 3/4 ÷ 5/9
Flip the second fraction: 9/5
Change to multiplication: 3/4 x 9/5
Multiply: 3 x 9 = 27, 4 x 5 = 20
Result: 27/20 (No simplification needed)
Example 2: 2/3 ÷ 4/5
Flip the second fraction: 5/4
Change to multiplication: 2/3 x 5/4
Multiply: 2 x 5 = 10, 3 x 4 = 12
Result: 10/12
Simplify: Divide by common factor of 2 to get 5/6
Dividing Mixed Numbers:
Convert mixed numbers to improper fractions first.
Example: 3 1/2 ÷ 2/5
Convert 3 1/2 to improper: (3 x 2) + 1 = 7/2
Flip second fraction: 5/2
Change to multiplication: 7/2 x 5/2
Multiply: 7 x 5 = 35, 2 x 2 = 4
Result: 35/4
Convert to mixed number: 8 3/4
Conclusion
Understanding how to multiply and divide fractions involves straightforward steps of basic arithmetic and conversion between mixed and improper fractions.
Simplification is often necessary to obtain the final answer in simplest form.
Practice these steps to master fraction operations.