How to Cancel Multiply

To multiply fractions using full cancellation, follow these steps:

Identify Common Factors

When multiplying two fractions, identify one numerator and one denominator that share a common factor. This common factor must be a number that divides both the numerator and the denominator without leaving a remainder.

Cancel Out Common Factors

Cancel out the common factor from the numerator and the denominator. To do this, divide each number by the common factor and replace the original numbers with the results of this division.

Example

For the fractions (frac{9}{10} times frac{5}{12}):

• Identify the common factor: 9 and 12 share a common factor of 3, and 10 and 5 share a common factor of 5.
• Cancel out the common factors:
  • For 9 and 12, divide both by 3: (9 div 3 = 3) and (12 div 3 = 4).
  • For 10 and 5, divide both by 5: (10 div 5 = 2) and (5 div 5 = 1).

Rewrite the Fractions

Rewrite the fractions using the results of the cancellation:
[
frac{9}{10} times frac{5}{12} = frac{3}{2} times frac{1}{4}
]

Multiply the Numerators and Denominators

Multiply the new numerators together and the new denominators together:
[
frac{3 times 1}{2 times 4} = frac{3}{8}
]

Final Result

The result is already in simplest form, so no further simplification is needed.

Key Points

• Always cancel diagonally (one numerator with one denominator), never horizontally.
• Ensure that the cancellation is done before multiplying to avoid complex simplification later.
• If multiple common factors exist, cancel them out one by one until no further simplification is possible.

By following these steps, you can efficiently multiply fractions and obtain the result in its simplest form.