Compare simplifying before multiplying fractions with simplifying after multiplying fractions
(6/12 ) * (20/30) = 120/360
1/2 * 2/3 = 2/6 = 1/3
When comparing the process of simplifying before multiplying fractions with simplifying after multiplying fractions, it's important to understand the underlying principles involved.
Simplifying before multiplying fractions involves reducing the fractions to their simplest form before performing the multiplication.
Here's how you can simplify before multiplying fractions:
1. Take each fraction and factorize the numerator and denominator.
2. Identify the common factors between the numerators and denominators.
3. Cancel out these common factors by dividing them from both the numerator and the denominator.
4. After canceling out all the common factors, multiply the remaining numerators and denominators to get the final result.
On the other hand, simplifying after multiplying fractions involves performing the multiplication first, and then reducing the resulting fraction to its simplest form.
Here's how you can simplify after multiplying fractions:
1. Multiply the numerators of the fractions to get the resulting numerator.
2. Multiply the denominators of the fractions to get the resulting denominator.
3. If possible, factorize the resultant numerator and denominator.
4. Determine any common factors in the numerator and denominator and cancel them out.
5. Continue canceling out common factors until no more can be found.
6. Finally, write the remaining numerator and denominator as the simplified fraction.
So, to summarize:
- Simplifying before multiplying fractions involves canceling out common factors before performing the multiplication.
- Simplifying after multiplying fractions involves first performing the multiplication and then reducing the resulting fraction.
Both methods yield the same result; however, simplifying before multiplying fractions can sometimes make the calculations easier by reducing the numbers involved earlier in the process.