compare simpifying before multiplying fractions with simpifying after mutipihiing the fractions?
When comparing the process of simplifying before multiplying fractions with simplifying after multiplying the fractions, it is important to understand the order of operations in mathematics.
Simplifying before multiplying involves reducing the fractions to their simplest form before performing the multiplication. This can be done by finding the greatest common divisor (GCD) of the numerator and denominator of each fraction and then dividing both by the GCD.
For example:
1/2 * 2/3 = (1 * 2) / (2 * 3) = 2/6
In this case, if we simplify before multiplying, we would simplify 1/2 to 1/2, and 2/3 to 2/3, resulting in 1/2 * 2/3 = 1/2 * 2/3 = 2/6.
Simplifying after multiplying involves performing the multiplication first and then reducing the resulting fraction to its simplest form. This can be done in the same way as simplifying before multiplying.
For example:
1/2 * 2/3 = (1 * 2) / (2 * 3) = 2/6
In this case, if we multiply first and then simplify, we would multiply 1/2 by 2/3 to get 2/6. Then, we can simplify 2/6 by finding its GCD, which is 2. Dividing both the numerator and denominator by 2 gives us the simplified fraction of 1/3.
So, while the intermediate steps may differ, both approaches lead to the same simplified result of 1/3.
In summary, whether you simplify before or after multiplying fractions, the result will be the same. However, simplifying after multiplying can often involve larger numbers, which may make the process more complex. Simplifying before multiplying can help simplify the calculations and reduce the possibility of errors.