Can someone explain to me the reasoning involved in each step when simplifying the fraction 42/56. I had this question wrong in my previous exam...I don't know what i was thinking when answering it......but i like to know what was the actual responce for it....thanks ...:-)
I don't know all of the "technical steps" one goes through. I divide first by 2 to obtain
21/28. Mentally, then, I go through 2, 3, 4, 5, 6 and none of those will go into both 21 and 28. Then I try 7 and that works to give 3/4. That tells me that 2*7=14 would have been the largest divisor but I already have my answer with 3/4 and the factor of 14 is just an interesting tidbid of information. Of course, IF your exam question was to divide by the largest divisor to simplify, then I would have used 2 and 7 anyway, but put on paper 14. I hope this helps.
212 in base 3 and divide 3
To simplify the fraction 42/56, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by that common factor.
In this case, you started by dividing both 42 and 56 by 2. This step is correct as 2 is a common factor of both numbers.
42 ÷ 2 = 21
56 ÷ 2 = 28
So, you obtained the fraction 21/28.
Next, you mentally checked for other common factors. You tried dividing by 3, 4, 5, and 6, but none of these numbers divided both 21 and 28. When you tried dividing by 7, it worked.
21 ÷ 7 = 3
28 ÷ 7 = 4
Now, you found that the fraction 21/28 simplifies to 3/4.
So, the correct answer for simplifying 42/56 is 3/4.
Additionally, you realized that 14 would have been the largest divisor because it is the product of the prime factors 2 and 7. Although this information is not necessary for simplifying the fraction, it is indeed an interesting fact.