How Do You Answer This In Simplest Form?

3/5+1/2+3/10=


Answer:
When adding or subtracting fractions, usually you do it by expressing the fractions involved in such a way that respectively has the same denominator. Sometimes the process of finding a suitable denominator can be a challenge by itself. In this problem, one is suggested: 10.

We know that 3/5 is the "simplest form" of that fraction. In command for it to play well with the others, it needs to be within less simple form. We can change it to have a denominator of 10 resembling this: (3/5)*1 = (3/5)*(2/2) = (3*2)/(5*2) = 6/10. We choose 2/2 for this purpose because we have a denominator of 5 and we want a denominator of 10. We know that 5*2=10 (because we are well-versed in our multiplication tables, or because we can use a calculator).

Likewise, we express the fraction 1/2 as 1/2 = 1/2*1 = (1/2)*(5/5) = (1*5)/(2*5) = 5/10.

So, we can express the problem as
3/5 + 1/2 + 3/10 = 6/10 + 5/10 + 3/10 = (1/10)*(6 + 5 + 3) = (1/10)*14 = 14/10
  = (10/10) + (4/10) = 1 4/10 = 1 2/5.

For the later step, we had to reduce the fraction 4/10 to simplest terms by dividing both numerator and denominator by 2: 4/10 = (2*2)/(5*2) = (2/5)*(2/2) = (2/5)*1 = 2/5


Comment: 3/10 is already contained by simplest form 1/2 will be 5/10 and 3/5 will be 6/10
Answer: 2/10

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