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Question

How would I solve: 2 1/6 + 3(4 5/12 + 1/6) ?


Answer

First, do the addition inside the brackets. Converting 4 5/12 to an improper fraction might make this easier. 4 5/12 is equivalent to 53/12.

So our question can now be written: 2 1/6 + 3(53/12 + 1/6).

Now, when adding fractions (for some help with adding fractions click here) the denominators of the fractions need to be the same. If we multiply 1/6 by 2/2, we change it to a form with a denominator of 12, without changing the value of the fraction.

So, 1/6 x 2/2 = 2/12

Remember that 1/6 is the same amount as 2/12; it is just written in a different way.

Now that we have the fractions inside the brackets with the same denominator, we can add them.

(53/12 + 2/12) = 55/12

So, our question can now be written:

2 1/6 + 3(55/12)

Next, we will do the multiplication. 3(55/12) is the same as 3 x 55/12.

3/1 x 55/12 = 165/12 (for help with multiplying fractions, click here)

Now, an addition is all that we have left to do.

2 1/6 + 165/12

We can convert 2 1/6 to an improper fraction - this might make the addition easier.

2 1/6 = 13/6

Then, we can multiply 13/6 by 2/2 so that it has the same denominator as 165/12.

13/6 x 2/2 = 26/12

Now, just add these fractions

26/12 + 165/12 = 191/12 (which is the same as 15 11/12)

Our answer is 15 11/12.


Here is the working without my explanations included: