The first half of the problem:
[(1/3)(1/4)]
When you multiply fractions, you multiply the two numerators (the numbers on the top of the fractions) and you multiply the two denominators (the numbers on the bottom of the fractions).
So,
1/3 times 1/4 =
1x1 / 3x4 =
1/12
And the second half of the problem:
[(1/6)/(8/3)]
Now, when you DIVIDE BY a fraction, you can flip the fraction you are dividing by (in this case, the fraction you are dividing by is 8/3) and multiply it to the first fraction.
So,
(1/6) divided by (8/3) is the same thing as
(1/6) times (3/8)
And what is (1/6) x (3/8)? it's going to be:
(1 times 3) divided by (6 times 8).
which equals:
3/48
Alright, so now you need to add (1/12) + (3/48). To do this, we need to find a common denominator. In other words, a common denominator is a number that is a multiple of all the denominators of a set of fractions. We're trying to get all the denominators to be the same number before we add.
The lowest common denominator of 12 and 48 is 48, since 12 times 4 = 48. So we can leave the 3/48 alone, but we need to change the 1/12.
When we change fractions, all we can do is multiply both the numerator and denominator by the same number. So our new fraction will reduce to the same fraction as before, the same way 6/3 = 2/1. If you multiply 2 by 3 and multiply 1 by 3, you get 6 and 3.
So, since 12 times 4 = 48, we can multiply both the numerator and denominator of 1/12 by 4.
So, 1/12 = (1 x 4) / (12 x 4) = 4/48
Does 4/48 still equal 1/12? Yes.
Now we can finally add the two numbers.
4/48 + 3/48 =
7/48
And 7/48 is your final answer.
The first half of the problem:
[(1/3)(1/4)]
When you multiply fractions, you multiply the two numerators (the numbers on the top of the fractions) and you multiply the two denominators (the numbers on the bottom of the fractions).
So,
1/3 times 1/4 =
1x1 / 3x4 =
1/12
And the second half of the problem:
[(1/6)/(8/3)]
Now, when you DIVIDE BY a fraction, you can flip the fraction you are dividing by (in this case, the fraction you are dividing by is 8/3) and multiply it to the first fraction.
So,
(1/6) divided by (8/3) is the same thing as
(1/6) times (3/8)
And what is (1/6) x (3/8)? it's going to be:
(1 times 3) divided by (6 times 8).
which equals:
3/48
Alright, so now you need to add (1/12) + (3/48). To do this, we need to find a common denominator. In other words, a common denominator is a number that is a multiple of all the denominators of a set of fractions. We're trying to get all the denominators to be the same number before we add.
The lowest common denominator of 12 and 48 is 48, since 12 times 4 = 48. So we can leave the 3/48 alone, but we need to change the 1/12.
When we change fractions, all we can do is multiply both the numerator and denominator by the same number. So our new fraction will reduce to the same fraction as before, the same way 6/3 = 2/1. If you multiply 2 by 3 and multiply 1 by 3, you get 6 and 3.
So, since 12 times 4 = 48, we can multiply both the numerator and denominator of 1/12 by 4.
So, 1/12 = (1 x 4) / (12 x 4) = 4/48
Does 4/48 still equal 1/12? Yes.
Now we can finally add the two numbers.
4/48 + 3/48 =
7/48
And 7/48 is your final answer.