Choose all of the options which are equal to: 1/2(2/3 + 3/4)

A: 1/3 + 3/8

B: 17/24

C: 4/11

D: 1/2 x 17/12

E: 1/2(3/4 + 2/3)

F: (1/2 + 2/3) + 3/4

Someone please help- I don't understand anything to do with fractions...

Study this site very carefully, then try some of those problems.

https://www.mathsisfun.com/fractions.html

1/2(2/3 + 3/4) = 1/2(8/12+9/12) = 1/2 * 17/12 = 17/24 = 1/3 + 3/8 = 1/2(3/4+2/3).

No worries! I'll explain how to work with fractions and solve this problem step by step.

To add fractions, you need to have a common denominator. The common denominator is a number that can be divided evenly by the denominators of all the fractions you are adding.

In this case, the denominators are 3 and 4. To find the common denominator, you need to find the least common multiple (LCM) of 3 and 4.

To find the LCM of 3 and 4, you can list the multiples of each number and find the smallest number that appears in both lists. The multiples of 3 are 3, 6, 9, 12, 15, 18, ... and the multiples of 4 are 4, 8, 12, 16, 20, 24, ...

From these lists, you can see that 12 is the smallest number that appears in both lists, so the LCM of 3 and 4 is 12.

Now, we can rewrite the fractions with the common denominator of 12.

2/3 becomes (2/3)(4/4) = 8/12
3/4 becomes (3/4)(3/3) = 9/12

Next, we can add the fractions using the common denominator:

1/2(2/3 + 3/4) = 1/2(8/12 + 9/12)

Adding the fractions:
8/12 + 9/12 = 17/12

Finally, we can simplify the expression:

1/2(2/3 + 3/4) = 1/2(17/12)

To multiply a fraction by a whole number, you multiply the numerator of the fraction by the whole number and keep the denominator the same. So:

1/2(17/12) = 1/2 x 17/12 = 17/24

Therefore, the option that is equal to 1/2(2/3 + 3/4) is B: 17/24.