Please help just get started

Sarah went trick-or-treating for Halloween. Because of her braces, she could not eat of the candy she received since it was either sticky or chewy. Of the candy she could not eat, she gave 2/3 of it to her older brother Bradley and3/7 of it to her younger brother Shane.
Bradley and Shane were trying to determine how much of Sarah's candy they received in all. Bradley said that they could find the amount by simplifying the expression 2/3 x (3/7 + 2/7). Shane thought for a moment and determined that Bradley must be wrong and said that they could find the amount by simplifying the expression (2/3 x 3/7) + (2/3 x 2/7).

The absolute value of the difference between the two methods proposed by Bradly and Shane is ????

After all that wordsalad, where does the 2/7 come from??

why not just 2/3 + 3/7 ?

That's
14/21 + 9/21 = 23/21
Oops. How's that possible?

So, I guess the question is, what part of the candy could she not eat?

To find the absolute value of the difference between the two methods proposed by Bradley and Shane, we need to evaluate both expressions and subtract them. Let's break it down step by step.

Bradley's expression is 2/3 multiplied by the sum of 3/7 and 2/7:
2/3 x (3/7 + 2/7).

To simplify this expression, we need to find a common denominator for the fractions inside the parentheses. The common denominator for 7 and 7 is 7, so we can rewrite the expression as:
2/3 x (5/7).

Now, we multiply the numerators and the denominators together:
(2 x 5) / (3 x 7) = 10/21.

So according to Bradley's method, Bradley and Shane received a total of 10/21 of the candy.

Shane's expression is (2/3 x 3/7) + (2/3 x 2/7).

We can simplify this expression by multiplying each fraction separately:
(2/3 x 3/7) = 6/21
(2/3 x 2/7) = 4/21

Now, we add the two fractions together:
(6/21) + (4/21) = 10/21.

According to Shane's method, Bradley and Shane also received a total of 10/21 of the candy.

To find the absolute value of the difference between the two methods, subtract one expression from the other and take the absolute value:
|10/21 - 10/21| = |0| = 0.

Therefore, the absolute value of the difference between Bradley and Shane's methods is 0.