Question

Alexia makes 8 submarine sandwiches. She cuts 4 of the sandwiches into thirds and the remaining 4 into halves. If Alexia eats 2 of the

1/3-sandwich pieces, and her brother Bob eats 2 of the 1/2-sandwich pieces, what fraction of the 8 sandwiches does Bob eat?
a)1/4

b)1/3

c)3/8

d)5/8
​

Answer 1

Bob eats a total of 8/5 or 1 and 3/5 sandwiches out of the 8 sandwiches.

Step-by-step explanation:

To find out what fraction of the 8 sandwiches Bob eats, we need to figure out how many sandwich pieces he eats in total and then compare it to the total number of sandwich pieces.

Alexia cuts 4 of the sandwiches into thirds, so each third-sandwich piece is 1/3 of a sandwich. She eats 2 of these pieces, so she eats 2/3 of a sandwich in total.

Alexia cuts the remaining 4 sandwiches into halves, so each half-sandwich piece is 1/2 of a sandwich. Her brother Bob eats 2 of these pieces, so he eats 2/2 or 1 whole sandwich in total.

To find the fraction of the 8 sandwiches that Bob eats, we add the fractions of sandwich pieces eaten by Alexia and Bob. 2/3 + 1 = 5/3. Since Bob eats 1 whole sandwich and there are 3 pieces in a whole sandwich, we can write 1 as 3/3.

Adding the fractions gives us 5/3 + 3/3 = 8/3. To simplify the fraction, we divide both the numerator and denominator by 5, yielding 8/3 ÷ 5/5 = 8/5.

So, Bob eats a total of 8/5 or 1 and 3/5 sandwiches out of the 8 sandwiches.