Question

Marcus ate half of a pizza on Monday night. He then ate one third of the remaining pizza on Tuesday. Which of the following expressions shows how much pizza Marcus ate in total?
Responses




1 - 1 2 · 1 3





1 2 + 1 2 + 1 3




1 2 + 1 3

Answer 1

To find out how much pizza Marcus ate in total, we need to consider both the amount he ate on Monday and Tuesday.

1. On Monday, Marcus ate half of the pizza, which is represented as \( \frac{1}{2} \).
2. After Monday, the remaining pizza is \( 1 - \frac{1}{2} = \frac{1}{2} \).
3. On Tuesday, he ate one third of the remaining pizza, which is \( \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \).

Now, we can add the amount he ate on both days:

Total pizza eaten = Amount eaten on Monday + Amount eaten on Tuesday
Total pizza eaten = \( \frac{1}{2} + \frac{1}{6} \)

To add these fractions, we need a common denominator. The least common multiple of 2 and 6 is 6.

Converting \( \frac{1}{2} \) to sixths:
\[
\frac{1}{2} = \frac{3}{6}
\]

Now we can add the two fractions:
\[
\frac{3}{6} + \frac{1}{6} = \frac{4}{6}
\]

We can simplify \( \frac{4}{6} = \frac{2}{3} \).

Thus, the total amount of pizza Marcus ate is \( \frac{2}{3} \).

Given the response options, the correct expression that represents the amount of pizza Marcus ate in total is:

**\( \frac{1}{2} + \frac{1}{3} \)**.