Mcguire Savage
10/05/2023 · Middle School
(40) Which of the expression(s) below is greater than \( \frac{2}{3} \) ? Select all that apply. \( \begin{array}{l}\text { A) } \frac{1}{3} \div \frac{2}{8} \\ \text { B) } \frac{3}{4} \div \frac{3}{2} \\ \text { O C) } \frac{1}{2} \div \frac{3}{5}\end{array} \)
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Tutor-Verified Answer
Step-by-step Solution
To determine which of the given expressions is greater than \( \frac{2}{3} \), we will evaluate each expression one by one.
**A) \( \frac{1}{3} \div \frac{2}{8} \)**
First, we simplify \( \frac{2}{8} \):
\[
\frac{2}{8} = \frac{1}{4}
\]
Now, we perform the division:
\[
\frac{1}{3} \div \frac{1}{4} = \frac{1}{3} \times \frac{4}{1} = \frac{4}{3}
\]
Now we compare \( \frac{4}{3} \) with \( \frac{2}{3} \):
\[
\frac{4}{3} > \frac{2}{3}
\]
So, expression A is greater than \( \frac{2}{3} \).
---
**B) \( \frac{3}{4} \div \frac{3}{2} \)**
Now we perform the division:
\[
\frac{3}{4} \div \frac{3}{2} = \frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{2}{4} = \frac{1}{2}
\]
Now we compare \( \frac{1}{2} \) with \( \frac{2}{3} \):
\[
\frac{1}{2} < \frac{2}{3}
\]
So, expression B is not greater than \( \frac{2}{3} \).
---
**C) \( \frac{1}{2} \div \frac{3}{5} \)**
Now we perform the division:
\[
\frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{1 \times 5}{2 \times 3} = \frac{5}{6}
\]
Now we compare \( \frac{5}{6} \) with \( \frac{2}{3} \):
To compare, we can convert \( \frac{2}{3} \) to sixths:
\[
\frac{2}{3} = \frac{4}{6}
\]
Now we see that:
\[
\frac{5}{6} > \frac{4}{6}
\]
So, expression C is greater than \( \frac{2}{3} \).
---
In conclusion, the expressions that are greater than \( \frac{2}{3} \) are:
- **A) \( \frac{1}{3} \div \frac{2}{8} \)**
- **C) \( \frac{1}{2} \div \frac{3}{5} \)**
Thus, the final answer is:
**A and C**.
Quick Answer
The expressions greater than \( \frac{2}{3} \) are A) \( \frac{1}{3} \div \frac{2}{8} \) and C) \( \frac{1}{2} \div \frac{3}{5} \).
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