Question

Write the ratio that compares 24 apples to 14 oranges using fractional notation. simplify improper fraction lowest terms

Which of the following, Option 1 or Option 2, is a proportion?

A. 4/5= 20/25
B. 4/5= 16/30

Answer 1

First, let's express the ratio of 24 apples to 14 oranges in fractional notation and simplify it.

The ratio is:

\[
\frac{24}{14}
\]

To simplify this improper fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:

\[
\frac{24 \div 2}{14 \div 2} = \frac{12}{7}
\]

So, the simplified ratio of 24 apples to 14 oranges is:

\[
\frac{12}{7}
\]

Next, let's determine which of the following is a proportion:

A. \( \frac{4}{5} = \frac{20}{25} \)

To check if this is true, we can simplify \( \frac{20}{25} \):

\[
\frac{20 \div 5}{25 \div 5} = \frac{4}{5}
\]

Since \( \frac{4}{5} = \frac{4}{5} \), this is a true proportion.

B. \( \frac{4}{5} = \frac{16}{30} \)

Next, let's simplify \( \frac{16}{30} \):

\[
\frac{16 \div 2}{30 \div 2} = \frac{8}{15}
\]

Now we compare:

\[
\frac{4}{5} \neq \frac{8}{15}
\]

Thus, this option is not a true proportion.

In conclusion:
- The simplified ratio of 24 apples to 14 oranges is \( \frac{12}{7} \).
- Option 1 (\( \frac{4}{5} = \frac{20}{25} \)) is a true proportion, while Option 2 (\( \frac{4}{5} = \frac{16}{30} \)) is not.