Questions: Determine whether the fractions 12/15 and 15/30 are equivalent. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) A. The fractions are equivalent because the product of the numerator of the first fraction and the denominator of the second fraction is equal to the product of the numerator of the second fraction and the denominator of the first fraction. That is, the cross product for each multiplication is . B. The fractions are not equivalent because the product of the numerator of the first fraction and the denominator of the second fraction is , which is not equal to the product of the numerator of the second fraction and the denominator of the first fraction, .

$Determine whether the fractions 12/15 and 15/30 are equivalent. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) A. The fractions are equivalent because the product of the numerator of the first fraction and the denominator of the second fraction is equal to the product of the numerator of the second fraction and the denominator of the first fraction. That is, the cross product for each multiplication is . B. The fractions are not equivalent because the product of the numerator of the first fraction and the denominator of the second fraction is , which is not equal to the product of the numerator of the second fraction and the denominator of the first fraction, .$

Transcript text: Determine whether the fractions $\frac{12}{15}$ and $\frac{15}{30}$ are equivalent. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) A. The fractions are equivalent because the product of the numerator of the first fraction and the denominator of the second fraction is equal to the product of the numerator of the second fraction and the denominator of the first fraction. That is, the cross product for each multiplication is $\square$ . B. The fractions are not equivalent because the product of the numerator of the first fraction and the denominator of the second fraction is $\square$ , which is not equal to the product of the numerator of the second fraction and the denominator of the first fraction, $\square$ $\square$.

Solution

Solution Steps

Step 1: Simplify the Fractions

First, we simplify both fractions to see if they are equivalent.

For $\frac{12}{15}$:

The greatest common divisor (GCD) of 12 and 15 is 3.
Simplifying: $\frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5}$.

For $\frac{15}{30}$:

The greatest common divisor (GCD) of 15 and 30 is 15.
Simplifying: $\frac{15}{30} = \frac{15 \div 15}{30 \div 15} = \frac{1}{2}$.

Step 2: Compare the Simplified Fractions

Now, compare the simplified fractions:

$\frac{4}{5}$ and $\frac{1}{2}$ are not equal.

Step 3: Verify Using Cross Multiplication

To verify using cross multiplication, calculate the cross products:

The product of the numerator of the first fraction and the denominator of the second fraction: $12 \times 30 = 360$.
The product of the numerator of the second fraction and the denominator of the first fraction: $15 \times 15 = 225$.

Since $360 \neq 225$, the fractions are not equivalent.

Final Answer

The fractions are not equivalent because the product of the numerator of the first fraction and the denominator of the second fraction is $360$, which is not equal to the product of the numerator of the second fraction and the denominator of the first fraction, $225$.

\[ \boxed{\text{The answer is B.}} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!