Question

Use properties of rational numbers to multiply the following.

- 26(- 52/195)

OA. - 2/5

OB. 52/15

OC. 195/2

OD. 104/15

Answer 1

To multiply \( 26 \times \left(-\frac{52}{195}\right) \), we can simplify the calculation using properties of fractions and rational numbers.

First, we can express the whole number 26 as a fraction:

\[
26 = \frac{26}{1}
\]

Now, we can multiply:

\[
26 \times \left(-\frac{52}{195}\right) = \frac{26}{1} \times \left(-\frac{52}{195}\right) = -\frac{26 \times 52}{195}
\]

Next, we can perform the multiplication in the numerator:

\[
26 \times 52 = 1352
\]

Thus, we have:

\[
-\frac{1352}{195}
\]

Now we simplify \(-\frac{1352}{195}\). To do this, we need to find the greatest common divisor (GCD) of 1352 and 195.

Calculating the GCD, we see that both numbers can be divided by 13:

\[
1352 \div 13 = 104
\]
\[
195 \div 13 = 15
\]

So this gives us:

\[
-\frac{1352}{195} = -\frac{104}{15}
\]

Thus, the final answer is:

\[
-\frac{104}{15}
\]

This corresponds to none of the options you've provided, but we reached the conclusion that the answer is:

\(-\frac{104}{15}\)

If we consider only the answer choices provided, it appears the format may have been influenced by positive equivalents omitted in choice presentation. In terms of negativity, the value \(-\frac{104}{15}\) aligns perfectly as a rational representation of the calculation done based on fundamental properties of multiplication with fractions.