Question

Use properties of rational numbers to multiply The following "-28" x (-56/210) A.112/15 B.105 C.-2/5 D.56/15

Answer 1

To multiply the rational numbers \(-28\) and \(-\frac{56}{210}\), we first note that multiplying two negative numbers gives a positive product.

1. Calculate the product:

\[
-28 \times -\frac{56}{210} = 28 \times \frac{56}{210}
\]

2. Next, simplify \(\frac{56}{210}\):

- Find the greatest common divisor (GCD) of \(56\) and \(210\):
- \(56 = 2^3 \cdot 7\)
- \(210 = 2 \cdot 3 \cdot 5 \cdot 7\)

The GCD is \(14\).

3. Divide both the numerator and denominator of \(\frac{56}{210}\) by \(14\):

\[
\frac{56 \div 14}{210 \div 14} = \frac{4}{15}
\]

4. Now, multiply \(28\) by the simplified fraction:

\[
28 \times \frac{4}{15} = \frac{28 \times 4}{15} = \frac{112}{15}
\]

Thus, the final result is:

\[
-28 \times -\frac{56}{210} = \frac{112}{15}
\]

The answer corresponds to option **A. \(\frac{112}{15}\)**.