Question

Use properties of rational numbers to multiply the following.
-7/5× 3.625
ㅇA. -21/4
O B.-203/40
C. 89/40
D. -145/56

Answer 1

To multiply the rational number \(-\frac{7}{5}\) by \(3.625\), we first convert \(3.625\) into a fraction.

The decimal \(3.625\) can be written as:

\[
3.625 = \frac{3625}{1000}
\]

Next, we simplify the fraction \(\frac{3625}{1000}\):

1. Find the GCD (Greatest Common Divisor) of 3625 and 1000.
- The prime factorization of 3625 is \(5^2 \times 145\) (since \(3625 = 5 \times 725\), and \(725 = 5 \times 145\)).
- The prime factorization of 1000 is \(10^3 = 2^3 \times 5^3\).
- The GCD is \(5^2 = 25\).

Now, divide the numerator and denominator by 25:

\[
\frac{3625 \div 25}{1000 \div 25} = \frac{145}{40}
\]

So, \(3.625\) as a fraction is:

\[
3.625 = \frac{145}{40}
\]

Now we can multiply \(-\frac{7}{5}\) by \(\frac{145}{40}\):

\[
-\frac{7}{5} \times \frac{145}{40} = \frac{-7 \times 145}{5 \times 40}
\]

Calculating the numerator and denominator:

- Numerator: \(-7 \times 145 = -1015\)
- Denominator: \(5 \times 40 = 200\)

So we have:

\[
-\frac{1015}{200}
\]

Now we can simplify this fraction. Divide both the numerator and denominator by 5:

\[
-\frac{1015 \div 5}{200 \div 5} = -\frac{203}{40}
\]

Thus, \(-7/5 \times 3.625\) simplifies to:

\[
\boxed{-\frac{203}{40}}
\]

This corresponds to option B.