Use properties of operations and rules for multiplying signed numbers to multiply −2/5 by 3/10

Question

. Write the answer in simplest form.(1 point)
Responses

−6/5
negative Start Fraction 6 over 5 End Fraction

−6/50
negative Start Fraction 6 over 50 End Fraction

−3/25
negative Start Fraction 3 over 25 End Fraction

3/5
Start Fraction 3 over 5 End Fraction

Answer 1

To multiply \(-\frac{2}{5}\) by \(\frac{3}{10}\), we follow the rules for multiplying signed numbers and the properties of operations.

1. Multiply the numerators: \(-2 \times 3 = -6\)
2. Multiply the denominators: \(5 \times 10 = 50\)

Now we combine these results:

\[ -\frac{6}{50} \]

Next, we can simplify \(-\frac{6}{50}\). Both 6 and 50 can be divided by their greatest common divisor, which is 2:

\[ -\frac{6 \div 2}{50 \div 2} = -\frac{3}{25} \]

Thus, the answer in simplest form is:

−3/25 (negative Start Fraction 3 over 25 End Fraction).

Answer 2

Multiply 4 by −5/8 . Write the answer as a mixed number in simplest form.(1 point)
Responses

−5/2
negative Start Fraction 5 over 2 End Fraction

−10
negative 10

−2 1/2
negative 2 Start Fraction 1 over 2 End Fraction

−2 4/8

Answer 3

To multiply \(4\) by \(-\frac{5}{8}\), we proceed as follows:

1. First, express \(4\) as a fraction: \(4 = \frac{4}{1}\).

2. Now we can multiply: \[ \frac{4}{1} \times -\frac{5}{8} = -\frac{4 \times 5}{1 \times 8} = -\frac{20}{8}. \]

3. Simplifying \(-\frac{20}{8}\): \[ -\frac{20 \div 4}{8 \div 4} = -\frac{5}{2}. \]

Since \(-\frac{5}{2}\) can also be expressed as a mixed number, we divide \(5\) by \(2\):

• \(5\) divided by \(2\) is \(2\) with a remainder of \(1\).

Thus, \(-\frac{5}{2}\) can also be written as \(-2 \frac{1}{2}\).

Therefore, the answer in mixed number form is:

−2 1/2 (negative 2 Start Fraction 1 over 2 End Fraction).

Answer 4

Multiply 6.5 by 0.3. Write the answer as a decimal.(1 point)
Responses

0.195
0.195

1.86
1.86

19.5
19.5

1.95

Answer 5

To multiply \(6.5\) by \(0.3\), we proceed as follows:

\[ 6.5 \times 0.3 = 1.95 \]

Thus, the answer as a decimal is:

1.95.

Answer 6

Multiply −19.3 by 6.(1 point)
Responses

−115.8
negative 115.8

−114.8
negative 114.8

−25.3
negative 25.3

115.8

Answer 7

To multiply \(-19.3\) by \(6\), we simply perform the multiplication:

\[ -19.3 \times 6 = -115.8 \]

Thus, the answer is:

−115.8 (negative 115.8).

Answer 8

Multiply −2 1/2 by −1 3/5 . Write the answer as a decimal.(1 point)
Responses

−4.1
negative 4.1

2.86
2.86

−4
negative 4

4

Answer 9

To multiply \(-2 \frac{1}{2}\) by \(-1 \frac{3}{5}\), we first convert the mixed numbers to improper fractions.

1. Convert \(-2 \frac{1}{2}\): \[ -2 \frac{1}{2} = -\frac{5}{2} \]

2. Convert \(-1 \frac{3}{5}\): \[ -1 \frac{3}{5} = -\frac{8}{5} \]

Now we multiply the two improper fractions:

\[ -\frac{5}{2} \times -\frac{8}{5} \]

When multiplying two negatives, the result is positive:

\[ = \frac{5 \times 8}{2 \times 5} = \frac{40}{10} = 4 \]

Thus, the answer as a decimal is:

4.