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

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

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

3/5
Start Fraction 3 over 5 End Fraction

−6/50

Answer 1

To multiply \(-\frac{2}{5}\) by \(\frac{3}{10}\), follow these steps:

1. Multiply the numerators: \(-2 \times 3 = -6\)

2. Multiply the denominators: \(5 \times 10 = 50\)

3. Combine the results: \[ -\frac{6}{50} \]

4. Simplify the fraction: The GCD (greatest common divisor) of 6 and 50 is 2. Therefore, divide the numerator and the denominator by 2: \[ -\frac{6 \div 2}{50 \div 2} = -\frac{3}{25} \]

The final answer in simplest form is \(-\frac{3}{25}\).

So, the correct response is: −3/25.

Answer 2

Multiply 4 by −58 . Write the answer as a mixed number in simplest form.(1 point)
Responses

−52
negative Start Fraction 5 over 2 End Fraction

−10
negative 10

−248
negative 2 Start Fraction 4 over 8 End Fraction

−212

Answer 3

To multiply \(4\) by \(-58\), follow these steps:

1. Perform the multiplication: \[ 4 \times -58 = -232 \]

Now, convert \(-232\) into a mixed number. Since \(-232\) is a whole number, we can express it in simplest form directly:

• As a mixed number, \(-232\) can simply be written as \(-232 \frac{0}{1}\), but we typically just express it as \(-232\).

None of the answer choices provided match this result exactly. Here’s a breakdown of the choices:

• −52: Incorrect
• −10: Incorrect
• −248: This is not the correct answer, but mathematically shows mixed fraction styling incorrectly.
• −212: Incorrect.

It appears that options provided do not contain the correct result of \(-232\). Therefore, if there is an option to directly represent \(-232\), it should be stated.

To clarify, the expected correct answer to the multiplication of \(4\) and \(-58\) is:

−232 (not listed among the responses).

Answer 4

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 4/8
negative 2 Start Fraction 4 over 8 End Fraction

−2 1/2

Answer 5

To multiply \(4\) by \(-\frac{5}{8}\), follow these steps:

1. Convert the whole number to a fraction: \[ 4 = \frac{4}{1} \]

2. Multiply the fractions: \[ \frac{4}{1} \times -\frac{5}{8} = -\frac{4 \times 5}{1 \times 8} = -\frac{20}{8} \]

3. Simplify the fraction: \[ -\frac{20}{8} = -\frac{20 \div 4}{8 \div 4} = -\frac{5}{2} \]

4. Convert to a mixed number: \(-\frac{5}{2}\) can be written as a mixed number: \[ -2 \frac{1}{2} \]

So the final answer is: −2 1/2.

Answer 6

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

0.195
0.195

1.86
1.86

1.95
1.95

19.5
19.5

Answer 7

To multiply \(6.5\) by \(0.3\), follow these steps:

1. Perform the multiplication: \[ 6.5 \times 0.3 = 1.95 \]

Thus, the answer is:

1.95.

Answer 8

Multiply −19.3 by 6.(1 point)
Responses

−114.8
negative 114.8

−25.3
negative 25.3

−115.8
negative 115.8

115.8

Answer 9

To multiply \(-19.3\) by \(6\), follow these steps:

1. Perform the multiplication: \[ -19.3 \times 6 = -115.8 \]

Thus, the answer is:

−115.8.