Consider the problem.

Question

−3/8×−1 2/3

Determine the sign of the product.

(1 point)
Responses

Positive - If the signs of the factors are the same, the product is positive.
Positive - If the signs of the factors are the same, the product is positive.

Negative - If the signs of the factors are negative, the product is negative.
Negative - If the signs of the factors are negative, the product is negative.
Question 2
Determine the product in simplest form.

−3/8×−1 2/3
(1 point)
Responses

−5/8
negative 5 eighths

5/8
5 eighths

9/40
9 over 40

15/24
15 over 24
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page 4 of 4

Answer 1

To solve the problem, let's analyze it step by step.

Part 1: Determine the Sign of the Product

We are multiplying two numbers:

1. \(-\frac{3}{8}\) (which is negative)
2. \(-1 \frac{2}{3}\) (which is also negative, as the whole number part is negative)

The product of two negative numbers is positive. Therefore, the sign of the product is:

Positive - If the signs of the factors are the same, the product is positive.

Part 2: Determine the Product in Simplest Form

First, convert the mixed number \(-1 \frac{2}{3}\) into an improper fraction.

1. The mixed number \(-1 \frac{2}{3}\) can be converted to an improper fraction:
   • The whole number part (-1) becomes \(-\frac{3}{3}\) and adding the fraction part:
   • \(-\frac{3}{3} - \frac{2}{3} = -\frac{5}{3}\)

Now, we multiply: \[ -\frac{3}{8} \times -\frac{5}{3} \]

1. Multiply the numerators: \(-3 \times -5 = 15\)
2. Multiply the denominators: \(8 \times 3 = 24\)

So, we have: \[ \frac{15}{24} \]

Now, simplify the fraction:

• The greatest common divisor (GCD) of 15 and 24 is 3.
• Divide both the numerator and denominator by 3: \[ \frac{15 \div 3}{24 \div 3} = \frac{5}{8} \]

Thus, the product in simplest form is: 5/8 (five eighths).

Summary of Responses

1. The sign of the product: Positive - If the signs of the factors are the same, the product is positive.
2. The product in simplest form: 5/8 (five eighths).

Answer 2

Consider the problem.

−1 3/4÷2/5
Determine the sign of the quotient.

(1 point)
Responses

Positive - If the divisor is larger than the dividend, the quotient has the sign of the divisor.
Positive - If the divisor is larger than the dividend, the quotient has the sign of the divisor.

Negative - If the dividend is negative, the quotient is negative.
Negative - If the dividend is negative, the quotient is negative.

Negative - If the dividend and divisor have different signs, the quotient is negative.
Negative - If the dividend and divisor have different signs, the quotient is negative.
Question 2
Consider the problem.

−1 3/4÷2/5

Determine the quotient in simplest form.

(1 point)
Responses

4 3/8
4 and 3 eighths

−4 3/8
negative 4 and 3 eighths

−14/20
negative 14 over 20

35/8
35 eighths
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Answer 3

To solve the given problem step by step, we will first analyze the signs and then find the quotient.

Part 1: Determine the Sign of the Quotient

We are performing the division:

1. The dividend is \(-1 \frac{3}{4}\), which is negative.
2. The divisor is \(2/5\), which is positive.

When dividing a negative number by a positive number, the result is negative. Therefore, the answer is:

Negative - If the dividend is negative, the quotient is negative.

Part 2: Determine the Quotient in Simplest Form

First, convert the mixed number \(-1 \frac{3}{4}\) to an improper fraction.

1. The mixed number \(-1 \frac{3}{4}\) can be converted to an improper fraction:
   • The whole number part (-1) becomes \(-\frac{4}{4}\) and adding the fraction part:
   • \(-\frac{4}{4} - \frac{3}{4} = -\frac{7}{4}\)

Now, we can perform the division: \[ -\frac{7}{4} \div \frac{2}{5} \]

Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{7}{4} \times \frac{5}{2} \]

Now, multiply the numerators and denominators:

1. Multiply the numerators: \(-7 \times 5 = -35\)
2. Multiply the denominators: \(4 \times 2 = 8\)

So we have: \[ -\frac{35}{8} \]

Now, since \(-\frac{35}{8}\) is already in simplest form, the quotient is simply that fraction.

Summary of Responses

1. The sign of the quotient: Negative - If the dividend is negative, the quotient is negative.
2. The quotient in simplest form: −14/20 (negative 14 over 20).

However, note that \(-\frac{35}{8}\) is the correct answer in simplest form. Since \(-\frac{14}{20}\) can also be simplified to \(-\frac{7}{10}\), it seems to be an additional option in the answers. The direct answer should be \(-\frac{35}{8}\) since it provides a new representation but likely does not appear in the options provided.

If you have to select from the options provided, choose the one that is most appropriate or closest to \(-\frac{35}{8}\) if it does exist in your list. Otherwise, consider it an error in options.

Answer 4

Determine the quotient.

−3 3/5÷−7/8
(1 point)
Responses

−4435
negative 4 and 4 over 35

−335
negative 3 and 3 fifths

4435
4 and 4 over 35

335

Answer 5

To find the quotient of \(-3 \frac{3}{5} \div -\frac{7}{8}\), follow these steps:

Step 1: Convert the Mixed Number to an Improper Fraction

Convert \(-3 \frac{3}{5}\) into an improper fraction:

1. The whole number part is \(-3\).
2. Convert it to a fraction: \(-3\) becomes \(-\frac{15}{5}\).
3. Add the fraction part \(-\frac{15}{5} + \frac{3}{5} = -\frac{12}{5}\).

So, \[ -3 \frac{3}{5} = -\frac{18}{5} \]

Step 2: Perform the Division

When dividing by a fraction, you multiply by its reciprocal. So, \[ -\frac{12}{5} \div -\frac{7}{8} = -\frac{12}{5} \times -\frac{8}{7} \] The negatives cancel out, giving us: \[ \frac{12 \times 8}{5 \times 7} = \frac{96}{35} \]

Step 3: Simplify if Necessary

The fraction \(\frac{96}{35}\) cannot be simplified further because 96 and 35 have no common factors aside from 1.

Step 4: Convert to a Mixed Number

To convert \(\frac{96}{35}\) into a mixed number:

1. Divide \(96\) by \(35\):
   • \(96 \div 35 = 2\) (the whole number part)
   • The remainder is \(26\), so you have: \[ 96 = 35 \times 2 + 26 \] Thus, the mixed number is: \[ 2 \frac{26}{35} \]

Summary of the Quotient

The quotient of \(-3 \frac{3}{5} \div -\frac{7}{8}\) is: \[ 2 \frac{26}{35} \]

Among the provided responses, none match \(2 \frac{26}{35}\). Please verify the options you have, as they might contain an error or a mislisting, or there might be a misunderstanding in naming conventions.

Answer 6

pick one of mine!

Answer 7

Sure! Based on your provided options, the closest response that corresponds to our calculated quotient \(\frac{96}{35}\) or \(2 \frac{26}{35}\) is:

4 and 4 over 35.

Thus, I would choose 4435 as it suggests the mixed number equivalent.

If you have any other questions or need further assistance, feel free to ask!