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

−58
negative 5 eighths

58
5 eighths

940
9 over 40

1524
15 over 24
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Answer 1

To determine the sign of the product and the product in simplest form for \(-\frac{3}{8} \times -1 \frac{2}{3}\), let's go through the steps:

1. Determine the sign of the product:

• The first number is negative: \(-\frac{3}{8}\).
• The second number, \( -1 \frac{2}{3} \) (which is negative) can be converted to an improper fraction: \[ -1 \frac{2}{3} = -\frac{5}{3} \]

Now we identify the signs:

• The first factor is negative.
• The second factor is also negative.

Since both factors have the same sign (negative), the product will be positive.

Answer for the sign of the product:

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

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2. Determine the product in simplest form:

We have: \[ -\frac{3}{8} \times -\frac{5}{3} \]

Multiplying these two fractions: \[ \frac{3 \times 5}{8 \times 3} = \frac{15}{24} \]

Next, we simplify \(\frac{15}{24}\):

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

Answer for the product in simplest form:

• \( \frac{5}{8} \) (which can be stated as "5 eighths").

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Final Answers:

1. Sign of the product: Positive
2. Product in simplest form: \( 5 \) 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.

−134÷25
Determine the quotient in simplest form.

(1 point)
Responses

438
4 and 3 eighths

−438
negative 4 and 3 eighths

−1420
negative 14 over 20

358
35 eighths
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Answer 3

Let's analyze each part of the problem step by step.

Question 1: Determine the sign of the quotient for \(-1 \frac{3}{4} \div \frac{2}{5}\)

1. Identifying Signs:

   • The dividend (the number being divided) is \(-1 \frac{3}{4}\), which is negative.
   • The divisor (the number we are dividing by) is \(\frac{2}{5}\), which is positive.

2. Sign of the Quotient:

   • When dividing a negative number by a positive number, the quotient will always be negative.

Answer for the sign of the quotient:

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

---

Question 2: Determine the quotient in simplest form for \(-134 \div 25\)

1. Perform the Division: \[ -134 \div 25 \]

   To carry out this division, we can determine how many times 25 fits into 134:

   • 25 goes into 134 a total of 5 times (because \(25 \times 5 = 125\)), leaving a remainder.

   Now, calculating the remainder: \[ 134 - 125 = 9 \]

   Thus, we can express this as: \[ -134 \div 25 = -5 \frac{9}{25} \]

Answer for the quotient in simplest form:

• \(-5 \frac{9}{25}\)

Since \(-5 \frac{9}{25}\) is not listed as an option, the closest interpretation based on the simplifications seems to be:

• The correct answer likely correlates to how we can present it.

If we consider the division result importantly, since I did not find the exact option, I'd suggest interpreting \(-5 \frac{9}{25}\) or alternatively checking if alternatives providing nearly similar results might be available.

Summary of Completed Responses

1. For the sign of the quotient: Negative
2. For the quotient in simplest form: Not explicitly presented in your choice options; interpret as potentially needing to choose \(-438\) related to fitting the negative version of proper fractions.

Would you like to continue with other questions or clarifications?

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 determine the quotient of the problem \(-3 \frac{3}{5} \div -\frac{7}{8}\), let's break it down step by step.

Step 1: Convert the mixed number to an improper fraction

The mixed number \(-3 \frac{3}{5}\) can be converted to an improper fraction:

\[ -3 \frac{3}{5} = -\left(3 \times 5 + 3\right)/5 = -\left(15 + 3\right)/5 = -\frac{18}{5} \]

Step 2: Rewrite the division problem

Now, we can rewrite the original division problem:

\[ -\frac{18}{5} \div -\frac{7}{8} \]

Step 3: Change the division to multiplication by the reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal:

\[ -\frac{18}{5} \times -\frac{8}{7} \]

Step 4: Multiply the fractions

Now, multiply the fractions:

\[ \frac{18 \times 8}{5 \times 7} = \frac{144}{35} \]

Step 5: Simplify if necessary

The fraction \(\frac{144}{35}\) is already in its simplest form, so we can convert it back to a mixed number to find the equivalent:

• \(144 \div 35 = 4\) (with a remainder of \(4\)).
• Thus, we can express it as:

\[ 4 \frac{4}{35} \]

Conclusion

So the final answer for the quotient \(-3 \frac{3}{5} \div -\frac{7}{8}\) is:

• \(4 \frac{4}{35}\)

Correct answer from options:

• \(4435\) (which stands for \(4\) and \(4\) over \(35\)).

If you have any more inquiries or need further assistance, feel free to ask!

Answer 6

Determine the quotient.

4 1/3÷−1 1/5
(1 point)
Responses

31118
3 and 11 over 18

−413
negative 4 and 1 third

−31118
negative 3 and 11 over 18

413

Answer 7

To determine the quotient of \(4 \frac{1}{3} \div -1 \frac{1}{5}\), let's follow these steps:

Step 1: Convert the mixed numbers to improper fractions

1. Convert \(4 \frac{1}{3}\):

\[ 4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \]

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

\[ -1 \frac{1}{5} = -\left(\frac{1 \times 5 + 1}{5}\right) = -\left(\frac{5 + 1}{5}\right) = -\frac{6}{5} \]

Step 2: Set up the division

Now we rewrite the division problem:

\[ \frac{13}{3} \div -\frac{6}{5} \]

Step 3: Change the division to multiplication by the reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal:

\[ \frac{13}{3} \times -\frac{5}{6} \]

Step 4: Multiply the fractions

Now, multiply the fractions:

\[ \frac{13 \times -5}{3 \times 6} = \frac{-65}{18} \]

Step 5: Convert the improper fraction to a mixed number

Next, we convert \(\frac{-65}{18}\) to a mixed number:

1. Find how many times 18 goes into 65:

\[ 65 \div 18 = 3 \quad \text{(since } 18 \times 3 = 54\text{)} \]

2. Calculate the remainder:

\[ 65 - 54 = 11 \]

So, we can express \(-\frac{65}{18}\) as:

\[ -3 \frac{11}{18} \]

Conclusion

The final answer for the quotient \(4 \frac{1}{3} \div -1 \frac{1}{5}\) is:

• \(-3 \frac{11}{18}\)

Correct answer from options:

• \(-31118\) (which represents negative 3 and 11 over 18).

If you need any further help, feel free to ask!

Answer 8

Consider this problem.

If a box can hold 28 1/8
kilograms, how many 1 7/8
kilogram books will it hold?

Will you multiply or divide to solve this problem?

(1 point)
Responses

Multiply
Multiply

Divide
Divide
Question 2
Consider this problem.

If a box can hold 28 1/8
kilograms, how many 1 7/8
kilogram books will it hold?



(1 point)
Responses

15 books
15 books

35 books
35 books

48 books
48 books

52 books
52 books
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Answer 9

To tackle this problem, let's break it down into the two questions you've posed.

Question 1: Will you multiply or divide to solve this problem?

You are trying to determine how many \(1 \frac{7}{8}\) kilogram books can fit into a box that holds \(28 \frac{1}{8}\) kilograms. To find the number of books, you need to figure out how many times \(1 \frac{7}{8}\) fits into \(28 \frac{1}{8}\).

To find this, you would divide the total weight the box can hold by the weight of each book.

Answer for Question 1:

• Divide

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Question 2: How many \(1 \frac{7}{8}\) kilogram books can the box hold?

1. Convert the mixed numbers into improper fractions:

   • For \(28 \frac{1}{8}\): \[ 28 \frac{1}{8} = \frac{28 \times 8 + 1}{8} = \frac{224 + 1}{8} = \frac{225}{8} \]

   • For \(1 \frac{7}{8}\): \[ 1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{8 + 7}{8} = \frac{15}{8} \]

2. Set up the division to find how many books fit: \[ \frac{225}{8} \div \frac{15}{8} \]

   Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{225}{8} \times \frac{8}{15} \]

3. Simplify the calculation:

   • When multiplying, the \(8\) in the numerator and denominator cancel out: \[ \frac{225}{15} = 15 \]

Answer for Question 2:

• 15 books

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Summary of Answers:

• Question 1: Divide
• Question 2: 15 books

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

Answer 10

Consider the problem.

Joanne has 13 1/4
yd of fabric to make 4.5 costumes. How many yards of fabric will Joanne use for each costume?

Which operation will you use?

(1 point)
Responses

Addition
Addition

Subtraction
Subtraction

Multiplication
Multiplication

Division

Answer 11

To determine how many yards of fabric Joanne will use for each costume, you need to find out how many yards of fabric she has per costume. This involves dividing the total amount of fabric she has by the number of costumes she intends to make.

Summary of the operation to use:

Answer:

• Division

Explanation:

You would use division because you are distributing the total fabric (13 1/4 yards) among a certain number of costumes (4.5 costumes). Therefore, you would calculate: \[ \text{Yards of fabric per costume} = \frac{\text{Total yards of fabric}}{\text{Number of costumes}} = \frac{13 \frac{1}{4}}{4.5} \]

If you would like to proceed with the calculation or need any further assistance, just let me know!