Which expression represents another method of computing the product given below?

Question

- 2 3/7 x 0.01

Answer 1

To compute the product \( 2 \frac{3}{7} \times 0.01 \) using another method, we can convert the mixed number to an improper fraction and then multiply.

First, convert \( 2 \frac{3}{7} \) to an improper fraction:

\[ 2 \frac{3}{7} = \frac{(2 \times 7) + 3}{7} = \frac{14 + 3}{7} = \frac{17}{7} \]

Now we can express the product \( \frac{17}{7} \times 0.01 \).

We know that \( 0.01 \) can be expressed as a fraction:

\[ 0.01 = \frac{1}{100} \]

Now we have:

\[ \frac{17}{7} \times 0.01 = \frac{17}{7} \times \frac{1}{100} \]

When multiplying fractions, we multiply the numerators and the denominators:

\[ \frac{17 \times 1}{7 \times 100} = \frac{17}{700} \]

Therefore, another method of computing the product \( 2 \frac{3}{7} \times 0.01 \) can be expressed as:

\[ \frac{17}{700} \]

So, the expression that represents another method of computing the product is \( \frac{17}{700} \).

Answer 2

Which expression represents another method of computing the product given below?
-5 2/3 x 7

A. (-5 x 7) + (-2/3 x 7)

B. (-5 x (-7)) + (-2/3 x (-7))

C. (-5 2/3) (-7)

D. (-1)(5 - 2/3)(7)

Answer 3

To compute the product \(-5 \frac{2}{3} \times 7\), we can look at the given options and see which one expresses this calculation correctly.

1. First, we can convert the mixed number \(-5 \frac{2}{3}\) to an improper fraction:

   \[ -5 \frac{2}{3} = -\left(5 + \frac{2}{3}\right) = -\left(\frac{15}{3} + \frac{2}{3}\right) = -\frac{17}{3} \]

   Therefore, we want to compute:

   \[ -\frac{17}{3} \times 7 \]

2. Let's analyze each option:

   A. \((-5 \times 7) + (-\frac{2}{3} \times 7)\)

   This can be evaluated as:

   \[ -35 + (-\frac{14}{3}) = -35 - \frac{14}{3} \]

   This is correct since it breaks down the multiplication into separate components and then combines them.

   B. \((-5 \times (-7)) + (-\frac{2}{3} \times (-7))\)

   This would yield:

   \[ 35 + \frac{14}{3} \]

   This is incorrect as it uses opposite signs and does not yield the original product.

   C. \((-5 \frac{2}{3}) \times (-7)\)

   This expression features two negative signs, which makes it positive. So, it is incorrect.

   D. \((-1)(5 - \frac{2}{3})(7)\)

   This option also modifies the signs incorrectly and alters the value.

3. Given this analysis, the correct answer is:

   A. \((-5 \times 7) + (-\frac{2}{3} \times 7)\)

This expression accurately represents another method of computing the product \(-5 \frac{2}{3} \times 7\).

Answer 4

A number is multiplied by 47. The result is a positive number greater than 47.

Which of these was multiplied by 47?
A.
a number between zero and one
B.
zero
C.
a number less than zero
D.
a number greater than one

Answer 5

To analyze what was multiplied by 47 to obtain a positive number greater than 47, we can evaluate each option:

1. A. a number between zero and one:

   • If we multiply a number in this range (e.g., 0.5) by 47, the result is less than 47 (e.g., \( 0.5 \times 47 = 23.5 \)). Therefore, this option cannot be correct.

2. B. zero:

   • Multiplying zero by any number, including 47, results in 0. Thus, this option does not yield a positive number and cannot be correct.

3. C. a number less than zero:

   • If a negative number (e.g., -1) is multiplied by 47, the result will also be negative (e.g., \( -1 \times 47 = -47 \)). Therefore, this cannot yield a positive result either.

4. D. a number greater than one:

   • If we multiply a number greater than one (e.g., \( 2 \)) by 47, the result is greater than 47 (e.g., \( 2 \times 47 = 94 \)). This option satisfies the condition of yielding a positive number greater than 47.

From this analysis, the correct answer is:

D. a number greater than one.

Answer 6

A ferry carries passengers a distance of 3 5/8 miles across a river. The ferry made 28 trips across the river in one day. Which of the following is true?
A.
The ferry traveled total miles in one day.
B.
The ferry traveled total miles in one day.
C.
The ferry traveled total miles in one day.
D.
The ferry traveled total miles in one day.

Answer 7

To find the total distance traveled by the ferry in one day, we need to multiply the distance of one trip by the number of trips made in a day.

1. The distance of one trip is \(3 \frac{5}{8}\) miles. First, convert this mixed number to an improper fraction: \[ 3 \frac{5}{8} = \frac{(3 \times 8) + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8} \]

2. The ferry made 28 trips across the river. Therefore, the total distance traveled in one day is: \[ \text{Total distance} = \text{Distance per trip} \times \text{Number of trips} \] \[ \text{Total distance} = \frac{29}{8} \times 28 \]

3. To simplify the multiplication: \[ \text{Total distance} = \frac{29 \times 28}{8} \]

4. Calculate \(29 \times 28\): \[ 29 \times 28 = 812 \]

5. Now divide by 8: \[ \text{Total distance} = \frac{812}{8} = 101.5 \text{ miles} \]

So, the ferry traveled 101.5 miles in one day.

Since the options are not provided with specific numerical values filled in, assuming placeholders (total miles) should be 101.5 miles for the statements, the correct statement could be written like this:

The ferry traveled 101.5 total miles in one day.

If the options provided had numerical placeholders, the one that matches this calculated value would be the correct answer. Based on what we calculated, you would fill in the total miles accordingly.

Answer 8

A ferry carries passengers a distance of 3 5/8 miles across a river. The ferry made 28 trips across the river in one day. Which of the following is true?
A.
The ferry traveled 101 1/2 total miles in one day.
B.
The ferry traveled 6 4/9 total miles in one day.
C.
The ferry traveled 22 5/9 total miles in one day.
D.
The ferry traveled 8 2/7 total miles in one day.

Answer 9

Let's confirm the total distance the ferry travels in one day by calculating it based on the given distance per trip and the number of trips.

1. The distance per trip is \(3 \frac{5}{8}\) miles. Converting this mixed number to an improper fraction: \[ 3 \frac{5}{8} = \frac{(3 \times 8) + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8} \text{ miles} \]

2. The ferry made 28 trips, so we calculate the total distance traveled in one day: \[ \text{Total distance} = \text{Distance per trip} \times \text{Number of trips} \] \[ \text{Total distance} = \frac{29}{8} \times 28 \]

3. Simplify the multiplication: \[ \text{Total distance} = \frac{29 \times 28}{8} \] Now calculate \(29 \times 28\): \[ 29 \times 28 = 812 \] Thus, \[ \text{Total distance} = \frac{812}{8} = 101.5 \text{ miles} \]

This converts to: \[ 101.5 = 101 \frac{1}{2} \]

Now, we can evaluate the options:

A. The ferry traveled \(101 \frac{1}{2}\) total miles in one day. (True, as we calculated)

B. The ferry traveled \(6 \frac{4}{9}\) total miles in one day. (False)

C. The ferry traveled \(22 \frac{5}{9}\) total miles in one day. (False)

D. The ferry traveled \(8 \frac{2}{7}\) total miles in one day. (False)

Thus, the correct answer is:

A. The ferry traveled \(101 \frac{1}{2}\) total miles in one day.

Answer 10

Use properties of rational numbers to multiply the following. 7/12 x 253/5

Answer 11

To multiply the fractions \( \frac{7}{12} \) and \( \frac{253}{5} \), we can use the property of multiplying fractions, which states:

\[ \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \]

Step 1: Multiply the numerators

Multiply the numerators together: \[ 7 \times 253 \]

Calculating \( 7 \times 253 \): \[ 7 \times 253 = 1771 \]

Step 2: Multiply the denominators

Multiply the denominators together: \[ 12 \times 5 \]

Calculating \( 12 \times 5 \): \[ 12 \times 5 = 60 \]

Step 3: Combine the results

Now we can combine the results: \[ \frac{7}{12} \times \frac{253}{5} = \frac{1771}{60} \]

Final Result

The final result of the multiplication is: \[ \frac{1771}{60} \]

This fraction cannot be simplified further since 1771 and 60 do not have common factors.

Thus, the answer is: \[ \frac{1771}{60} \]

If needed, this can also be expressed as a mixed number: \[ 1771 \div 60 = 29 \quad \text{remainder } 31 \] So, it can be represented as: \[ 29 \frac{31}{60} \]

Therefore, \( \frac{7}{12} \times \frac{253}{5} \) is \( \frac{1771}{60} \) or \( 29 \frac{31}{60} \).