Find the quotient of 9/10

and 2/3
.(1 point)
Responses

30/18
Start Fraction 30 over 18 End Fraction

18/30
Start Fraction 18 over 30 End Fraction

20/27
Start Fraction 20 over 27 End Fraction

27/20

11 answers

To divide two fractions, you multiply the first fraction by the reciprocal of the second fraction. Here’s how we do it for \( \frac{9}{10} \) and \( \frac{2}{3} \):

\[ \frac{9}{10} \div \frac{2}{3} = \frac{9}{10} \times \frac{3}{2} \]

Now, we can multiply the numerators and the denominators:

\[ \frac{9 \times 3}{10 \times 2} = \frac{27}{20} \]

Thus, the quotient of \( \frac{9}{10} \) and \( \frac{2}{3} \) is:

\[ \frac{27}{20} \]

The correct response is:

27/20

What is 3/10÷1/3
?(1 point)
Responses

10/9
Start Fraction 10 over 9 End Fraction

9/10
Start Fraction 9 over 10 End Fraction

3/30
Start Fraction 3 over 30 End Fraction

10

To divide the fractions \( \frac{3}{10} \) by \( \frac{1}{3} \), we multiply by the reciprocal of the second fraction. Here's the calculation:

\[ \frac{3}{10} \div \frac{1}{3} = \frac{3}{10} \times \frac{3}{1} \]

Now, we multiply the numerators and the denominators:

\[ \frac{3 \times 3}{10 \times 1} = \frac{9}{10} \]

Thus, \( \frac{3}{10} \div \frac{1}{3} = \frac{9}{10} \).

The correct response is:

9/10

Stacy is painting her bedroom. She is able to paint 3/4
of the bedroom in 3 hours. At this rate, how long will it take her to paint the entire room?(1 point)
Responses

9/4
hours
Start Fraction 9 over 4 End Fraction hours

4 hours
4 hours

12 hours
12 hours

6 hours

To determine how long it will take Stacy to paint the entire room, we first find her painting rate.

Stacy paints \( \frac{3}{4} \) of the bedroom in 3 hours. To find the time it takes to paint the entire room (1 whole room), we can set up the following proportion:

If it takes 3 hours to paint \( \frac{3}{4} \) of the room, let \( x \) be the time it takes to paint the entire room:

\[ \frac{3}{4} \text{ room} \quad \text{in} \quad 3 \text{ hours} = \text{1 room} \quad \text{in} \quad x \text{ hours} \]

We can establish the equation:

\[ \frac{3/4}{3} = \frac{1}{x} \]

Cross-multiplying gives us:

\[ 3x = 4 \]

Now, solving for \( x \):

\[ x = \frac{4}{3} \times 3 = 4 \]

Now we can confirm it:

To find the time to paint 1 whole room based on the rate:

  1. Calculate the amount of room painted per hour: \[ \text{Rate} = \frac{3/4 \text{ room}}{3 \text{ hours}} = \frac{1}{4} \text{ room/hour} \]

  2. To find out how many hours it takes to paint 1 room: \[ \text{Time} = \frac{1 \text{ room}}{\text{Rate}} = \frac{1 \text{ room}}{1/4 \text{ room/hour}} = 4 \text{ hours} \]

Therefore, it will take Stacy 4 hours to paint the entire room.

The correct response is:

4 hours

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