Find the quotient of 9/10

Question

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

Answer 1

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 $\frac{2}{3}$:

$$\frac{9}{10}÷\frac{2}{3}=\frac{9}{10}\times \frac{3}{2}$$

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

Answer 2

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

Answer 3

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

$$\frac{3}{10}÷\frac{1}{3}=\frac{3}{10}\times \frac{3}{1}$$

Now, we multiply the numerators and the denominators:

$$\frac{3\times 3}{10\times 1}=\frac{9}{10}$$

Thus, $\frac{3}{10}÷\frac{1}{3}=\frac{9}{10}$.

The correct response is:

9/10

Answer 4

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

Answer 5

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:

$$\frac{3}{4}\text{ room}\text{in}3\text{ hours}=\text{1 room}\text{in}x\text{ hours}$$

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

Answer 6

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