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