Find the quotient of 9/10 and 2/3 .

Question

Find the quotient of 9/10 and 2/3 .
27/20 
30/18 
20/27 
18/30

GPT-4o mini · Answer

To find the quotient of $ \frac{9}{10} $ and $ \frac{2}{3} $, you need to divide $ \frac{9}{10} $ by $ \frac{2}{3} $. Dividing by a fraction is the same as multiplying by its reciprocal. So, we calculate: $$ \frac{9}{10} \div \frac{2}{3} = \frac{9}{10} \times \frac{3}{2} $$ Now, 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 answer is $ \frac{27}{20} $.

hhfhfhfhf · Answer

are you sure

GPT-4o mini · Answer

Yes, I am sure. Let's recheck the calculation to confirm:

We want to find the quotient of $ \frac{9}{10} $ and $ \frac{2}{3} $.

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

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

Now, multiply the numerators and the denominators together:

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

So, the resulting quotient is indeed $ \frac{27}{20} $.

Therefore, $ \frac{27}{20} $ is correct.

hhfhfhfhf · Answer

what is 3/10÷1/3 9/10 10/9 3/30 10

GPT-4o mini · Answer

To calculate $ \frac{3}{10} \div \frac{1}{3} $, you can multiply $ \frac{3}{10} $ by the reciprocal of $ \frac{1}{3} $: $$ \frac{3}{10} \div \frac{1}{3} = \frac{3}{10} \times \frac{3}{1} $$ Now, multiply the numerators and the denominators: $$ \frac{3 \times 3}{10 \times 1} = \frac{9}{10} $$ So, $ \frac{3}{10} \div \frac{1}{3} = \frac{9}{10} $. The correct answer is $ \frac{9}{10} $.

hhfhfhfhf · Answer

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? 6 hours 12 hours 9/4 hours 4 hours

GPT-4o mini · Answer

Stacy is able to paint $ \frac{3}{4} $ of her bedroom in 3 hours. To find out how long it will take her to paint the entire bedroom, we can set up a proportion based on her current rate. First, we want to find her painting rate: $$ \text{Rate} = \frac{\text{Work Done}}{\text{Time}} = \frac{3/4 \text{ of the room}}{3 \text{ hours}} = \frac{3/4}{3} = \frac{3}{4} \times \frac{1}{3} = \frac{3}{12} = \frac{1}{4} \text{ of the room per hour}. $$ Now, if she paints $ \frac{1}{4} $ of the room in 1 hour, to find out how long it takes to paint $ 1 $ (the entire room), we can use the equation: $$ \text{Time} = \frac{\text{Total Work}}{\text{Rate}}. $$ So: $$ \text{Time to paint the entire room} = \frac{1 \text{ room}}{\frac{1}{4} \text{ room per hour}} = 1 \times 4 = 4 \text{ hours}. $$ Thus, it will take Stacy **4 hours** to paint the entire room. The correct answer is **4 hours**.

hhfhfhfhf · Answer

Iris is asked to sweep the gymnasium floor after a basketball game. This requires her to push a sweeper from one end of the gym to the other and repeating the pattern until she has covered the entire floor. She completes 23 of the floor in 13 of an hour. At this rate, how long will it take her to complete the entire floor?
1 hour
2/3 hours
1/2 hours
1 1/2

GPT-4o mini · Answer

To find out how long it will take Iris to complete the entire gymnasium floor, we start by determining her rate:

Iris completes $ \frac{2}{3} $ of the floor in $ \frac{1}{2} $ hour.

First, we can find her rate (the fraction of the floor she completes in one hour) by scaling up her completion:

If she completes $ \frac{2}{3} $ of the floor in $ \frac{1}{2} $ hour, we can find the completion per hour as follows:

\[ \text{Completion rate} = \left(\frac{2}{3} \div \frac{1}{2}\right) = \frac{2}{3} \times \frac{2}{1} = \frac{4}{3} \text{ of the floor per hour}. \]

Now, if she completes $ \frac{4}{3} $ of the floor in one hour, we can determine how long it will take her to complete the entire floor (1 floor):

\[ \text{Time to complete 1 floor} = \frac{1 \text{ floor}}{\frac{4}{3} \text{ floors/hour}} = \frac{1 \times 3}{4} = \frac{3}{4} \text{ hours}. \]

So, it will take her $ \frac{3}{4} $ hours to complete the entire floor.

To convert $ \frac{3}{4} $ hours into hours and minutes:

$ \frac{3}{4} $ hours is equivalent to $ 45 $ minutes.

Thus, the answer to how long it will take her to complete the entire floor is 1 hour.