Abucket is being filled at a rate of 5/6 gallon in 1/4 minute. what is the unit rate in gallons per minute?

3 1/3  gallons per minute

Step-by-step explanation:

We can use ratio's to solve this problem.  We will put gallons on top and time on the bottom

5/6 gallons          x gallons

=

1/4 minute            1 minute

Using cross products

5/6*1 = 1/4 x

Multiply by 4 on each side

5/6 * 4 = 1/4 *4 x

20/6 = x

Dividing the top and bottom by 2

10/3 =x

Changing this back to a mixed number

3 goes into 10   3 times with 1 left over

3 1/3  gallons per minute

10/3 gallons/minute

Step-by-step explanation:

There are 4 quarters in 1, so four quarter-minutes in one minute.

The the number of gallons going into buckets in one minute will be 4 times the number in 1/4 minute:

... 4 × 5/6 gal = 20/6 gal = 10/3 gal

This is the quantity per minute, so the unit rate is

... 10/3 gal/min

Alternate solution

You are asked for the rate in gallons per minute. In this context, "per" means "divided by", so you find the desired quantity by dividing gallons by minutes.

... (5/6 gal)/(1/4 min) = (5/6×4/1) gal/min = 10/3 gal/min

Comment on dividing fractions

You're generally taught one or two ways to divide fractions:

Please note that if you invert and multiply after doing the adjustment in the second method, you would have (10/12)×(12/3) = (10/3)×(12/12) = 10/3. That is, the denominators cancel. It's just another way to think about the quotient of fractions.

There's actually a third method you can use, but you need to be really careful.

3. Express both fractions using the same numerator, then invert the result after losing the numerator: (5/6)/(1/4) = (5/6)/(5/20) = 20/6 = 10/3. Again, this is a variation that takes advantage of cancellation after "invert and multiply."

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