Before your soccer game, you filled a water cooler with 6 1/2
gallons of water.
You forgot to close the plug before you began filling the cooler with water and 2 5/6
gallons leaked out.
How much water was in the cooler after you closed the plug?
(4 points)
To find the amount of water left in the cooler, we need to subtract the amount of water that leaked out (2 5/6 gallons) from the amount of water originally filled (6 1/2 gallons).
First, let's convert 6 1/2 gallons to an improper fraction.
6 1/2 = (2*6 + 1)/2 = 13/2
Next, let's convert 2 5/6 gallons to an improper fraction.
2 5/6 = (6*2 + 5)/6 = 17/6
Now, we can subtract the fraction of water leaked from the fraction of water filled.
(13/2) - (17/6)
To subtract fractions, we need to have the same denominator. The least common multiple of 2 and 6 is 6, so we need to rewrite the fractions with a denominator of 6.
(13/2) = (13/2) * (3/3) = 39/6
(17/6) = (17/6) * (1/1) = 17/6
Now, we can subtract the two fractions.
39/6 - 17/6 = 22/6
So, there were 22/6 gallons of water left in the cooler after closing the plug.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2.
22/6 = (22/2)/(6/2) = 11/3
Therefore, there were 11/3 gallons of water left in the cooler after closing the plug.
To find out how much water is left in the cooler after the leak, we need to subtract the amount of water that leaked from the initial amount.
Initial amount of water in the cooler: 6 ½ gallons
Amount of water that leaked: 2 5/6 gallons
To subtract fractions, we need to have a common denominator. In this case, the denominators are already the same, so we can subtract the fractions directly.
6 ½ - 2 5/6
To subtract the whole numbers, we need to convert 6 ½ to an improper fraction.
6 ½ = 12/2 + 1/2 = 13/2
Now we can subtract the fractions.
13/2 - 2 5/6
To subtract fractions, we need to have a common denominator. The common denominator for 2 and 6 is 6.
13/2 - 17/6
We need to convert 13/2 into 6ths, so we multiply the numerator and denominator by 3.
(13/2) * (3/3) = 39/6
Now we can subtract the fractions.
39/6 - 17/6 = 22/6
22/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
(22/6) ÷ (2/2) = 11/3
Therefore, after closing the plug, there will be 11/3 gallons of water left in the cooler.