Lucy has 7/10 gallon of milk left in her refrigerator, and her mugs hold 1/8 gallon. If she fills as many full mugs as she can, how much milk will be left in gallons? Answers should be in simplest form.
Lucy has 7/10 gallon of milk left, which can be written as 7 ÷ 10 = 0.7 gallon.
Each mug holds 1/8 of a gallon.
To find out how many mugs Lucy can fill, we divide the amount of milk left by the amount each mug can hold: 0.7 ÷ 1/8 = 0.7 × 8 = 5.6 mugs.
Since Lucy can't have a fraction of a mug, we round down to the nearest whole number: 5 mugs.
If Lucy fills 5 mugs, she uses 5 × 1/8 = 5/8 = 0.625 gallon of milk.
Therefore, there will be 0.7 - 0.625 = 0.075 gallon of milk left in gallons, or simplified 75/1000 = 3/40 = 0.075 gallon of milk. Answer: \boxed{3/40}.
To find out how many mugs Lucy can fill, we need to divide the amount of milk she has left by the capacity of each mug.
The amount of milk Lucy has left is 7/10 gallon.
The capacity of each mug is 1/8 gallon.
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
(7/10) ÷ (1/8) = (7/10) * (8/1)
Next, we can simplify the expression by canceling out common factors.
(7/10) * (8/1) = (7 * 8) / (10 * 1) = 56/10 = 5.6/1 = 5.6
Lucy can fill 5.6 mugs with the amount of milk she has left.
However, since we are asked to answer in the simplest form, we need to convert the decimal to a fraction.
Since there are 10 equal parts in a gallon, each part represents a tenth.
Therefore, 0.6 of a gallon can be written as 6/10 or 3/5.
Thus, Lucy will have 3/5 gallon of milk left in her refrigerator after filling as many full mugs as she can.
To find out how many mugs Lucy can fill, we need to divide the amount of milk she has (7/10 gallon) by the capacity of each mug (1/8 gallon).
To divide fractions, we invert the second fraction (1/8) and multiply it by the first fraction (7/10).
(7/10) / (1/8) = (7/10) * (8/1)
To multiply fractions, we simply multiply the numerators together and the denominators together.
(7 * 8) / (10 * 1) = 56/10
Now, we simplify the fraction.
56/10 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
(56/2) / (10/2) = 28/5
So, Lucy can fill 28/5 mugs.
Now, to find out how much milk will be left, we need to subtract the amount used from the total amount:
Total amount of milk - Used amount of milk = Remaining amount of milk
Since we already found out Lucy can fill 28/5 mugs with milk, we need to find (28/5) * (1/8) to determine the amount of milk used.
To multiply fractions, we multiply the numerators together and the denominators together:
(28/5) * (1/8) = (28/5) * (1/8) = 28/40
Now, we simplify the fraction:
28/40 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
(28/4) / (40/4) = 7/10
Therefore, Lucy uses 7/10 gallon of milk to fill as many full mugs as she can.
Finally, to find out how much milk will be left, we subtract this amount from the total amount:
Total amount of milk - Used amount of milk = Remaining amount of milk
7/10 - 7/10 = 0
Therefore, Lucy will have 0 gallons of milk left in her refrigerator.