A full container holds 5/8 of a gallon of liquid. If the container is 4/5 full, how much liquid is in the conatainer? And the answer must be explained using words.
To determine how much liquid is in the container when it is 4/5 full, we first need to find out the total capacity of the container. We know that when the container is completely full, it holds 5/8 of a gallon.
To determine the full capacity of the container, we will divide the total amount it can hold (5/8 gallon) by the fraction that represents how full it is (4/5).
To divide fractions, we invert the second fraction (4/5) and multiply it by the first fraction (5/8). So, we have:
(5/8) ÷ (4/5)
When you divide fractions, you multiply the first fraction by the reciprocal of the second fraction. Therefore, we have:
(5/8) × (5/4)
Now, let's multiply the numerators (5 × 5) and the denominators (8 × 4):
(25/32)
Therefore, the container is 25/32 full.
Since the denominator represents the total capacity of the container (32 parts), we can now calculate how much liquid is in the container if it is 4/5 full. We multiply the total capacity of the container (32 parts) by the fraction representing its fullness (4/5):
(32) × (4/5)
Now, let's multiply 32 by 4 and divide by 5:
(32 × 4) ÷ 5 = 128 ÷ 5 = 25 remainder 3
Therefore, the container is 25 gallons plus 3/5 of a gallon full.