Final answer:
To calculate how many 1 1/4 gallon buckets can fill a 14 1/2 gallon tank, we must divide the total volume by the bucket's volume. The correct expressions are (29/2) ÷ (5/4) and (29/2) ÷ (4/5), representing the total gallons divided by the gallons per bucket.
Step-by-step explanation:
To find out how many 1 1/4 gallon buckets of water are needed to fill a tank that holds 14 1/2 gallons, we need to divide the total gallons the tank can hold by the gallons each bucket can hold.
Expressions Representing the Scenario
- A) (29/2) ÷ (5/4)
- E) (29/2) ÷ (4/5)
First, we need to convert the mixed numbers to improper fractions. 14 1/2 gallons become 29/2 and 1 1/4 gallons become 5/4. To determine how many buckets are needed, you divide the total volume of the tank by the volume of each bucket. Hence, the correct expressions for the scenario are:
- A) (29/2) ÷ (5/4) - Dividing the total tank volume by the bucket volume.
- E) (29/2) ÷ (4/5) - This is equivalent to A because dividing by a number is the same as multiplying by its reciprocal.
Options B and C are incorrect because multiplication won't give you the number of buckets, while option D has the fractions set up incorrectly for the scenario.