the total amount of water a tank can hold is $14\\frac{1}{2}$ gallons. raul wants to find out how many…

the total amount of water a tank can hold is $14\\frac{1}{2}$ gallons. raul wants to find out how many $\\frac{1}{4}$-gallon buckets of water can be used to fill the tank. which expressions could be used to represent this scenario? select two options.\n$\\frac{33}{2} \\div \\frac{1}{4}$\n$\\frac{33}{2} \\times \\frac{1}{4}$\n$\\frac{33}{2} \\times \\frac{4}{1}$\n$\\frac{33}{2} \\times \\frac{1}{4}$\n$\\frac{33}{2} \\div \\frac{4}{1}$

the total amount of water a tank can hold is $14\\frac{1}{2}$ gallons. raul wants to find out how many $\\frac{1}{4}$-gallon buckets of water can be used to fill the tank. which expressions could be used to represent this scenario? select two options.\n$\\frac{33}{2} \\div \\frac{1}{4}$\n$\\frac{33}{2} \\times \\frac{1}{4}$\n$\\frac{33}{2} \\times \\frac{4}{1}$\n$\\frac{33}{2} \\times \\frac{1}{4}$\n$\\frac{33}{2} \\div \\frac{4}{1}$

Answer

Explanation:

Step1: Understand the problem

We need to find the number of (\frac{1}{4})-gallon buckets needed to fill a tank that holds (14\frac{1}{2}) gallons. This is a division problem, where we divide the total volume of the tank by the volume of each bucket. So the operation is (14\frac{1}{2}\div\frac{1}{4}). We can also rewrite division by a fraction as multiplication by its reciprocal, so (14\frac{1}{2}\times4) is also equivalent.

First, convert the mixed number (14\frac{1}{2}) to an improper fraction. (14\frac{1}{2}=\frac{14\times2 + 1}{2}=\frac{29}{2}).

Step2: Analyze the division as multiplication

Dividing by (\frac{1}{4}) is the same as multiplying by (4) (since the reciprocal of (\frac{1}{4}) is (4)). So (\frac{29}{2}\div\frac{1}{4}=\frac{29}{2}\times4). Also, (14\frac{1}{2}\div\frac{1}{4}) is the original division expression.

Looking at the options (even though some are a bit unclear from the image, but based on the logic):

  • The expression (14\frac{1}{2}\div\frac{1}{4}) is correct because we are dividing total volume by bucket volume.
  • The expression (14\frac{1}{2}\times4) is also correct because dividing by (\frac{1}{4}) is multiplying by (4).

Answer:

The correct expressions are (14\frac{1}{2}\div\frac{1}{4}) and (14\frac{1}{2}\times4) (or the equivalent improper fraction forms like (\frac{29}{2}\div\frac{1}{4}) and (\frac{29}{2}\times4)). If we assume the options have these or similar, the two correct ones would be the division of the total by the bucket size and the multiplication by the reciprocal.