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Use multiplication or division to solve the following word problem. Reduce the answer if needed.

One cup holds 8 ounces of liquid. If a cup is [tex]\frac{2}{3}[/tex] full, how many ounces are in that cup?

Sagot :

To solve this problem, we'll determine how many ounces are in a cup when it is filled to [tex]\(\frac{2}{3}\)[/tex] of its capacity.

1. Identify the total capacity of the cup: The cup holds 8 ounces of liquid when it is full.

2. Determine the fraction of the cup that is filled: The cup is [tex]\(\frac{2}{3}\)[/tex] full.

3. Calculate the amount of liquid in the cup: To find out how many ounces are in the cup when it is [tex]\(\frac{2}{3}\)[/tex] full, we multiply the total capacity of the cup by the fraction that it is filled.
[tex]\[ \text{Amount of liquid} = \text{Total capacity} \times \text{Fraction filled} \][/tex]

4. Substituting the values into the equation:
[tex]\[ \text{Amount of liquid} = 8 \, \text{ounces} \times \frac{2}{3} \][/tex]

5. Perform the multiplication:
[tex]\[ 8 \times \frac{2}{3} = \frac{8 \times 2}{3} = \frac{16}{3} \][/tex]

6. Simplify the fraction:
[tex]\[ \frac{16}{3} \approx 5.3333 \, \text{ounces} \][/tex]

So, when the cup is [tex]\(\frac{2}{3}\)[/tex] full, it contains approximately 5.3333 ounces of liquid.