- Define the amount the kitten eats as \(\frac{1}{4}\) cup.
- Multiply this amount by \(6\) to find the second cat's consumption: \(6 \times \frac{1}{4} = \frac{6}{4}\).
- Simplify the fraction \(\frac{6}{4}\) to \(\frac{3}{2}\), which is equal to \(1 \frac{1}{2}\).
- All three values \(\frac{3}{2}\), \(1 \frac{1}{2}\), and \(\frac{6}{4}\) represent the correct amount of \(\boxed{1 \frac{1}{2}}\) cups.
Explanation
- Calculating the amount of food consumed
The kitten eats \(\frac{1}{4}\) cup of cat food. The other cat eats \(6\) times the amount that the kitten eats. To find the total amount consumed by the second cat, we need to multiply the kitten's portion by \(6\).
\[6 \times \frac{1}{4} = \frac{6 \times 1}{4} = \frac{6}{4}\]
This result, \(\frac{6}{4}\) cups, can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is \(2\):
\[\frac{6 \div 2}{4 \div 2} = \frac{3}{2}\]
Converting the improper fraction \(\frac{3}{2}\) to a mixed number gives:
\[\frac{3}{2} = 1 \frac{1}{2}\]
Comparing these results to the options provided:
- \(\frac{3}{2}\) cups is equivalent to \(1.5\) cups.
- \(\frac{6}{24}\) cups is equivalent to \(0.25\) cups.
- \(1 \frac{1}{2}\) cups is equivalent to \(1.5\) cups.
- \(\frac{6}{4}\) cups is equivalent to \(1.5\) cups.
Since \(\frac{6}{4}\), \(\frac{3}{2}\), and \(1 \frac{1}{2}\) are all equivalent, each of these expressions represents the correct amount of food eaten. Typically, \(1 \frac{1}{2}\) is the most common form for such measurements.
Examples
In everyday life, measuring ingredients for cooking or pet food often involves fractions. For example, if a recipe calls for a specific fraction of a cup of flour and you need to double or triple that recipe, you are performing similar arithmetic. Understanding how to multiply and simplify fractions ensures that you provide the right proportions for your tasks, such as ensuring your pets get the correct nutrition or that your baking comes out just right.