What is half of 3 and 1/4 cups?
Understand the Problem
The question is asking for the mathematical operation of finding half of a mixed number, specifically 3 and 1/4 cups. To solve this, we will first convert the mixed number into an improper fraction, and then divide by 2.
Answer
$1 \frac{5}{8}$
Answer for screen readers
The final answer is (1 \frac{5}{8}).
Steps to Solve
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Convert the mixed number to an improper fraction
A mixed number can be converted into an improper fraction. For the mixed number (3 \frac{1}{4}), multiply the whole number (3) by the denominator (4) and add the numerator (1).
[ 3 \times 4 + 1 = 12 + 1 = 13 ]
So, (3 \frac{1}{4} = \frac{13}{4}).
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Divide the improper fraction by 2
Next, we need to find half of (\frac{13}{4}). Dividing by 2 can be done by multiplying by (\frac{1}{2}):
[ \frac{13}{4} \div 2 = \frac{13}{4} \times \frac{1}{2} ]
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Perform the multiplication
To multiply fractions, multiply the numerators and the denominators:
[ \frac{13 \times 1}{4 \times 2} = \frac{13}{8} ]
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Convert the improper fraction back to a mixed number
Finally, we can convert (\frac{13}{8}) back to a mixed number. Since 8 goes into 13 once with a remainder:
[ \frac{13}{8} = 1 \frac{5}{8} ]
So, half of (3 \frac{1}{4}) is (1 \frac{5}{8}).
The final answer is (1 \frac{5}{8}).
More Information
Finding half of a mixed number, like (3 \frac{1}{4}), involves converting it to an improper fraction and then performing simple division. This method shows how mixed numbers can easily be manipulated using improper fractions.
Tips
- Forgetting to convert the mixed number to an improper fraction before dividing can lead to incorrect results.
- Incorrectly adding or multiplying fractions by not properly multiplying the numerators and denominators.
