How many 1/2 cup can you get in 7/8 cups
The Correct Answer and Explanation is:
To determine how many ( \frac{1}{2} ) cups can fit into ( \frac{7}{8} ) cups, we need to divide ( \frac{7}{8} ) by ( \frac{1}{2} ).
Step-by-step explanation:
- Division of Fractions:
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of ( \frac{1}{2} ) is ( \frac{2}{1} ). Thus, the problem becomes:
[
\frac{7}{8} \div \frac{1}{2} = \frac{7}{8} \times \frac{2}{1}
] - Multiplying Fractions:
Now, multiply the numerators and the denominators:
[
\frac{7 \times 2}{8 \times 1} = \frac{14}{8}
] - Simplifying the Fraction:
The fraction ( \frac{14}{8} ) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[
\frac{14 \div 2}{8 \div 2} = \frac{7}{4}
] - Converting the Fraction to a Mixed Number:
The fraction ( \frac{7}{4} ) is an improper fraction, meaning the numerator is larger than the denominator. To express it as a mixed number, divide 7 by 4:
[
7 \div 4 = 1 \text{ remainder } 3
]
So, ( \frac{7}{4} = 1 \frac{3}{4} ).
Final Answer:
Thus, you can fit ( 1 \frac{3}{4} ) (or 1 and three-quarters) of ( \frac{1}{2} ) cups into ( \frac{7}{8} ) cups.
Explanation:
When dividing fractions, we are essentially determining how many times one fraction fits into another. By multiplying by the reciprocal of the divisor, we convert the division problem into a multiplication problem. The result, ( 1 \frac{3}{4} ), shows that ( \frac{1}{2} ) cups can be measured out 1 full time, with a remainder of ( \frac{3}{4} ), or one and three-quarters times. This is a common way of dividing portions in cooking or liquid measurements.