Divide: 5 1/2 divided by 2 1/2 =
A.
2 1/5
B.
2.0
C.
21/2
D.
23/4
The correct answer and Explanation is :
To divide the mixed numbers (5 \frac{1}{2}) and (2 \frac{1}{2}), we first convert them into improper fractions.
Step 1: Convert Mixed Numbers to Improper Fractions
For (5 \frac{1}{2}):
- Multiply the whole number (5) by the denominator (2): (5 \times 2 = 10)
- Add the numerator (1): (10 + 1 = 11)
- So, (5 \frac{1}{2} = \frac{11}{2})
For (2 \frac{1}{2}):
- Multiply the whole number (2) by the denominator (2): (2 \times 2 = 4)
- Add the numerator (1): (4 + 1 = 5)
- So, (2 \frac{1}{2} = \frac{5}{2})
Step 2: Set Up the Division
Now we have:
[
\frac{11}{2} \div \frac{5}{2}
]
Step 3: Convert Division to Multiplication
To divide by a fraction, we multiply by its reciprocal:
[
\frac{11}{2} \div \frac{5}{2} = \frac{11}{2} \times \frac{2}{5}
]
Step 4: Multiply the Fractions
Now, we multiply the numerators and the denominators:
[
\frac{11 \times 2}{2 \times 5} = \frac{22}{10}
]
Step 5: Simplify the Fraction
Now we simplify (\frac{22}{10}):
- Both the numerator and denominator can be divided by 2:
[
\frac{22 \div 2}{10 \div 2} = \frac{11}{5}
]
Step 6: Convert Back to a Mixed Number
To convert (\frac{11}{5}) back to a mixed number:
- Divide 11 by 5, which equals 2 with a remainder of 1.
- So, (\frac{11}{5} = 2 \frac{1}{5}).
Conclusion
Thus, the answer to (5 \frac{1}{2} \div 2 \frac{1}{2}) is (2 \frac{1}{5}), which corresponds to option A.
Answer
A. (2 \frac{1}{5})