What is 11
4
3
divided by 2?
The Correct Answer and Explanation is :
The correct answer is: ( \frac{11}{8} ) or ( 1 \frac{3}{8} )
To solve the division of the fraction ( \frac{11}{4} ) divided by ( 2 ), we first need to express the operation clearly. When we divide by a number, it’s equivalent to multiplying by the reciprocal of that number. Therefore, dividing ( \frac{11}{4} ) by ( 2 ) can be rewritten as:
[
\frac{11}{4} \div 2 = \frac{11}{4} \times \frac{1}{2}
]
Next, we can multiply the fractions:
[
\frac{11 \times 1}{4 \times 2} = \frac{11}{8}
]
Now, we can convert this improper fraction into a mixed number. An improper fraction is one where the numerator is larger than the denominator. To convert ( \frac{11}{8} ) into a mixed number, we divide ( 11 ) by ( 8 ):
- ( 8 ) goes into ( 11 ) once (1) with a remainder of ( 3 ) (because ( 11 – 8 = 3 )).
- Thus, ( \frac{11}{8} ) can be expressed as ( 1 \frac{3}{8} ).
Explanation
Understanding Division of Fractions:
Dividing fractions can be less intuitive than dividing whole numbers, so it’s essential to remember the reciprocal rule. When dividing by a whole number, we can transform it into a fraction to simplify the calculation.
In our example, we took ( 2 ) and expressed it as ( \frac{2}{1} ) to perform the operation easily. By converting division into multiplication, we utilize the property of fractions that allows us to combine numerators and denominators directly.
Mixed Numbers vs. Improper Fractions:
Mixed numbers are often used in everyday situations, such as cooking or measuring, because they are more intuitive for representing quantities greater than one. Improper fractions, while mathematically valid, can be less convenient for comprehension and practical use.
Final Result
Thus, the final result of ( \frac{11}{4} \div 2 ) is ( \frac{11}{8} ) or ( 1 \frac{3}{8} ).