Divide 65 by 26 and write the answer as a mixed number
The Correct Answer and Explanation is:
To divide 65 by 26 and express the answer as a mixed number, we start with the division:
[
65 \div 26 = 2.5
]
To express this in the form of a mixed number, we separate the whole number part from the fractional part. The whole number part of ( 2.5 ) is ( 2 ), and the fractional part ( 0.5 ) can be converted into a fraction.
The decimal ( 0.5 ) can be expressed as:
[
0.5 = \frac{5}{10}
]
This fraction can be simplified. Both the numerator and denominator can be divided by ( 5 ):
[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
]
Therefore, we can combine the whole number ( 2 ) with the simplified fraction ( \frac{1}{2} ) to write the final answer as:
[
2 \frac{1}{2}
]
Thus, ( 65 \div 26 = 2 \frac{1}{2} ).
Explanation of the Process
Dividing numbers is a fundamental arithmetic operation. In this case, we are dividing ( 65 ) by ( 26 ). To find out how many times ( 26 ) fits into ( 65 ), we can perform the division. Since both numbers are integers, this is a straightforward operation. The quotient we found is ( 2.5 ), which signifies that ( 26 ) fits into ( 65 ) exactly ( 2 ) times, with some remainder that translates into a fractional part.
Next, we convert the decimal part ( 0.5 ) into a fraction to form a mixed number. Understanding how to convert between decimals and fractions is a critical skill in mathematics. The ability to simplify fractions further enhances comprehension and is essential for clarity in expressing numbers.
Mixed numbers, which consist of a whole number and a fraction, provide a way to represent numbers that are not whole. They are particularly useful in measurements and situations where the precision of fractions is important. This particular calculation demonstrates the utility of mixed numbers in expressing division results that are not whole.