Expressed as the simplest mixed number, $33 / 8$ is equal to?
A. $3 \frac{5}{4}$
B. $3 \frac{9}{8}$
C. $4 \frac{1}{8}$
D. $4^{3 / 8}$
Answer (2)
Divide 33 by 8 to get the quotient and remainder.
The quotient is 4 and the remainder is 1.
Form the mixed number with the quotient as the whole number and the remainder as the numerator: 4 8 1 .
The simplest mixed number is 4 8 1 .
Explanation
Understanding the Problem We need to convert the improper fraction 8 33 into a mixed number. A mixed number consists of a whole number and a proper fraction.
Conversion Process To convert 8 33 to a mixed number, we divide 33 by 8. The quotient will be the whole number part, and the remainder will be the numerator of the fractional part, with the denominator remaining 8.
Performing the Division When we divide 33 by 8, we get a quotient of 4 and a remainder of 1. This is because 8 × 4 = 32 , and 33 − 32 = 1 .
Forming the Mixed Number Therefore, the mixed number is 4 8 1 . The whole number part is 4, the numerator of the fractional part is 1, and the denominator is 8.
Final Answer The simplest mixed number representation of 8 33 is 4 8 1 .
Examples
Mixed numbers are useful in everyday situations, such as measuring ingredients for a recipe. For example, if a recipe calls for 8 33 cups of flour, it's easier to measure out 4 8 1 cups. This helps in practical applications where precise measurements are needed.
The improper fraction 8 33 can be converted to the mixed number 4 8 1 by dividing 33 by 8, yielding a quotient of 4 and a remainder of 1. This makes option C, 4 8 1 , the correct answer. Thus, the simplest mixed number is 4 8 1 .
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