Verified Answer :

  • To convert an improper fraction to a mixed number, divide the numerator by the denominator.
  • For \(\frac{65}{8}\), divide 65 by 8 to get a quotient of 8 and a remainder of 1.
  • Write the result as the whole number (quotient) followed by the remainder over the original denominator.
  • The final mixed number is \(\boxed{8 \frac{1}{8}}\).

Explanation

  1. Understanding Improper Fractions and Mixed Numbers

To convert an improper fraction to a mixed number, we divide the numerator by the denominator. An improper fraction occurs when the numerator is larger than the denominator, such as \(\frac{65}{8}\). A mixed number consists of a whole number and a proper fraction, representing the same total value.

  1. Division of Numerator by Denominator

To convert \(\frac{65}{8}\), we divide the numerator, 65, by the denominator, 8. We look for the largest integer multiple of 8 that is less than or equal to 65. Calculating \(65 \div 8\), we find that \(8 \times 8 = 64\). Subtracting this from 65 leaves a remainder: \(65 - 64 = 1\). Therefore, 65 divided by 8 is 8 with a remainder of 1.

  1. Constructing the Mixed Number

The quotient, which is 8, becomes the whole number part of the mixed number. The remainder, 1, becomes the numerator of the fractional part, and the original denominator, 8, stays the same. Thus, \(\frac{65}{8} = 8 \frac{1}{8}\).

  1. Final Answer

The result of converting the improper fraction \(\frac{65}{8}\) into a mixed number is \(\boxed{8 \frac{1}{8}}\).

Examples

Imagine you are baking cookies and the recipe requires \(\frac{65}{8}\) cups of flour. Since measuring cups are usually marked in whole numbers and common fractions, converting \(\frac{65}{8}\) to a mixed number helps you see that you need exactly \(8 \frac{1}{8}\) cups. This conversion makes it much easier to measure out your ingredients accurately using standard kitchen tools.

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