Verified Answer :

  • Divide the numerator 34 by the denominator 7 to find the quotient and the remainder.
  • The division \(34 \div 7\) gives a quotient of 4 and a remainder of 6.
  • Express the result as the integer quotient followed by the fraction with the remainder as the numerator: \(4 \frac{6}{7}\).
  • The final answer is \(\boxed{4 \frac{6}{7}}\).

Explanation

  1. Problem Analysis

To express the improper fraction \(\frac{34}{7}\) as a mixed number, we first analyze its components. An improper fraction is one where the numerator is greater than or equal to the denominator. A mixed number, on the other hand, consists of an integer part and a proper fraction part, written in the form \(A \frac{b}{c}\), where \(A\) is an integer and \(\frac{b}{c}\) is a fraction with \(b < c\). In our case, the denominator remains 7.

  1. Performing Integer Division

To find the integer part and the remainder, we perform integer division of the numerator by the denominator. We divide 34 by 7. Calculating how many times 7 goes into 34, we find that \(7 \times 4 = 28\). The remaining difference is \(34 - 28 = 6\). Thus, 34 can be written as \(7 \times 4 + 6\).

  1. Final Result Formulation

Using the results from the division, the quotient is 4 and the remainder is 6. This means that \(\frac{34}{7}\) is equivalent to \(4\) wholes and a fraction \(\frac{6}{7}\). Putting these together, the improper fraction \(\frac{34}{7}\) written as a mixed number is \(4 \frac{6}{7}\).

Examples

Converting improper fractions to mixed numbers is useful when managing physical quantities, such as cooking measurements or construction materials. For example, if a recipe requires \(\frac{34}{7}\) cups of flour, and your measuring cup only measures 1 cup at a time, calculating that \(\frac{34}{7} = 4 \frac{6}{7}\) tells you immediately that you need 4 full cups and an additional \(\frac{6}{7}\) of a cup. This helps in visual estimation and practical preparation of materials.

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