The mixed number equivalent of the improper fraction 31/5 is 6(1/5).

Verified step by step guidance

1. Identify the improper fraction given: \(\frac{31}{5}\), where the numerator (31) is greater than the denominator (5).
2. Divide the numerator by the denominator to find the whole number part: perform the division \$31 \div 5$.
3. Determine the quotient (whole number) and the remainder from the division. The quotient will be the whole number part of the mixed number.
4. Write the remainder as the numerator of the fractional part, keeping the original denominator (5). So the fractional part is \(\frac{\text{remainder}}{5}\).
5. Combine the whole number and the fractional part to express the mixed number as \(\text{quotient} \left( \frac{\text{remainder}}{5} \right)\), which is the mixed number equivalent of the improper fraction.

Key Concepts

Improper Fractions

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, indicating a value equal to or greater than one. For example, 31/5 is improper because 31 > 5. Understanding improper fractions is essential for converting them into mixed numbers.

Mixed Numbers

A mixed number combines a whole number and a proper fraction, representing values greater than one in a more intuitive form. For instance, 6(1/5) means 6 whole parts and one-fifth of another part. Converting improper fractions to mixed numbers helps in easier interpretation and calculation.

Conversion Process from Improper Fraction to Mixed Number

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder over the original denominator forms the fractional part. For 31/5, dividing 31 by 5 gives 6 with a remainder of 1, so the mixed number is 6(1/5).