Ctrl+k

Convert mixed numbers to improper fractions

A mixed number represents a whole-number quantity plus a fractional part, and its equivalent improper fraction expresses all parts with one common denominator: abc=ac+bca\frac{b}{c}=\frac{ac+b}{c}. On a number line or partitioned bar, the whole units are regrouped into equal fractional parts; the denominator stays the same while the numerator counts all such parts, preserving value. This treatment is limited to positive mixed numbers with whole-number parts and proper fractional parts, not negative or algebraic forms.

Detailed Explanation: Convert mixed numbers to improper fractions

A mixed number has a whole-number part and a fraction part. To convert it to an improper fraction:

  1. Multiply the whole number by the denominator.
  2. Add the numerator.
  3. Keep the denominator the same.

Example: Convert 2352\frac{3}{5} to an improper fraction.

  • Multiply the whole number by the denominator:
    2×5=102 \times 5 = 10
  • Add the numerator:
    10+3=1310 + 3 = 13
  • Keep the denominator, 55.

So,

235=1352\frac{3}{5}=\frac{13}{5}

This makes sense because each whole has 55 fifths. The 22 wholes give 2×5=102 \times 5=10 fifths, and the extra fraction gives 33 more fifths. Altogether, there are 1313 fifths.

Learn by doing: Convert mixed numbers to improper fractions

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Fraction Conversion - To Improper - From Image

      ?