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K.3 Convert between mixed numbers and improper fractions

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What are mixed numbers and improper fractions?

A mixed number shows a whole number and a fraction together. An improper fraction has a numerator that is greater than or equal to its denominator.

Examples:
  • Mixed number: 212
  • Improper fraction: 52
Note

Mixed numbers show parts of a whole beyond one. Improper fractions represent the same amount but written as a single fraction.

How to convert a mixed number to an improper fraction

To change a mixed number into an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the same denominator.

Example:
  • Start with 213
  • Multiply the whole number by the denominator: 2 × 3 = 6
  • Add the numerator: 6 + 1 = 7
  • Write the answer as a fraction with the same denominator: 73
Note

Always keep the denominator the same. Only the numerator changes when converting.

How to convert an improper fraction to a mixed number

To convert an improper fraction into a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator.

Example:
  • Start with 94
  • Divide 9 ÷ 4 = 2 with a remainder of 1
  • Write the quotient as the whole number: 2
  • Write the remainder over the denominator: 214
Note

The remainder always becomes the numerator of the fraction part. The denominator stays the same.

Understanding the relationship between the two forms

Mixed numbers and improper fractions show the same value in different ways. You can move between the two forms by using multiplication, addition, or division.

Example:
  • 234 = 114
  • 114 = 234
Note

Both forms represent the same amount. You can choose the form that fits best for solving a problem or explaining your reasoning.

Checking your work

After converting, check your answer by reversing the process. Converting back and getting the same value shows your answer is correct.

Example:
  • Start with 325
  • Convert to improper fraction: (3 × 5) + 2 = 17 → 175
  • Now convert back: 17 ÷ 5 = 325
Note

If you can convert both ways and return to the same number, your understanding is strong and your math is correct.