Mixed Numbers – Whole Numbers and Fractions Together
A mixed number combines a whole number and a proper fraction into one value. They appear everywhere — distances, cooking measurements, time — wherever a quantity falls between two whole numbers.
What Does a Mixed Number Look Like?
2½ means 2 whole units plus half a unit. 3⅔ means 3 whole units plus two-thirds of a unit.
Converting a Mixed Number to an Improper Fraction
Multiply the whole number by the denominator, add the numerator, keep the denominator.
a b/c = (a × c + b) / c
Convert 3¾ to an improper fraction
3 × 4 + 3 = 15. Answer: 15/4. Check: 15 ÷ 4 = 3.75 = 3¾ ✓
Convert 5⅔ to an improper fraction
5 × 3 + 2 = 17. Answer: 17/3.
Converting an Improper Fraction to a Mixed Number
Divide the numerator by the denominator. The quotient is the whole part; the remainder over the denominator is the fractional part.
Convert 22/5 to a mixed number
22 ÷ 5 = 4 remainder 2. Answer: 4⅔.
Adding Mixed Numbers
2⅓ + 1½
Convert: 7/3 + 3/2. LCM = 6: 14/6 + 9/6 = 23/6 = 3⅞.
Subtracting Mixed Numbers
4¼ − 1⅔
Convert: 17/4 − 5/3. LCM = 12: 51/12 − 20/12 = 31/12 = 2⁷/12.
Key Takeaways
- Mixed number → improper: (whole × denominator + numerator) / denominator.
- Improper → mixed: divide numerator by denominator; use quotient and remainder.
- For operations, convert to improper fractions first, then convert back.
Practice Questions
- Convert 4⅔ to an improper fraction.
- Convert 19/6 to a mixed number.
- Add 1½ + 2⅓.
- Subtract 3¼ − 1¾.
- A recipe needs 2½ cups of flour and 1⅓ cups of sugar. What is the total volume?