Quick answer
To convert a mixed number to an improper fraction: whole × denominator + numerator, over the same denominator. For 2¾: (2 × 4) + 3 = 11 → 11/4.
How to use this calculator
Enter the whole number, numerator, and denominator of the mixed number. The calculator returns the improper fraction, decimal value, and step-by-step conversion.
Conversion formula
$$w\frac{n}{d} = \frac{w \times d + n}{d}$$
The denominator is unchanged. The new numerator is the whole number multiplied by the denominator, plus the original numerator.
Why the formula works
A mixed number is a whole number plus a fraction. To write the whole part as a fraction with the same denominator, multiply the whole by d/d (which equals 1):
$$2\frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}$$
2 = 8/4 (since 2 × 4/4 = 8/4). Add 3/4: 8/4 + 3/4 = 11/4. The formula shortcut skips the intermediate step.
Worked examples
Example 1: 2¾
$$2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}$$
(2 × 4) + 3 = 11. Improper fraction: 11/4. Decimal: 2.75.
Example 2: 3⅓
$$3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$$
(3 × 3) + 1 = 10. Improper fraction: 10/3. Decimal: 3.333…
Example 3: 5 2/7
(5 × 7) + 2 = 37. Improper fraction: 37/7. Decimal: 5.2857…
| Mixed number | Whole × denom | + numerator | Improper fraction |
|---|---|---|---|
| 1½ | 1 × 2 = 2 | 2 + 1 = 3 | 3/2 |
| 2⅓ | 2 × 3 = 6 | 6 + 1 = 7 | 7/3 |
| 3¾ | 3 × 4 = 12 | 12 + 3 = 15 | 15/4 |
| 4 2/5 | 4 × 5 = 20 | 20 + 2 = 22 | 22/5 |
| 1 5/6 | 1 × 6 = 6 | 6 + 5 = 11 | 11/6 |
| 2 7/8 | 2 × 8 = 16 | 16 + 7 = 23 | 23/8 |
Negative mixed numbers
Apply the negative sign to the entire result after converting the absolute value:
$$-1\frac{2}{5} = -\frac{1 \times 5 + 2}{5} = -\frac{7}{5}$$
−1 2/5: (1 × 5) + 2 = 7 → −7/5. The negative sign applies to the whole mixed number, not just the whole-number part.
When you need this conversion
Converting to improper fractions is required before performing arithmetic on mixed numbers. To add 1½ + 2⅓, convert both to improper fractions (3/2 and 7/3), find the LCD (6), add (9/6 + 14/6 = 23/6), then convert back (3⅚). Operating directly on the mixed number parts is error-prone when the fractional sum exceeds 1.
Frequently asked questions
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, then add the numerator. The result is the new numerator; the denominator stays the same.
What is 3½ as an improper fraction?
7/2. Calculation: (3 × 2) + 1 = 7. Denominator stays 2.
Why convert mixed numbers to improper fractions?
Arithmetic (add, subtract, multiply, divide) is more straightforward in improper fraction form. Convert first, operate, then convert the result back if a mixed number is preferred.