Mixed Number Calculator
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whole
and
fraction
Enter whole = 0 if it is a proper fraction only (e.g. 0 and 3/4)
whole
and
fraction
Enter two mixed numbers and choose an operation to calculate.
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Mixed Number Arithmetic Operations
A mixed number combines a whole number and a proper fraction, such as 2 and 1/2 or 3 and 3/4. To perform arithmetic on mixed numbers, the standard approach is to convert them to improper fractions first, perform the operation, then convert the result back to a mixed number.
Converting to improper fraction: multiply the whole number by the denominator, add the numerator, keep the same denominator. Example: 2 and 1/2 = (2×2+1)/2 = 5/2.
Adding Mixed Numbers
1 and 1/2 + 2 and 1/3. Convert: 3/2 + 7/3. LCD = 6: 9/6 + 14/6 = 23/6. Convert back: 3 and 5/6.
Subtracting Mixed Numbers
3 and 3/4 − 1 and 1/2. Convert: 15/4 − 3/2 = 15/4 − 6/4 = 9/4. Convert back: 2 and 1/4.
Multiplying Mixed Numbers
2 and 1/2 × 1 and 1/3. Convert: 5/2 × 4/3 = 20/6 = 10/3. Convert back: 3 and 1/3.
Dividing Mixed Numbers
3 and 1/2 ÷ 1 and 3/4. Convert: 7/2 ÷ 7/4. Flip and multiply: 7/2 × 4/7 = 28/14 = 2.
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Mixed Number Questions
What is a mixed number?+
A mixed number has a whole number part and a fractional part. Examples: 2 and 1/2, 3 and 3/4, 5 and 1/6. They represent quantities between two whole numbers and are used extensively in everyday measurement (1 and 1/2 cups, 2 and 3/4 inches). They are equivalent to improper fractions: 2 and 1/2 = 5/2, 3 and 3/4 = 15/4.
How do I convert a mixed number to an improper fraction?+
Multiply the whole number by the denominator and add the numerator, keeping the same denominator. Formula: a and b/c = (a×c + b) / c. Examples: 2 and 1/2 = (2×2+1)/2 = 5/2. 3 and 3/4 = (3×4+3)/4 = 15/4. 4 and 1/6 = (4×6+1)/6 = 25/6. This conversion is always the first step when doing arithmetic on mixed numbers.
How do I convert an improper fraction back to a mixed number?+
Divide numerator by denominator. The quotient is the whole number; the remainder is the new numerator over the original denominator. Example: 17/5. 17 ÷ 5 = 3 remainder 2. Mixed number: 3 and 2/5. Another: 22/7 = 3 remainder 1 = 3 and 1/7. If the remainder is 0 (like 15/5 = 3), the result is a whole number.
How do I add mixed numbers?+
Best method: convert both to improper fractions, find a common denominator, add numerators, simplify, convert back. Example: 1 and 1/2 + 2 and 1/3 = 3/2 + 7/3. LCD = 6: 9/6 + 14/6 = 23/6 = 3 and 5/6. Alternative: add whole number parts separately, add fraction parts, combine. If the fraction part exceeds 1, carry over to the whole number.
How do I multiply mixed numbers?+
Always convert to improper fractions first, then multiply numerators together and denominators together, then simplify. Example: 2 and 1/2 × 1 and 1/3 = 5/2 × 4/3 = 20/6 = 10/3 = 3 and 1/3. Never multiply the whole number parts and fraction parts separately — that gives a wrong answer. The improper fraction conversion is essential.
How do I divide mixed numbers?+
Convert both to improper fractions, then multiply the first by the reciprocal of the second (Keep-Change-Flip). Example: 3 and 1/2 ÷ 1 and 3/4 = 7/2 ÷ 7/4 = 7/2 × 4/7 = 28/14 = 2. The KCF rule works because dividing by a fraction equals multiplying by its reciprocal. Always simplify before or after multiplying.
How do I subtract a larger mixed number from a smaller one?+
Convert both to improper fractions and subtract. The result will be negative. Example: 1 and 1/4 − 2 and 3/4 = 5/4 − 11/4 = −6/4 = −3/2 = −1 and 1/2. Converting to improper fractions removes the ambiguity of working with negative mixed numbers. The result is simply a negative fraction which converts to a negative mixed number.
When is it better to use mixed numbers vs improper fractions?+
Mixed numbers are better for communication and measurement: "2 and a half cups of flour" is clearer than "5/2 cups." Improper fractions are better for calculation: arithmetic operations are simpler and less error-prone. In practice, you communicate in mixed numbers and calculate in improper fractions, converting between the two as needed. This calculator does both automatically.
What is 2 and 1/2 as a decimal?+
2.5. Convert: 2 and 1/2 = 5/2 = 5 ÷ 2 = 2.5. More examples: 3 and 1/4 = 13/4 = 3.25. 1 and 2/3 = 5/3 = 1.6666... (repeating). 4 and 3/8 = 35/8 = 4.375. To convert any mixed number to decimal: convert to improper fraction, then divide numerator by denominator.
How do mixed numbers appear in everyday life?+
Cooking: recipes use 1 and 1/2 cups, 2 and 3/4 teaspoons. Construction: lumber dimensions like 3 and 1/2 inches (a standard 2x4). Distance: races of 1 and 1/2 miles. Time: 2 and 1/4 hours. Sewing and fabric: 1 and 3/8 yards. Stock prices historically quoted in fractions (now decimals). Any situation where quantities fall between whole numbers naturally produces mixed numbers.