Mixed Number Calculator – Guide & Formulas
Perform arithmetic on mixed numbers. Add, subtract, multiply, and divide mixed numbers with step-by-step solutions and simplified results.
Perform arithmetic on mixed numbers with ease. Add, subtract, multiply, or divide mixed numbers and get instant results with step-by-step breakdowns and simplified answers.
Key Takeaway
Use the free Mixed Number Calculator to perform arithmetic on mixed numbers. add, subtract, multiply, and divide mixed numbers with step-by-step solutions and simplified results. Get instant results with step-by-step explanations.
How to Use the Mixed Number Calculator
- Select the operation: Add, Subtract, Multiply, or Divide.
- Enter the whole number, numerator, and denominator for the first mixed number.
- Enter the whole number, numerator, and denominator for the second mixed number.
- Click "Calculate" to see the result and step-by-step breakdown.
- Copy the result if needed.
The Formula
Variable Definitions
- a, d: Whole number parts of the mixed numbers
- b, e: Numerators of the fractional parts
- c, f: Denominators of the fractional parts
Adding 2 1/3 and 1 2/5
Add the mixed numbers 2 1/3 and 1 2/5.
- Step 1: Convert to improper fractions: 2 1/3 = 7/3, 1 2/5 = 7/5.
- Step 2: Find LCD of 3 and 5: LCD = 15.
- Step 3: Convert: 7/3 = 35/15, 7/5 = 21/15.
- Step 4: Add numerators: 35 + 21 = 56. Result: 56/15.
- Step 5: Convert back: 56/15 = 3 11/15.
Frequently Asked Questions
How do you add mixed numbers?
Convert each mixed number to an improper fraction, find a common denominator, add the numerators, then convert back to a mixed number and simplify.
How do you subtract mixed numbers?
Convert to improper fractions, find a common denominator, subtract the numerators, then convert back. If the first numerator is smaller, borrow from the whole number.
What is 2 1/2 + 1 1/3?
2 1/2 = 5/2, 1 1/3 = 4/3. LCD = 6. 5/2 = 15/6, 4/3 = 8/6. Sum = 23/6 = 3 5/6.
What is 3 3/4 - 1 1/2?
3 3/4 = 15/4, 1 1/2 = 3/2 = 6/4. Subtract: 15/4 - 6/4 = 9/4 = 2 1/4.
What is 2 1/3 × 1 1/4?
2 1/3 = 7/3, 1 1/4 = 5/4. Multiply: 7/3 × 5/4 = 35/12 = 2 11/12.
What is 3 1/2 ÷ 1 1/4?
3 1/2 = 7/2, 1 1/4 = 5/4. Divide: 7/2 ÷ 5/4 = 7/2 × 4/5 = 28/10 = 14/5 = 2 4/5.
How do you multiply mixed numbers?
Convert both mixed numbers to improper fractions, multiply numerators together and denominators together, then convert the result back to a mixed number.
How do you divide mixed numbers?
Convert to improper fractions, then multiply by the reciprocal of the second fraction (flip it). Simplify the result and convert back to a mixed number.
What is 1 1/2 + 2 2/3?
1 1/2 = 3/2, 2 2/3 = 8/3. LCD = 6. 3/2 = 9/6, 8/3 = 16/6. Sum = 25/6 = 4 1/6.
What is 4 1/3 - 2 1/6?
4 1/3 = 13/3, 2 1/6 = 13/6. LCD = 6. 13/3 = 26/6, 13/6 = 13/6. Subtract: 26/6 - 13/6 = 13/6 = 2 1/6.
What is 1 3/4 × 2 2/5?
1 3/4 = 7/4, 2 2/5 = 12/5. Multiply: 7/4 × 12/5 = 84/20 = 21/5 = 4 1/5.
What is 5 1/2 ÷ 2 1/3?
5 1/2 = 11/2, 2 1/3 = 7/3. Divide: 11/2 ÷ 7/3 = 11/2 × 3/7 = 33/14 = 2 5/14.
Can I add three mixed numbers at once?
Yes. Convert all three to improper fractions, find a common denominator for all three, add all numerators, then convert back and simplify.
What is 3 1/5 + 2 1/2 + 1 1/10?
Convert: 16/5, 5/2, 11/10. LCD = 10. 32/10 + 25/10 + 11/10 = 68/10 = 34/5 = 6 4/5.
What is 2 3/8 × 1 1/3?
2 3/8 = 19/8, 1 1/3 = 4/3. Multiply: 19/8 × 4/3 = 76/24 = 19/6 = 3 1/6.
How do you handle borrowing in subtraction?
If the first fraction is smaller than the second, borrow 1 from the whole number (adding the denominator to the numerator), then subtract. For example, 3 1/4 - 1 3/4: borrow to get 2 5/4 - 1 3/4 = 1 2/4 = 1 1/2.
What is 4 2/3 - 1 5/6?
4 2/3 = 14/3, 1 5/6 = 11/6. LCD = 6. 28/6 - 11/6 = 17/6 = 2 5/6.
What is 1 1/8 + 3 3/8?
Since denominators are the same: 1 1/8 + 3 3/8 = 4 4/8 = 4 1/2.
What is 2 2/5 ÷ 1 1/10?
2 2/5 = 12/5, 1 1/10 = 11/10. Divide: 12/5 ÷ 11/10 = 12/5 × 10/11 = 120/55 = 24/11 = 2 2/11.
Why convert to improper fractions first?
Improper fractions make arithmetic straightforward. You can directly add, subtract, multiply, or divide without worrying about the whole number and fraction parts separately.