How do I calculate mixed numbers?
Calculate with mixed numbers and fractions. Perform arithmetic operations on mixed numbers.
- Result
- 3 11/12
1 2/3 + 2 1/4 = 3 11/12.
- As an improper fraction
- 47/12
- As a decimal
- 3.916667
Result: 3 11/12. 1 2/3 + 2 1/4 = 3 11/12.
How to calculate
Adds, subtracts, multiplies, or divides two mixed numbers or fractions exactly, as a mixed number, an improper fraction, and a decimal.
Example with the default inputs (First number 1 2/3, Operation +, Second number 2 1/4): 1 2/3 + 2 1/4 = 3 11/12.
Method: Turn each mixed number into an improper fraction, apply the operation, reduce by the GCF, and write the result as a mixed number.
- A minus sign applies to the whole mixed number: −1 1/2 means −(1 + 1/2) = −3/2.
- All arithmetic is exact with whole-number numerators and denominators of any size.
- Dividing by 0 has no answer.
Worked examples
Each example is checked against the calculator on every build.
- First number 1 2/3, Operation +, Second number 2 1/4 gives Result 3 11/12, As an improper fraction 47/12, As a decimal 3.916667.Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers
- First number 7/4, Operation +, Second number 5/6 gives Result 2 7/12, As an improper fraction 31/12.Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers
- First number 3 1/4, Operation −, Second number 1 1/2 gives Result 1 3/4, As an improper fraction 7/4, As a decimal 1.75.Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers
- First number 2 2/3, Operation ×, Second number 1 1/2 gives Result 4, As an improper fraction 4, As a decimal 4.Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers
- First number 2 1/3, Operation ÷, Second number 1 1/4 gives Result 1 13/15, As an improper fraction 28/15.Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers
- First number -2 1/3, Operation ×, Second number -1 2/3 gives Result 3 8/9, As an improper fraction 35/9.Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers
- First number -1 1/2, Operation +, Second number 1/4 gives Result -1 1/4, As an improper fraction -5/4, As a decimal -1.25.Source: OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers
How it works
- Improper fractions. Write each mixed number w n/d as one fraction: (w × d + n)/d. A minus sign applies to the whole number: −w n/d = −(w × d + n)/d.
- Operation. For fractions a/b and c/d:
- add: a/b + c/d = (a × d + c × b)/(b × d)
- subtract: a/b − c/d = (a × d − c × b)/(b × d)
- multiply: a/b × c/d = (a × c)/(b × d)
- divide: a/b ÷ c/d = (a × d)/(b × c), when c is not 0
- Lowest terms. Divide the numerator and the denominator by their greatest common factor, and make the denominator positive.
- Mixed number. Divide the numerator by the denominator: the whole-number part is the quotient and the fraction is the remainder over the denominator. A negative result keeps its minus sign in front: −5/4 = −1 1/4.
The decimal is the exact fraction rounded to a 64-bit float and shown to at most 6 decimal places.
Assumptions
- You can enter a mixed number (1 2/3), a fraction (5/3), or a whole number (2).
- A minus sign applies to the whole mixed number: −1 1/2 = −3/2.
- All arithmetic is exact, with whole-number numerators and denominators of any size.
- Dividing by 0 has no answer.
Worked examples by hand
1 2/3 + 2 1/4. 1 2/3 = 5/3 and 2 1/4 = 9/4. 5/3 + 9/4 = 20/12 + 27/12 = 47/12. 47 ÷ 12 = 3 remainder 11, so the answer is 3 11/12 (47/12, 3.916667).
7/4 + 5/6. 7/4 + 5/6 = 21/12 + 10/12 = 31/12. 31 ÷ 12 = 2 remainder 7, so the answer is 2 7/12.
3 1/4 − 1 1/2. 13/4 − 3/2 = 13/4 − 6/4 = 7/4 = 1 3/4 (1.75).
2 2/3 × 1 1/2. 8/3 × 3/2 = 24/6 = 4.
2 1/3 ÷ 1 1/4. 7/3 ÷ 5/4 = 7/3 × 4/5 = 28/15 = 1 13/15.
−2 1/3 × −1 2/3. (−7/3) × (−5/3) = 35/9 = 3 8/9.
−1 1/2 + 1/4. −3/2 + 1/4 = −6/4 + 1/4 = −5/4 = −1 1/4 (−1.25).
Other questions people ask
What is a mixed number?
A mixed number is a combination of a whole number and a proper fraction. For example, 2 3/4 means 2 whole units plus 3/4 of another unit. Mixed numbers are commonly used in everyday measurements like cooking (1 1/2 cups) or construction (3 1/4 feet).
How do I convert a mixed number to an improper fraction?
To convert a mixed number to an improper fraction: 1) Multiply the whole number by the denominator, 2) Add the numerator to that product, 3) Write the result over the original denominator. For example, 2 3/4 becomes (2 × 4 + 3)/4 = 11/4.
How do I convert an improper fraction to a mixed number?
To convert an improper fraction to a mixed number: 1) Divide the numerator by the denominator, 2) The quotient becomes the whole number, 3) The remainder becomes the numerator of the fraction, 4) Keep the same denominator. For example, 11/4 becomes 2 3/4.
How do I add mixed numbers?
To add mixed numbers: 1) Convert them to improper fractions, 2) Find a common denominator, 3) Add the numerators, 4) Convert the result back to a mixed number if needed. For example, 2 1/3 + 1 1/4 = 7/3 + 5/4 = 28/12 + 15/12 = 43/12 = 3 7/12.
How do I subtract mixed numbers?
To subtract mixed numbers: 1) Convert them to improper fractions, 2) Find a common denominator, 3) Subtract the numerators, 4) Convert the result back to a mixed number if needed. If the first fraction is smaller, you may need to borrow from the whole number.
How do I multiply mixed numbers?
To multiply mixed numbers: 1) Convert them to improper fractions, 2) Multiply the numerators and denominators, 3) Simplify the result, 4) Convert back to a mixed number if needed. For example, 2 1/3 × 1 1/4 = 7/3 × 5/4 = 35/12 = 2 11/12.
How do I divide mixed numbers?
To divide mixed numbers: 1) Convert them to improper fractions, 2) Invert the second fraction (reciprocal), 3) Multiply the fractions, 4) Simplify and convert back to a mixed number if needed. For example, 2 1/3 ÷ 1 1/4 = 7/3 ÷ 5/4 = 7/3 × 4/5 = 28/15 = 1 13/15.
When should I use mixed numbers vs. improper fractions?
Mixed numbers are better for everyday measurements and when you want to emphasize the whole number part. Improper fractions are better for mathematical calculations and when you need to perform operations. Our calculator can work with both formats and convert between them.
How do I simplify mixed numbers?
To simplify a mixed number: 1) Convert to an improper fraction, 2) Simplify the fraction by dividing numerator and denominator by their greatest common factor, 3) Convert back to a mixed number if needed. For example, 2 8/12 simplifies to 2 2/3.
What are some real-world applications of mixed numbers?
Mixed numbers are used in cooking (recipe measurements), construction (lengths and measurements), time (hours and minutes), money (dollars and cents), and many other everyday situations where you need to express whole units plus fractional parts.
How do negative mixed numbers work?
The minus sign belongs to the whole mixed number. −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2. For example, −1 1/2 + 1/4 = −6/4 + 1/4 = −5/4 = −1 1/4, and −2 1/3 × −1 2/3 = (−7/3) × (−5/3) = 35/9 = 3 8/9.