Mixed Numbers Calculator

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.