Mixed number calculator



This calculator performs basic and advanced operations with mixed numbers, fractions, integers, and decimals. Mixed numbers are also called mixed fractions. A mixed number is a whole number and a proper fraction combined, i.e. one and three-quarters. The calculator evaluates the expression or solves the equation with step-by-step calculation progress information. Solve problems with two or more mixed numbers fractions in one expression.

The result:

1 3/8 + 6 11/13 + 5 7/8 = 733/52 = 14 5/5214.0961538

Spelled result in words is fourteen and five fifty-seconds (or seven hundred thirty-three fifty-seconds).

Calculation steps

  1. Conversion a mixed number 1 3/8 to a improper fraction: 1 3/8 = 1 3/8 = 1 · 8 + 3/8 = 8 + 3/8 = 11/8

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 8. Whole number 1 equally 1 * 8/8 = 8/8
    b) Add the answer from the previous step 8 to the numerator 3. New numerator is 8 + 3 = 11
    c) Write a previous answer (new numerator 11) over the denominator 8.

    One and three eighths is eleven eighths.
  2. Conversion a mixed number 6 11/13 to a improper fraction: 6 11/13 = 6 11/13 = 6 · 13 + 11/13 = 78 + 11/13 = 89/13

    To find a new numerator:
    a) Multiply the whole number 6 by the denominator 13. Whole number 6 equally 6 * 13/13 = 78/13
    b) Add the answer from the previous step 78 to the numerator 11. New numerator is 78 + 11 = 89
    c) Write a previous answer (new numerator 89) over the denominator 13.

    Six and eleven thirteenths is eighty-nine thirteenths.
  3. Add: 11/8 + 89/13 = 11 · 13/8 · 13 + 89 · 8/13 · 8 = 143/104 + 712/104 = 143 + 712/104 = 855/104
    It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 13) = 104. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 13 = 104. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - eleven eighths plus eighty-nine thirteenths is eight hundred fifty-five one-hundred fourths.
  4. Conversion a mixed number 5 7/8 to a improper fraction: 5 7/8 = 5 7/8 = 5 · 8 + 7/8 = 40 + 7/8 = 47/8

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8
    b) Add the answer from the previous step 40 to the numerator 7. New numerator is 40 + 7 = 47
    c) Write a previous answer (new numerator 47) over the denominator 8.

    Five and seven eighths is forty-seven eighths.
  5. Add: the result of step No. 3 + 47/8 = 855/104 + 47/8 = 855/104 + 47 · 13/8 · 13 = 855/104 + 611/104 = 855 + 611/104 = 1466/104 = 2 · 733/2 · 52 = 733/52
    It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(104, 8) = 104. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 104 × 8 = 832. In the following intermediate step, cancel by a common factor of 2 gives 733/52.
    In other words - eight hundred fifty-five one-hundred fourths plus forty-seven eighths is seven hundred thirty-three fifty-seconds.

What is a mixed number?

A mixed number is an integer and fraction acb whose value equals the sum of that integer and fraction. For example, we write two and four-fifths as 254. Its value is 254=2+54=510+54=514. The mixed number is the exception - the missing operand between a whole number and a fraction is not multiplication but an addition: 254=2 54. A negative mixed number - the minus sign also applies to the fractional 254=(254)=(2+54)=514. A mixed number is sometimes called a mixed fraction. Usually, a mixed number contains a natural number and a proper fraction, and its value is an improper fraction, that is, one where the numerator is greater than the denominator.

How do I imagine a mixed number?

We can imagine mixed numbers in the example of cakes. We have three cakes, and we have divided each into five parts. We thus obtained 3 * 5 = 15 pieces of cake. One piece when we ate, there were 14 pieces left, which is 254 of cake. When we eat two pieces, 253 of the cake remains.

Mixed number in word problems:



more math problems »