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 5/52 ≅ 14.0961538

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

Calculation steps

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.
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.
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) denominator for adding 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 equals eight hundred fifty-five one-hundred fourths.
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.
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) denominator for adding 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 equals seven hundred thirty-three fifty-seconds.

What is a mixed number?

A mixed number is an integer and fraction

a \frac{b}{c}

whose value equals the sum of that integer and fraction. For example, we write two and four-fifths as

2 \frac{4}{5}

. Its value is

2 \frac{4}{5} = 2 + \frac{4}{5} = \frac{1 0}{5} + \frac{4}{5} = \frac{1 4}{5}

. The mixed number is the exception - the missing operand between a whole number and a fraction is not multiplication but an addition:

2 \frac{4}{5} \neq = 2 \cdot \frac{4}{5}

. A negative mixed number - the minus sign also applies to the fractional

- 2 \frac{4}{5} = - (2 \frac{4}{5}) = - (2 + \frac{4}{5}) = - \frac{1 4}{5}

. 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

2 \frac{4}{5}

of cake. When we eat two pieces,

2 \frac{3}{5}

of the cake remains.

Examples:

• sum of two mixed numbers: 1 3/4 + 2 3/8
• addition of three mixed numbers: 1 3/8 + 6 11/13 + 5 7/8
• addition of two mixed numbers: 2 1/2 + 4 2/3
• subtracting two mixed numbers: 7 1/2 - 5 3/4
• multiplication of mixed numbers: 3 3/4 * 2 2/5
• comparing mixed numbers: 3 1/4 2 1/3
• What is 3/4 as a mixed number: 3/4
• subtracting mixed number and fraction: 1 3/5 - 5/6
• sum mixed number and an improper fraction: 1 3/5 + 11/5