Fraction Calculator

Actions with fractions

Adding and subtracting fractions with unlike denominators

Let's give an example, add two mixed fractions ${\displaystyle 5⁤\frac{6}{7}}$ and ${\displaystyle 3⁤\frac{5}{9}}$

To add fractions with unlike denominators, you need to convert those fractions to the improper fractions. To convert a fraction to an improper fraction, it is necessary to leave the denominator the same, and write the numerator as a sum, where the first term is the product of the whole number part and the denominator, and the second term is the numerator.

${\displaystyle 5⁤\frac{6}{7}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{(7\; ·\; 5)\; +\; 6}}{7}}$$=$${\displaystyle \mathrm{}⁤\frac{41}{7}}$ and the second fraction ${\displaystyle 3⁤\frac{5}{9}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{(9\; ·\; 3)\; +\; 5}}{9}}$$=$${\displaystyle \mathrm{}⁤\frac{32}{9}}$

Next, you need to make the denominators the same. There are several ways to make the denominators the same, we will consider the simplest. The common denominator is the product of the denominators of the first and second fractions. Next, it will be necessary to multiply the numerator of the first fraction by the denominator of the second fraction, and multiply the numerator of the second fraction by the denominator of the first fraction.

${\displaystyle \mathrm{}⁤\frac{41}{7}}$$+$${\displaystyle \mathrm{}⁤\frac{32}{9}}$ $=$ ${\displaystyle \mathrm{}⁤\frac{\mathrm{41\; ·\; 9}}{\mathrm{7\; ·\; 9}}}$$+$${\displaystyle \mathrm{}⁤\frac{\mathrm{32\; ·\; 7}}{\mathrm{7\; ·\; 9}}}$$=$${\displaystyle \mathrm{}⁤\frac{369}{63}}$$+$${\displaystyle \mathrm{}⁤\frac{224}{63}}$

Now that the fractions have a common denominator, their numerators can be added.

${\displaystyle \mathrm{}⁤\frac{\mathrm{369\; +\; 224}}{63}}$$=$${\displaystyle \mathrm{}⁤\frac{593}{63}}$

The result is an irreducible fraction, so let's just make the fraction mixed. To do this, you need to divide the numerator of the fraction by the denominator.
593 : 63 = 9 (remainder 26)
9 - whole number
26 - numerator
63 - denominator

${\displaystyle \mathrm{}⁤\frac{593}{63}}$$=$${\displaystyle 9⁤\frac{26}{63}}$$=\; 9.412698$

Let's write the whole example:

${\displaystyle 5⁤\frac{6}{7}}$$+$${\displaystyle 3⁤\frac{5}{9}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{(7\; ·\; 5)\; +\; 6}}{7}}$$+$${\displaystyle \mathrm{}⁤\frac{\mathrm{(9\; ·\; 3)\; +\; 5}}{9}}$$=$${\displaystyle \mathrm{}⁤\frac{41}{7}}$$+$${\displaystyle \mathrm{}⁤\frac{32}{9}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{41\; ·\; 9}}{\mathrm{7\; ·\; 9}}}$$+$${\displaystyle \mathrm{}⁤\frac{\mathrm{32\; ·\; 7}}{\mathrm{7\; ·\; 9}}}$$=$${\displaystyle \mathrm{}⁤\frac{369}{63}}$$+$${\displaystyle \mathrm{}⁤\frac{224}{63}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{369\; +\; 224}}{63}}$$=$${\displaystyle \mathrm{}⁤\frac{593}{63}}$$=$${\displaystyle 9⁤\frac{26}{63}}$$=\; 9.412698$

When subtracting fractions, it is necessary to perform all the same actions as when adding fractions, only the numerators of fractions should not be added, but subtracted. Subtract two fractions from the addition example:

${\displaystyle 5⁤\frac{6}{7}}$$-$${\displaystyle 3⁤\frac{5}{9}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{(7\; ·\; 5)\; +\; 6}}{7}}$$-$${\displaystyle \mathrm{}⁤\frac{\mathrm{(9\; ·\; 3)\; +\; 5}}{9}}$$=$${\displaystyle \mathrm{}⁤\frac{41}{7}}$$-$${\displaystyle \mathrm{}⁤\frac{32}{9}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{41\; ·\; 9}}{\mathrm{7\; ·\; 9}}}$$-$${\displaystyle \mathrm{}⁤\frac{\mathrm{32\; ·\; 7}}{\mathrm{7\; ·\; 9}}}$$=$${\displaystyle \mathrm{}⁤\frac{369}{63}}$$-$${\displaystyle \mathrm{}⁤\frac{224}{63}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{369\; -\; 224}}{63}}$$=$${\displaystyle \mathrm{}⁤\frac{145}{63}}$$=$${\displaystyle 2⁤\frac{19}{63}}$$=\; 2.301587$

Multiplication and division of fractions

Multiply two fractions ${\displaystyle 15⁤\frac{3}{8}}$ and ${\displaystyle \mathrm{}⁤\frac{4}{5}}$

To multiply two fractions, you need to multiply their numerators and denominators. In our example, the first fraction is mixed, so you first need to convert this fraction to an improper fraction, and then multiply the numerators and denominators.

${\displaystyle 15⁤\frac{3}{8}}$$\times$${\displaystyle \mathrm{}⁤\frac{4}{5}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{(8\; ·\; 15)\; +\; 3}}{8}}$$\times$${\displaystyle \mathrm{}⁤\frac{4}{5}}$$=$${\displaystyle \mathrm{}⁤\frac{123}{8}}$$\times$${\displaystyle \mathrm{}⁤\frac{4}{5}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{123\; ·\; 4}}{\mathrm{8\; ·\; 5}}}$$=$${\displaystyle \mathrm{}⁤\frac{492}{40}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{123\; ·\; 4}}{\mathrm{10\; ·\; 4}}}$$=$${\displaystyle \mathrm{}⁤\frac{123}{10}}$$=$${\displaystyle 12⁤\frac{3}{10}}$$=\; 12.3$

After multiplying the numerators and denominators, we get a fraction of four hundred and ninety-two forties, this fraction can be reduced by dividing the numerator and denominator by 4, or write the numerator as one hundred twenty-three times four, and the denominator as ten times four. And just like in the previous examples, we make a mixed fraction, 123: 10 = 12 (remainder 3), 12 is the whole number, 3 is the numerator, 10 is the denominator.

To divide fractions, you need to swap the numerator and denominator of the second fraction, and then multiply the fractions.

${\displaystyle \mathrm{}⁤\frac{5}{7}}$$÷$${\displaystyle \mathrm{}⁤\frac{9}{3}}$$=$${\displaystyle \mathrm{}⁤\frac{5}{7}}$$\times$${\displaystyle \mathrm{}⁤\frac{3}{9}}$

Further calculations are similar to the rules for multiplying fractions discussed above.

${\displaystyle \mathrm{}⁤\frac{5}{7}}$$÷$${\displaystyle \mathrm{}⁤\frac{9}{3}}$$=$${\displaystyle \mathrm{}⁤\frac{5}{7}}$$\times$${\displaystyle \mathrm{}⁤\frac{3}{9}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{5\; ·\; 3}}{\mathrm{7\; ·\; 9}}}$$=$${\displaystyle \mathrm{}⁤\frac{15}{63}}$$=$${\displaystyle \mathrm{}⁤\frac{\mathrm{5\; ·\; 3}}{\mathrm{21\; ·\; 3}}}$$=$${\displaystyle \mathrm{}⁤\frac{5}{21}}$$=\; 0.238095$