# Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### 6 2/5 + 3 1/8 + 2/3 = 1223/120 = 10 23/120 ≅ 10.1916667

Spelled result in words is one thousand two hundred twenty-three one-hundred twentieths (or ten and twenty-three one-hundred twentieths).### How do we solve fractions step by step?

- Conversion a mixed number 6 2/5 to a improper fraction: 6 2/5 = 6 2/5 = 6 · 5 + 2/5 = 30 + 2/5 = 32/5

To find a new numerator:

a) Multiply the whole number 6 by the denominator 5. Whole number 6 equally 6 * 5/5 = 30/5

b) Add the answer from previous step 30 to the numerator 2. New numerator is 30 + 2 = 32

c) Write a previous answer (new numerator 32) over the denominator 5.

Six and two fifths is thirty-two fifths - Conversion a mixed number 3 1/8 to a improper fraction: 3 1/8 = 3 1/8 = 3 · 8 + 1/8 = 24 + 1/8 = 25/8

To find a new numerator:

a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8

b) Add the answer from previous step 24 to the numerator 1. New numerator is 24 + 1 = 25

c) Write a previous answer (new numerator 25) over the denominator 8.

Three and one eighth is twenty-five eighths - Add: 32/5 + 25/8 = 32 · 8/5 · 8 + 25 · 5/8 · 5 = 256/40 + 125/40 = 256 + 125/40 = 381/40

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(5, 8) = 40. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 8 = 40. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - thirty-two fifths plus twenty-five eighths is three hundred eighty-one fortieths. - Add: the result of step No. 3 + 2/3 = 381/40 + 2/3 = 381 · 3/40 · 3 + 2 · 40/3 · 40 = 1143/120 + 80/120 = 1143 + 80/120 = 1223/120

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(40, 3) = 120. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 40 × 3 = 120. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - three hundred eighty-one fortieths plus two thirds is one thousand two hundred twenty-three one-hundred twentieths.

#### Rules for expressions with fractions:

**Fractions**- use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter

**5/100**. If you use mixed numbers, leave a space between the whole and fraction parts.

**Mixed numerals**(mixed numbers or fractions) keep one space between the integer and

fraction and use a forward slash to input fractions i.e.,

**1 2/3**. An example of a negative mixed fraction:

**-5 1/2**.

Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e.,

**1/2 : 1/3**.

Decimals (decimal numbers) enter with a decimal point

**.**and they are automatically converted to fractions - i.e.

**1.45**.

### Math Symbols

Symbol | Symbol name | Symbol Meaning | Example |
---|---|---|---|

+ | plus sign | addition | 1/2 + 1/3 |

- | minus sign | subtraction | 1 1/2 - 2/3 |

* | asterisk | multiplication | 2/3 * 3/4 |

× | times sign | multiplication | 2/3 × 5/6 |

: | division sign | division | 1/2 : 3 |

/ | division slash | division | 1/3 / 5 |

: | colon | complex fraction | 1/2 : 1/3 |

^ | caret | exponentiation / power | 1/4^3 |

() | parentheses | calculate expression inside first | -3/5 - (-1/4) |

#### Examples:

• adding fractions: 2/4 + 3/4• subtracting fractions: 2/3 - 1/2

• multiplying fractions: 7/8 * 3/9

• dividing Fractions: 1/2 : 3/4

• reciprocal of a fraction: 1 : 3/4

• square of a fraction: 2/3^2

• cube of a fraction: 2/3^3

• exponentiation of a fraction: 1/2^4

• fractional exponents: 16 ^ 1/2

• adding fractions and mixed numbers: 8/5 + 6 2/7

• dividing integer and fraction: 5 ÷ 1/2

• complex fractions: 5/8 : 2 2/3

• decimal to fraction: 0.625

• Fraction to Decimal: 1/4

• Fraction to Percent: 1/8 %

• comparing fractions: 1/4 2/3

• multiplying a fraction by a whole number: 6 * 3/4

• square root of a fraction: sqrt(1/16)

• reducing or simplifying the fraction (simplification) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22

• expression with brackets: 1/3 * (1/2 - 3 3/8)

• compound fraction: 3/4 of 5/7

• fractions multiple: 2/3 of 3/5

• divide to find the quotient: 3/5 ÷ 2/3

The calculator follows well-known rules for

**the order of operations**. The most common mnemonics for remembering this order of operations are:

**PEMDAS**- Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

**BEDMAS**- Brackets, Exponents, Division, Multiplication, Addition, Subtraction

**BODMAS**- Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.

**GEMDAS**- Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.

**MDAS**- Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.

Be careful; always do

**multiplication and division**before

**addition and subtraction**. Some operators (+ and -) and (* and /) have the same priority and must evaluate from left to right.

## Fractions in word problems:

- Adding two fractions

Find the missing fraction: 2/5 + 7/10 = - There 22

There is 5/8 of a pizza in one box and 9/12 of a pizza in another box. How much do you have altogether? - Add two fractions

What is 1/4 + 10/16? - Adding mixed fractions

Add these two mixed numbers: 1 5/6 + 2 2/11= - Hardware store

At the hardware store, 1/4 of the nails are size 2d, and 3/8 of the nails are size 4d. What fraction of the nails are either size 2d or 4d? - Mary read

Mary read 2/9 books in the morning and 5/9 in the evening. What fraction of books has she read? - Party pizza

At a party, there were some pizzas of the same size. Amelia ate 1/3 of a pizza. Chris ate 1/3 of a pizza. Miguel ate 5/12 of a pizza. How many pizzas did the three children eat? - Adding denominators

Max is working out 2/3+7/9. He says the answer is 9/12. What mistake has Max made? - Sum three fractions

Work out the sum of 1/4, 1/5, and 3/10. - Integer add to fraction

Seven is added to the sum of 4/5 and 6/7 - Samuel

Samuel has 1/3 of a bag of rice, and Isabella has a 1/2 bag of rice. What fraction of our bag of rice do they have altogether?

more math problems »