# Fraction calculator

This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

## The result:

### 1 2/3 + 2 1/4 = 47/12 = 3 11/12 ≅ 3.9166667

The spelled result in words is forty-seven twelfths (or three and eleven twelfths).### How do we solve fractions step by step?

- Conversion a mixed number 1 2/3 to a improper fraction: 1 2/3 = 1 2/3 = 1 · 3 + 2/3 = 3 + 2/3 = 5/3

To find a new numerator:

a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/3 = 3/3

b) Add the answer from the previous step 3 to the numerator 2. New numerator is 3 + 2 = 5

c) Write a previous answer (new numerator 5) over the denominator 3.

One and two thirds is five thirds. - Conversion a mixed number 2 1/4 to a improper fraction: 2 1/4 = 2 1/4 = 2 · 4 + 1/4 = 8 + 1/4 = 9/4

To find a new numerator:

a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/4 = 8/4

b) Add the answer from the previous step 8 to the numerator 1. New numerator is 8 + 1 = 9

c) Write a previous answer (new numerator 9) over the denominator 4.

Two and one quarter is nine quarters. - Add: 5/3 + 9/4 = 5 · 4/3 · 4 + 9 · 3/4 · 3 = 20/12 + 27/12 = 20 + 27/12 = 47/12

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(3, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - five thirds plus nine quarters is forty-seven twelfths.

### 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

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

• 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 be evaluated from left to right.

## Fractions in word problems:

- A cake 2

Karen sliced a cake into 10 slices. She ate 2/10 of it and after some time she ate another 4/10 of it. How much of the cake did Karen eat? - Work out 2

Work out the sum of 2/6 and 1/6. Give your answer in its simplest form. - My whole

My whole number is 88 if you add 5 thousandths, 8 tenths, and 7 thousandths. What number will I be? - Mary read

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

- 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? - 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? - 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?

more math problems »

Last Modified: June 4, 2024