# Fraction calculator

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

## The result:

### 3 1/2 - 2 5/9 = 17/18 ≅ 0.9444444

The spelled result in words is seventeen eighteenths.### How do we solve fractions step by step?

- Conversion a mixed number 3 1/2 to a improper fraction: 3 1/2 = 3 1/2 = 3 · 2 + 1/2 = 6 + 1/2 = 7/2

To find a new numerator:

a) Multiply the whole number 3 by the denominator 2. Whole number 3 equally 3 * 2/2 = 6/2

b) Add the answer from the previous step 6 to the numerator 1. New numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 2.

Three and one half is seven halfs. - Conversion a mixed number 2 5/9 to a improper fraction: 2 5/9 = 2 5/9 = 2 · 9 + 5/9 = 18 + 5/9 = 23/9

To find a new numerator:

a) Multiply the whole number 2 by the denominator 9. Whole number 2 equally 2 * 9/9 = 18/9

b) Add the answer from the previous step 18 to the numerator 5. New numerator is 18 + 5 = 23

c) Write a previous answer (new numerator 23) over the denominator 9.

Two and five ninths is twenty-three ninths. - Subtract: 7/2 - 23/9 = 7 · 9/2 · 9 - 23 · 2/9 · 2 = 63/18 - 46/18 = 63 - 46/18 = 17/18

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(2, 9) = 18. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 9 = 18. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - seven halfs minus twenty-three ninths is seventeen eighteenths.

### 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:

- Mr Peter

Mr Peter bought a pizza. He ate 2/5. His son ate 1/5, and the rest his wife ate. What amount of pizza did his wife eat? - Saturday 5405

Of all Ferko's tasks, he worked out 1/8 on Friday and 3/8 on Saturday and Sunday. What part of the task did he have to work on Sunday? - Pizza 16

Kevin ate 5/12 of his pizza. Which is a better estimate for the amount of pizza that he ate: A. about half of the pizza or B. almost all of the pizza? - Three-eighths 81827

There were buns for lunch at school. The freshmen ate one-eighth of the buns. The sophomores ate two-eighths of the buns. Third and fourth graders ate three-eighths. How many eighths buns are left for the second stage?

- Dive Attempt

Dive Attempt ; Fraction of the distance to the pool bottom Dive 1; 1/4 Dive 2; 2/3 Dive 3; 5/6 Tony's second dive was deeper than his first dive by what fraction of the pool? - A tank

A tank is 7/9 full of water,1/5 of the tank is drawn in the morning, and 1/3 is drawn in the evening. What fraction of water is still in the tank? - A market

A market vendor was able to sell all the mangoes, papayas, and star apples. 1/5 of the fruits were mangoes, 2/3 of them were papayas, and the rest were star apples. How many parts of the fruits sold are star apples?

more math problems »

Last Modified: September 8, 2024