# 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 1/2 + 2 3/5 = 41/10 = 4 1/10 = 4.1

The spelled result in words is forty-one tenths (or four and one tenth).### How do we solve fractions step by step?

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

To find a new numerator:

a) Multiply the whole number 1 by the denominator 2. Whole number 1 equally 1 * 2/2 = 2/2

b) Add the answer from the previous step 2 to the numerator 1. New numerator is 2 + 1 = 3

c) Write a previous answer (new numerator 3) over the denominator 2.

One and one half is three halfs. - Conversion a mixed number 2 3/5 to a improper fraction: 2 3/5 = 2 3/5 = 2 · 5 + 3/5 = 10 + 3/5 = 13/5

To find a new numerator:

a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/5 = 10/5

b) Add the answer from the previous step 10 to the numerator 3. New numerator is 10 + 3 = 13

c) Write a previous answer (new numerator 13) over the denominator 5.

Two and three fifths is thirteen fifths. - Add: 3/2 + 13/5 = 3 · 5/2 · 5 + 13 · 2/5 · 2 = 15/10 + 26/10 = 15 + 26/10 = 41/10

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, 5) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 5 = 10. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - three halfs plus thirteen fifths is forty-one tenths.

### 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:

- In one day

In one day, a baker used 2/3 of a pound of flour, 3/4 of a pound of flour, and 5/12 of a pound of flour. How much flour was used that day? - A man 9

A man earns $2400 in his monthly salary. He spends 3/5 of his salary on food and rent. This month he decided to buy his family presents. What fraction of his money does he spend on presents? - 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? - A farmer 8

A farmer uses 1/3 of his land to plant cassava, 1/3 of the remaining land to plant maize, and the rest for vegetables. What fraction did the farmer use to plant vegetables?

- A city

A city received 11/4 cm of rainfall on Sunday and 11/2 cm on Monday. Find the total rain in the city on these two days. - Medical facility

Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal today, she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 o - Sum of fractions

What is the sum of 2/3+3/5?

more math problems »

Last Modified: June 4, 2024