# 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:

### 2 7/8 + 3/8 = 13/4 = 3 1/4 = 3.25

The spelled result in words is thirteen quarters (or three and one quarter).### How do we solve fractions step by step?

- Conversion a mixed number 2 7/8 to a improper fraction: 2 7/8 = 2 7/8 = 2 · 8 + 7/8 = 16 + 7/8 = 23/8

To find a new numerator:

a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/8 = 16/8

b) Add the answer from the previous step 16 to the numerator 7. New numerator is 16 + 7 = 23

c) Write a previous answer (new numerator 23) over the denominator 8.

Two and seven eighths is twenty-three eighths. - Add: 23/8 + 3/8 = 23 + 3/8 = 26/8 = 2 · 13/2 · 4 = 13/4

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(8, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the following intermediate step, cancel by a common factor of 2 gives 13/4.

In other words - twenty-three eighths plus three eighths is thirteen quarters.

### 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:

- Work out 2

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

Jiwan Incorrectly Wrote 1+ 1/2 + 1/3 + 1/4 =1 3/9 Show The Correct Working And Write Down The Answer As A Mixed Number. - A football 2

A football team wins 2/5 of their matches and draws 1/3. What fraction of their matches are lost?

- Expressions with variable

This is an algebra problem. Let n represent an unknown number and write the following expressions: 1. 4 times the sum of 7 and the number x 2. 4 times 7 plus the number x 3. 7 less than the product of 4 and the number x 4. 7 times the quantity 4 more than - Lengths of the pool

Miguel swam six lengths of the pool. Mat swam three times as far as Miguel. Lionel swam 1/3 as far as Miguel. How many lengths did Mat swim? - Five-eighths 5694

The car's tank was two-twelfths full. When Dad filled the tank with gas, the volume of gas increased by five-eighths of the tank's volume. What fraction of gasoline did the car use when the tank is now 1/3 full?

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Last Modified: June 4, 2024