# 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:

### 5 1/4 + 3 2/5 = 173/20 = 8 13/20 = 8.65

The spelled result in words is one hundred seventy-three twentieths (or eight and thirteen twentieths).### How do we solve fractions step by step?

- Conversion a mixed number 5 1/4 to a improper fraction: 5 1/4 = 5 1/4 = 5 · 4 + 1/4 = 20 + 1/4 = 21/4

To find a new numerator:

a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/4 = 20/4

b) Add the answer from the previous step 20 to the numerator 1. New numerator is 20 + 1 = 21

c) Write a previous answer (new numerator 21) over the denominator 4.

Five and one quarter is twenty-one quarters. - Conversion a mixed number 3 2/5 to a improper fraction: 3 2/5 = 3 2/5 = 3 · 5 + 2/5 = 15 + 2/5 = 17/5

To find a new numerator:

a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5

b) Add the answer from the previous step 15 to the numerator 2. New numerator is 15 + 2 = 17

c) Write a previous answer (new numerator 17) over the denominator 5.

Three and two fifths is seventeen fifths. - Add: 21/4 + 17/5 = 21 · 5/4 · 5 + 17 · 4/5 · 4 = 105/20 + 68/20 = 105 + 68/20 = 173/20

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(4, 5) = 20. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - twenty-one quarters plus seventeen fifths is one hundred seventy-three 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

• 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? - Sum of the fractions

Find the sum, express your answer to lowest terms. 1. 1/4 + 2/4= 2. 1/6 + 3/6= 3. 6/10 + 2/10= 4. ¾ + ⅛= 5. 5 3/5 + 2 ½= - Negative fractions

I am a number that is equal to -3/4 subtracted from the sum of 3/5 and -1/3. What number am I? - Ahsan

Ahsan has a large pizza. He gives 1/3 to his sister and 1/4 to his mother. What fraction of the pizza does Ahsan have left?

- Dexter

Dexter spent 1 2/3 hours working on his history homework and another 2 1/5 hours working on his math homework. How many hours did Dexter spend working on the two homework? - Alwyn

Alwyn spends 1 3/4 hours answering his math homework. He also spends 2 1/3 hours doing his homework in English. How much time does he spend doing his homework for these two subjects? - Half of the product

What is half the product of 8 1/7 and 7 4/5?

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Last Modified: October 9, 2024