# 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:

### 12 5/8 ÷ 3 19/24 = 303/91 = 3 30/91 ≅ 3.3296703

The spelled result in words is three hundred three ninety-firsts (or three and thirty ninety-firsts).### How do we solve fractions step by step?

- Conversion a mixed number 12 5/8 to a improper fraction: 12 5/8 = 12 5/8 = 12 · 8 + 5/8 = 96 + 5/8 = 101/8

To find a new numerator:

a) Multiply the whole number 12 by the denominator 8. Whole number 12 equally 12 * 8/8 = 96/8

b) Add the answer from the previous step 96 to the numerator 5. New numerator is 96 + 5 = 101

c) Write a previous answer (new numerator 101) over the denominator 8.

Twelve and five eighths is one hundred one eighths. - Conversion a mixed number 3 19/24 to a improper fraction: 3 19/24 = 3 19/24 = 3 · 24 + 19/24 = 72 + 19/24 = 91/24

To find a new numerator:

a) Multiply the whole number 3 by the denominator 24. Whole number 3 equally 3 * 24/24 = 72/24

b) Add the answer from the previous step 72 to the numerator 19. New numerator is 72 + 19 = 91

c) Write a previous answer (new numerator 91) over the denominator 24.

Three and nineteen twenty-fourths is ninety-one twenty-fourths. - Divide: 101/8 : 91/24 = 101/8 · 24/91 = 101 · 24/8 · 91 = 2424/728 = 8 · 303 /8 · 91 = 303/91

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 91/24 is 24/91) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 8 gives 303/91.

In other words - one hundred one eighths divided by ninety-one twenty-fourths is three hundred three ninety-firsts.

### 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:

- Compare two fractions

Find which is the larger of the two fractions: 11/32, 7/24, by expressing the numbers as a) fractions with the same denominator, b) decimals. - Subtract and compare

1-5/8 is the same as 11/8, true or false? - Small and large bread

Kipton's aunt bakes a large loaf of bread and a small loaf of bread. She cuts each loaf into tenths and gives Kipton 2 tenths of each loaf to take home. Kipton writes the equation 2/10 + 2/10 = 4/10 to show the amount of bread he takes home. Explain Kipto - The cost 7

The cost of a pen is Rs. 20/3, and that of a pencil is 25/6. Which costs more and by how much?

- 1/12 fraction

Which statement about determining the quotient 1/12÷3 is true? A.Because 1/36×3=1/12, 1/12 divided by 3 is 1/36. B.Because 1/4×3=1/12, 1/12 divided by 3 is 1/4. C.Because 3/4×3=1/12, 1/12 divided by 3 is 3/4. D.Because 4/3×3=1/12, 1/12 divided by 3 is 4/3 - The fuel

The car's fuel was ¾ full at the beginning of the week. At the end of the week, there was ⅛ of a tank left. a. Did the car use more or less than ½ of a fuel tank? How do you know? b. How much more or less than ½ of a tank did it use? Show your work using - Dividends

The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least?

more math problems »

Last Modified: July 13, 2024