# 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 4/7 * 2 3/5 = 143/35 = 4 3/35 ≅ 4.0857143

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

- Conversion a mixed number 1 4/7 to a improper fraction: 1 4/7 = 1 4/7 = 1 · 7 + 4/7 = 7 + 4/7 = 11/7

To find a new numerator:

a) Multiply the whole number 1 by the denominator 7. Whole number 1 equally 1 * 7/7 = 7/7

b) Add the answer from the previous step 7 to the numerator 4. New numerator is 7 + 4 = 11

c) Write a previous answer (new numerator 11) over the denominator 7.

One and four sevenths is eleven sevenths. - 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. - Multiple: 11/7 * 13/5 = 11 · 13/7 · 5 = 143/35

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(143, 35) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - eleven sevenths multiplied by thirteen fifths is one hundred forty-three thirty-fifths.

### 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:

- Identify improper fraction

How do you identify improper fractions? Which is improper: A) 3/4 B) 32/15 C) 3/9 D) 2 2/11 - 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? - For each

For each pair of expressions, circle the greater product without finding the product. (write 1=left expression, 2=right expression) a. 3/4 x 2/3 and 3/4 x 1/2 b. 2/3 x 3 1/4 and 4/3 x 3 1/4 c. 3/8 x 3/8 and 3/8 x 1/2

- Buing

Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK? - Compare 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. - Compare three fractions

Which of the three rational numbers is the largest? 1/7, 6/17, 4/17

more math problems »

Last Modified: August 1, 2024