# 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 1/6 * 2 2/7 = 248/21 = 11 17/21 ≅ 11.8095238

The spelled result in words is two hundred forty-eight twenty-firsts (or eleven and seventeen twenty-firsts).### How do we solve fractions step by step?

- Conversion a mixed number 5 1/6 to a improper fraction: 5 1/6 = 5 1/6 = 5 · 6 + 1/6 = 30 + 1/6 = 31/6

To find a new numerator:

a) Multiply the whole number 5 by the denominator 6. Whole number 5 equally 5 * 6/6 = 30/6

b) Add the answer from the previous step 30 to the numerator 1. New numerator is 30 + 1 = 31

c) Write a previous answer (new numerator 31) over the denominator 6.

Five and one sixth is thirty-one sixths. - Conversion a mixed number 2 2/7 to a improper fraction: 2 2/7 = 2 2/7 = 2 · 7 + 2/7 = 14 + 2/7 = 16/7

To find a new numerator:

a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7

b) Add the answer from the previous step 14 to the numerator 2. New numerator is 14 + 2 = 16

c) Write a previous answer (new numerator 16) over the denominator 7.

Two and two sevenths is sixteen sevenths. - Multiple: 31/6 * 16/7 = 31 · 16/6 · 7 = 496/42 = 248 · 2/21 · 2 = 248/21

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(496, 42) = 2. In the following intermediate step, cancel by a common factor of 2 gives 248/21.

In other words - thirty-one sixths multiplied by sixteen sevenths is two hundred forty-eight twenty-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:

- Anesa

Anesa ate 3/4 of her pizza, and Eman ate 1/4 of her pizza. Who ate the greater part of the pizza? - 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. - From least to greatest

Which set of rational numbers is arranged from least to greatest? A) -3.5, negative 1 over 4, 2, 1 over 3 B) -3.5, negative 1 over 4, 1 over 3, 2 C) 2, 1 over 3, negative 1 over 4, -3.5 D) negative 1 over 4, 1 over 3, 2, -3.5 - Rhea answered

Rhea answered 5/11 of the questions correctly, and Precious answered 7/11 of them correctly. Who got the higher score if each problem is worth the same amount?

- Fractions 3928

Arrange the fractions from the smallest to the largest. 2/5, 15/6, 1/4, 5/5, 5/4, 4/10, 6/5. - Closer to one

Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your work and state clearly whether the answer is A or B. - 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

more math problems »

Last Modified: October 9, 2024