# 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:

### 9 2/5 ÷ 1 3/10 = 94/13 = 7 3/13 ≅ 7.2307692

The spelled result in words is ninety-four thirteenths (or seven and three thirteenths).### How do we solve fractions step by step?

- Conversion a mixed number 9 2/5 to a improper fraction: 9 2/5 = 9 2/5 = 9 · 5 + 2/5 = 45 + 2/5 = 47/5

To find a new numerator:

a) Multiply the whole number 9 by the denominator 5. Whole number 9 equally 9 * 5/5 = 45/5

b) Add the answer from the previous step 45 to the numerator 2. New numerator is 45 + 2 = 47

c) Write a previous answer (new numerator 47) over the denominator 5.

Nine and two fifths is forty-seven fifths. - Conversion a mixed number 1 3/10 to a improper fraction: 1 3/10 = 1 3/10 = 1 · 10 + 3/10 = 10 + 3/10 = 13/10

To find a new numerator:

a) Multiply the whole number 1 by the denominator 10. Whole number 1 equally 1 * 10/10 = 10/10

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 10.

One and three tenths is thirteen tenths. - Divide: 47/5 : 13/10 = 47/5 · 10/13 = 47 · 10/5 · 13 = 470/65 = 5 · 94 /5 · 13 = 94/13

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 13/10 is 10/13) 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 5 gives 94/13.

In other words - forty-seven fifths divided by thirteen tenths is ninety-four thirteenths.

### 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 - Fraction multiplication

Solve six times three-sixths equals blank. Leave your answer as an improper fraction. thirty-six thirds eighteen-sixths eighteen-sixteenths three thirty-sixths - 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? - If you 4

If you take away 1 ¾ from 3 1/3, the answer is 2 2/3. Is this correct?

- Students 34

Students were surveyed as part of a Statistics project to determine if younger adults are more likely to have tattoos. The results are listed in the two-way table below: age; At least one tattoo; No tattoo; Row totals Age 18 - 29; 165 ; 342; 507 Age 30 - - Giraffes to monkeys

The ratio of the number of giraffes to the number of monkeys in a zoo is 2 to 5. Which statement about the giraffes and monkeys could be true? A. For every 10 monkeys in the zoo, there are 4 giraffes. B. For every giraffe in the zoo, there are three monke - Marcellus

Marcellus has two bottles of ketchup that are the same size. One bottle is 1/5 full, and the other bottle is 1/2 full. Can all the ketchup fit into one bottle without the ketchup overflowing?

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Last Modified: October 9, 2024