# 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:

### 3 3/4 * 4 2/3 = 35/2 = 17 1/2 = 17.5

The spelled result in words is thirty-five halfs (or seventeen and one half).### How do we solve fractions step by step?

- Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4

To find a new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4

b) Add the answer from the previous step 12 to the numerator 3. New numerator is 12 + 3 = 15

c) Write a previous answer (new numerator 15) over the denominator 4.

Three and three quarters is fifteen quarters. - Conversion a mixed number 4 2/3 to a improper fraction: 4 2/3 = 4 2/3 = 4 · 3 + 2/3 = 12 + 2/3 = 14/3

To find a new numerator:

a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/3 = 12/3

b) Add the answer from the previous step 12 to the numerator 2. New numerator is 12 + 2 = 14

c) Write a previous answer (new numerator 14) over the denominator 3.

Four and two thirds is fourteen thirds. - Multiple: 15/4 * 14/3 = 15 · 14/4 · 3 = 210/12 = 35 · 6/2 · 6 = 35/2

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(210, 12) = 6. In the following intermediate step, cancel by a common factor of 6 gives 35/2.

In other words - fifteen quarters multiplied by fourteen thirds is thirty-five halfs.

### 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:

- 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 - Parul

Parul and Tarun ran a race of 200m. Parul completed the race in 2/3 min and Taun in 3/5 mins. Who took more time? - Denominator 2883

Write a fraction with a denominator of 200 greater than 0.39 and less than a two-fifths fraction. Write its numerator x. - Pumpkin pie

Have some pumpkin pie. One-half of the pie is cut into four equal slices. The other half is cut into three equal slices. After eating one of the larger slices (on the three-piece side), I wonder if I will eat more if I have one more from the three sides o

- 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. - 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. - Pizza palace

Josh is at Enzo's pizza palace. He can sit at a table with 5 of his friends or at a different table with seven friends. The same size pizza is shared equally among the people at each table. At which table should Josh sit to get more pizza? (write the answ

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Last Modified: October 9, 2024