# Fraction calculator

This fraction calculator performs all fraction operations and evaluates expressions with fractions. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps find value from multiple fraction operations with two, three, or more fractions and numbers in one expression.

## The result:

### 2 2/7 * 5 1/6 = 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 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. - 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. - Multiple: 16/7 * 31/6 = 16 · 31/7 · 6 = 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 - sixteen sevenths multiplied by thirty-one sixths 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

• multiplying a fraction by a whole number: 6 * 3/4

• square root of a fraction: sqrt(1/16)

• reducing or simplifying the fraction (simplification) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction

• 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:

- Subtract and compare

1-5/8 is the same as 11/8, true or false? - 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 - Which 15

Which is larger, 1 2/7 or 10/4? - A student 4

A student knows that ¾ x 4 is the same as 4 x ¾ The student assumes that 4 ÷ ¾ is the same as ¾ ÷ 4 Is the student correct?

- What number 2

What number is between 3 1/4 and 3 1/8? Write at least three numbers. - The numerator

The numerator of the fraction is 5 more than its denominator. If 4 is added to the numerator and denominator, the fraction obtained is 6/5. What is that fraction? - Which 14

Which values of a, b, and c represent the answer in simplest form? 7/9 divided by 4/9 = a StartFraction b Over c EndFraction a = 1, b = 4, c = 3 a = 1, b = 3, c = 4 a = 1, b = 63, c = 36 a = 1, b = 36, c = 63 - Conner

Conner picked 8 1/5 pounds of apples. Louisa picked 9 2/3 pounds of apples. How many apples, more pounds, did Louisa pick than Conner? - Simplest form of a fraction

Which one of the following fractions is not equal to 3/2 after reducing to the simplest form? a) 15/20 b) 12/8 c) 27/18 d) 6/4

- Pitcher 20403

One pitcher is filled to 22/25 of its volume. The other pitcher is filled to 1/9 of its volume. Which pitcher is filled more? - Bigger 3204

How much is 1/3 bigger than 1/9? - Taylor

Taylor filled eight 5 oz glasses with orange juice ⅔ full. Emeline filled five 9 oz glasses with orange juice ¾ full. Who used more juice? - Compare three fractions

Which of the three rational numbers is the largest? 1/7, 6/17, 4/17 - What 11781

What is greater: 2/5 of 10, or 20% of 4000?

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