# 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 56/34 - 5 1/2 = -29/34 ≅ -0.8529412

The spelled result in words is minus twenty-nine thirty-fourths.### How do we solve fractions step by step?

- Conversion a mixed number 3 56/34 to a improper fraction: 3 56/34 = 3 56/34 = 3 · 34 + 56/34 = 102 + 56/34 = 158/34

To find a new numerator:

a) Multiply the whole number 3 by the denominator 34. Whole number 3 equally 3 * 34/34 = 102/34

b) Add the answer from the previous step 102 to the numerator 56. New numerator is 102 + 56 = 158

c) Write a previous answer (new numerator 158) over the denominator 34.

Three and fifty-six thirty-fourths is one hundred fifty-eight thirty-fourths. - Conversion a mixed number 5 1/2 to a improper fraction: 5 1/2 = 5 1/2 = 5 · 2 + 1/2 = 10 + 1/2 = 11/2

To find a new numerator:

a) Multiply the whole number 5 by the denominator 2. Whole number 5 equally 5 * 2/2 = 10/2

b) Add the answer from the previous step 10 to the numerator 1. New numerator is 10 + 1 = 11

c) Write a previous answer (new numerator 11) over the denominator 2.

Five and one half is eleven halfs. - Subtract: 158/34 - 11/2 = 158/34 - 11 · 17/2 · 17 = 158/34 - 187/34 = 158 - 187/34 = -29/34

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(34, 2) = 34. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 34 × 2 = 68. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one hundred fifty-eight thirty-fourths minus eleven halfs is minus twenty-nine thirty-fourths.

### 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 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? - 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 - - Chocolate 82258

How many pieces does the chocolate have if I ate 6/7 of it, which is 12 pieces?

- Stones in aquarium

In an aquarium with a length of 2 m, a width of 1.5 m, and a depth of 2.5 m is a water level up to three-quarters of the depth. Can we place stones with a volume of 2 m³ into the aquarium without water being poured out? - Decadic number

What is the expanded form of this number? 18.029 A: (1x10)+(8x1)+(2x1/10)+(9x1/100) B: (1×10)+(8×1)+(2×1/10)+(9×1/1,000) C: (1×10)+(8×1)+(2×1/100)+(9×1/1,000) D: (1×10)+(8×1)+(2×11/00)+(9×1/100) - Right-angled 64614

Arrange the given shapes according to their area, in descending order: S - Square with perimeter = 16 cm O - A rectangle with side a = 3 cm and perimeter o = 16 cm T - A right-angled triangle with a hypotenuse of 4.125 cm and a hypotenuse of 8.125 cm

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Last Modified: September 8, 2024