# 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:

### 4 2/3 - 1 4/5 = 43/15 = 2 13/15 ≅ 2.8666667

The spelled result in words is forty-three fifteenths (or two and thirteen fifteenths).### How do we solve fractions step by step?

- 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. - Conversion a mixed number 1 4/5 to a improper fraction: 1 4/5 = 1 4/5 = 1 · 5 + 4/5 = 5 + 4/5 = 9/5

To find a new numerator:

a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5

b) Add the answer from the previous step 5 to the numerator 4. New numerator is 5 + 4 = 9

c) Write a previous answer (new numerator 9) over the denominator 5.

One and four fifths is nine fifths. - Subtract: 14/3 - 9/5 = 14 · 5/3 · 5 - 9 · 3/5 · 3 = 70/15 - 27/15 = 70 - 27/15 = 43/15

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(3, 5) = 15. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - fourteen thirds minus nine fifths is forty-three fifteenths.

### 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:

- A loaf of bread

Tshegofatso and Saymore have a loaf of bread. Tshegofatso eats 4/7 of the loaf, and Saymore eats 1/3 of the loaf. What fraction of the loaf of bread is left over? - Muffins 2

Shayla is baking muffins that require 1/2 cup of vegetable oil. She only has 1/3 cup left. How much more does she need? - Koos spent

Koos spent 3/7 of his monthly pocket money during the first week. The following week he spends two-thirds of what he spent the previous week. The fraction of the pocket money that is still left? - A laundry

Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?

- Bitoo and Reena

Bitoo ate 3/5 part of the apple, and the remaining part was eaten by his sister Reena. How many parts of an apple did Renna eat? Who had the larger share? By how much? - Mr.de

Mr. Guzman bought 7 1/2 kg of meat. He used 2 3/4 kg for afritada, 3 1/8 kg for menudo, and the rest for pochero. How many kilograms of meat did he use for pochero? - Opening 6232

The bank has opening hours from 07:30 to 16:30. How many hours is the bank open?

more math problems »

Last Modified: October 9, 2024