# Fraction calculator

This fraction 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 3/5 + 7 1/2 = 121/10 = 12 1/10 = 12.1

The spelled result in words is one hundred twenty-one tenths (or twelve and one tenth).### How do we solve fractions step by step?

- Conversion a mixed number 4 3/5 to a improper fraction: 4 3/5 = 4 3/5 = 4 · 5 + 3/5 = 20 + 3/5 = 23/5

To find a new numerator:

a) Multiply the whole number 4 by the denominator 5. Whole number 4 equally 4 * 5/5 = 20/5

b) Add the answer from the previous step 20 to the numerator 3. New numerator is 20 + 3 = 23

c) Write a previous answer (new numerator 23) over the denominator 5.

Four and three fifths is twenty-three fifths. - Conversion a mixed number 7 1/2 to a improper fraction: 7 1/2 = 7 1/2 = 7 · 2 + 1/2 = 14 + 1/2 = 15/2

To find a new numerator:

a) Multiply the whole number 7 by the denominator 2. Whole number 7 equally 7 * 2/2 = 14/2

b) Add the answer from the previous step 14 to the numerator 1. New numerator is 14 + 1 = 15

c) Write a previous answer (new numerator 15) over the denominator 2.

Seven and one half is fifteen halfs. - Add: 23/5 + 15/2 = 23 · 2/5 · 2 + 15 · 5/2 · 5 = 46/10 + 75/10 = 46 + 75/10 = 121/10

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(5, 2) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 2 = 10. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - twenty-three fifths plus fifteen halfs is one hundred twenty-one tenths.

### 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 - 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? - 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 - Shandra

Shandra saved $24. She lends 1/3 of her savings to her brother. Shandra wants to buy an $18 bracelet. Will she have enough money to purchase the bracelet? Explain

- Three-quarters 47331

A cylindrical container is three-quarters full with six liters of water. We dip a cube-shaped body into the container, which sinks to the bottom. The length of the edge of the cube is 13 cm. Decide what happens to the sink after the cube is dipped. - Playing games

In a school, 9/10 of the students take part. 2/3 of these play football. What fraction of the students play football? - An Airbus

An Airbus A380 has one first-class section, one business-class section, and 4 economy-class sections. The first-class section of the Airbus A380 has 14 seats, 5/7 are being used. The business-class section has 64 seats. 5/16 is being used. Each Economy-cl

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Last Modified: June 4, 2024