# 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:

### 11 5/8 + 9 1/2 = 169/8 = 21 1/8 = 21.125

The spelled result in words is one hundred sixty-nine eighths (or twenty-one and one eighth).### How do we solve fractions step by step?

- Conversion a mixed number 11 5/8 to a improper fraction: 11 5/8 = 11 5/8 = 11 · 8 + 5/8 = 88 + 5/8 = 93/8

To find a new numerator:

a) Multiply the whole number 11 by the denominator 8. Whole number 11 equally 11 * 8/8 = 88/8

b) Add the answer from the previous step 88 to the numerator 5. New numerator is 88 + 5 = 93

c) Write a previous answer (new numerator 93) over the denominator 8.

Eleven and five eighths is ninety-three eighths. - Conversion a mixed number 9 1/2 to a improper fraction: 9 1/2 = 9 1/2 = 9 · 2 + 1/2 = 18 + 1/2 = 19/2

To find a new numerator:

a) Multiply the whole number 9 by the denominator 2. Whole number 9 equally 9 * 2/2 = 18/2

b) Add the answer from the previous step 18 to the numerator 1. New numerator is 18 + 1 = 19

c) Write a previous answer (new numerator 19) over the denominator 2.

Nine and one half is nineteen halfs. - Add: 93/8 + 19/2 = 93/8 + 19 · 4/2 · 4 = 93/8 + 76/8 = 93 + 76/8 = 169/8

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(8, 2) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 2 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - ninety-three eighths plus nineteen halfs is one hundred sixty-nine eighths.

### 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:

- The bucket

Anna and Joey share an 18-ounce bucket of clay. By the end of the week, Anna has used 1/3 of the bucket, and Joey has used 2/3 of the bucket of clay. How many ounces are left in the bucket? - Matthew

Matthew is saving up for a car. Last year he saved 3/5 of the total amount. In addition to what he saved last year, he saved 3/10 of the total amount in the summer. If the car costs 15 000$, how much has he saved so far? - 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? - Mrs. Dinah

Mrs. Dinah Tah Tanda divided her lot among her 4 children. The first got 3 1/2 ha, the second 3 1/3 ha, the third 3 1/4 ha, and the fourth 3 2/5 ha. How big is Mrs. Tanda's lot?

- Katelyn

Katelyn ate ⅓ of an apple pie, and Chad ate ⅜ of the same pie. What fraction of the pie was eaten? - Maximo

Maximo had 4/6 of a pancake. Kayla gave him another 5/6 of a similar pancake. How many pancakes did Maximo have in the end? - Summer vacation

Rekha spent 3/8 of her summer vacation in Delhi, 1/16 in Mumbai, and ¼ in Chennai. What fraction of her summer vacation did he spend in all?

more math problems »

Last Modified: June 4, 2024