# Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## The result:

### 1 1/2 + 2 3/4 = 17/4 = 4 1/4 = 4.25

Spelled result in words is seventeen quarters (or four and one quarter).### How do we solve fractions step by step?

- Conversion a mixed number 1 1/2 to a improper fraction: 1 1/2 = 1 1/2 = 1 · 2 + 1/2 = 2 + 1/2 = 3/2

To find a new numerator:

a) Multiply the whole number 1 by the denominator 2. Whole number 1 equally 1 * 2/2 = 2/2

b) Add the answer from the previous step 2 to the numerator 1. New numerator is 2 + 1 = 3

c) Write a previous answer (new numerator 3) over the denominator 2.

One and one half is three halfs. - Conversion a mixed number 2 3/4 to a improper fraction: 2 3/4 = 2 3/4 = 2 · 4 + 3/4 = 8 + 3/4 = 11/4

To find a new numerator:

a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/4 = 8/4

b) Add the answer from the previous step 8 to the numerator 3. New numerator is 8 + 3 = 11

c) Write a previous answer (new numerator 11) over the denominator 4.

Two and three quarters is eleven quarters. - Add: 3/2 + 11/4 = 3 · 2/2 · 2 + 11/4 = 6/4 + 11/4 = 6 + 11/4 = 17/4

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(2, 4) = 4. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - three halfs plus eleven quarters is seventeen quarters.

#### 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) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22

• 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 evaluate from left to right.

## Fractions in word problems:

- A man 9

A man earns $2400 in his monthly salary. He spends 3/5 of his salary on food and rent. This month he decided to buy his family presents. What fraction of his money does he spend on presents? - My whole

My whole number is 88 if you add 5 thousandths, 8 tenths, and 7 thousandths. What number will I be? - In one day

In one day, a baker used 2/3 of a pound of flour, 3/4 of a pound of flour, and 5/12 of a pound of flour. How much flour was used that day? - Add two fractions

What is the sum of 2/3 and 3/10? - Adding mixed fractions

Add these two mixed numbers: 1 5/6 + 2 2/11= - 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? - Randy

Randy solved the following problem: 7/8 + 9/16. He said: I can add 7 and 9 to get 16 and add 8 and 15 to get 23. The answer is 16/23. Is randy correct? Explain. - One evening

One evening, a restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread. How many loaves were served in all? - Work out 2

Work out the sum of 2/6 and 1/6. Give your answer in its simplest form. - Adding denominators

Max is working out 2/3+7/9. He says the answer is 9/12. What mistake has Max made? - Mary read

Mary read 2/9 books in the morning and 5/9 in the evening. What fraction of books has she read?

more math problems »