# 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:

### 8 5/8 + 5 3/4 = 115/8 = 14 3/8 = 14.375

Spelled result in words is one hundred fifteen eighths (or fourteen and three eighths).### How do we solve fractions step by step?

- Conversion a mixed number 8 5/8 to a improper fraction: 8 5/8 = 8 5/8 = 8 · 8 + 5/8 = 64 + 5/8 = 69/8

To find a new numerator:

a) Multiply the whole number 8 by the denominator 8. Whole number 8 equally 8 * 8/8 = 64/8

b) Add the answer from the previous step 64 to the numerator 5. New numerator is 64 + 5 = 69

c) Write a previous answer (new numerator 69) over the denominator 8.

Eight and five eighths is sixty-nine eighths. - Conversion a mixed number 5 3/4 to a improper fraction: 5 3/4 = 5 3/4 = 5 · 4 + 3/4 = 20 + 3/4 = 23/4

To find a new numerator:

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

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 4.

Five and three quarters is twenty-three quarters. - Add: 69/8 + 23/4 = 69/8 + 23 · 2/4 · 2 = 69/8 + 46/8 = 69 + 46/8 = 115/8

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, 4) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 4 = 32. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - sixty-nine eighths plus twenty-three quarters is one hundred fifteen 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

• multiplying a fraction by a whole number: 6 * 3/4

• square root of a fraction: sqrt(1/16)

• reducing or simplifying the fraction (simplification) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction

• 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 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? - Party pizza

At a party, there were some pizzas of the same size. Amelia ate 1/3 of a pizza. Chris ate 1/3 of a pizza. Miguel ate 5/12 of a pizza. How many pizzas did the three children eat? - Hardware store

At the hardware store, 1/4 of the nails are size 2d, and 3/8 of the nails are size 4d. What fraction of the nails are either size 2d or 4d? - Samuel

Samuel has 1/3 of a bag of rice, and Isabella has a 1/2 bag of rice. What fraction of our bag of rice do they have altogether? - Katelyn

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

Find the missing fraction: 2/5 + 7/10 = - Work out 2

Work out the sum of 2/6 and 1/6. Give your answer in its simplest form. - Evaluate 27

Evaluate the expression shown below and write your answer as a fraction in the simplest form. (8)/(3)+ (11)/(12) - HW store

At the hardware store, 1/4 of the nails are size 2d, and 1/6 of the nails are size 4d. What fraction of the nails are either size 2d or 4d? - Adding mixed fractions

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

What is the sum of 2/3 and 3/10?

more math problems »