# Fraction calculator

This fraction calculator performs all fraction operations and evaluates expressions with fractions. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps find value from multiple fraction operations with two, three, or more fractions and numbers in one expression.

## The result:

### 2 2/3 + 8 3/4 = 137/12 = 11 5/12 ≅ 11.4166667

The spelled result in words is one hundred thirty-seven twelfths (or eleven and five twelfths).### How do we solve fractions step by step?

- Conversion a mixed number 2 2/3 to a improper fraction: 2 2/3 = 2 2/3 = 2 · 3 + 2/3 = 6 + 2/3 = 8/3

To find a new numerator:

a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3

b) Add the answer from the previous step 6 to the numerator 2. New numerator is 6 + 2 = 8

c) Write a previous answer (new numerator 8) over the denominator 3.

Two and two thirds is eight thirds. - Conversion a mixed number 8 3/4 to a improper fraction: 8 3/4 = 8 3/4 = 8 · 4 + 3/4 = 32 + 3/4 = 35/4

To find a new numerator:

a) Multiply the whole number 8 by the denominator 4. Whole number 8 equally 8 * 4/4 = 32/4

b) Add the answer from the previous step 32 to the numerator 3. New numerator is 32 + 3 = 35

c) Write a previous answer (new numerator 35) over the denominator 4.

Eight and three quarters is thirty-five quarters. - Add: 8/3 + 35/4 = 8 · 4/3 · 4 + 35 · 3/4 · 3 = 32/12 + 105/12 = 32 + 105/12 = 137/12

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, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - eight thirds plus thirty-five quarters is one hundred thirty-seven twelfths.

### 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:

- Jiwan

Jiwan Incorrectly Wrote 1+ 1/2 + 1/3 + 1/4 =1 3/9 Show The Correct Working And Write Down The Answer As A Mixed Number. - Find two 4

Find two fractions between 1/4 and 2/3. How do you know you are right? - Evaluate 33

Evaluate x+y when x=- 4/5 and y= 1/3. Write your answer as a fraction or mixed number in simplest form. - Expressions

Let k represent an unknown number, express the following expressions: 1. The sum of the numbers n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n

- Cooking classes

Ms. Wright's two cooking classes are making a total of 60 sweet potato pies. Each pie requires 2 1/4 sweet potatoes. Her first class makes 1/3 of the total number of pies needed. Exactly how many sweet potatoes will her second class need in order to make - Sum of AP members

Find the sum of all the numbers between 8 and 258 that are divisible by 5. - Aubrey

Aubrey had 220.00, and Richard had 220.00. Richard shared 1/4 of his money, and Aubrey shared 2/3 of her money. How much money did they share to buy a teddy bear? - Peter 10

Peter covered 1/2 of the journey on Monday, 1/4 of the remainder on Tuesday, and the rest on Wednesday. What fraction of the journey was covered on the two days? - David 3

David was 1 3/5 m tall in the year 2020. This was 3/10 m taller than his height in the year 2019. What was his height in 2019?

- Rose and

Rose and Bill share a 30-ounce bucket of clay. By the end of the week, Rose has used 1/10 of the bucket, and Bill has used 2/5 of the bucket of clay. How many ounces are left in the bucket? - The lengths

The lengths of the twelve poles form an Arithmetic Progression (A. P). If the third pole is 3m and the eighth pole is 5 m, find the (i) Length of the first pole (ii) Sum of the length of the poles - 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? - Add fractions

Add/subtract the following similar fraction. Express the answer in the lowest terms if possible. Write your answer inside the box: 5/12 + 6/12 - Sum of three fractions

What is the sum of 6/7, 1/2 & 3/4?

more math problems »