# 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:

### 4 3/4 - 1/3 = 53/12 = 4 5/12 ≅ 4.4166667

The spelled result in words is fifty-three twelfths (or four and five twelfths).### How do we solve fractions step by step?

- Conversion a mixed number 4 3/4 to a improper fraction: 4 3/4 = 4 3/4 = 4 · 4 + 3/4 = 16 + 3/4 = 19/4

To find a new numerator:

a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/4 = 16/4

b) Add the answer from the previous step 16 to the numerator 3. New numerator is 16 + 3 = 19

c) Write a previous answer (new numerator 19) over the denominator 4.

Four and three quarters is nineteen quarters. - Subtract: 19/4 - 1/3 = 19 · 3/4 · 3 - 1 · 4/3 · 4 = 57/12 - 4/12 = 57 - 4/12 = 53/12

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

In other words - nineteen quarters minus one third is fifty-three 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:

- Nida had

Nida had 1/12 of a pizza. She gave 1/8 of it to her friend Madeeha. Find what part of the whole pizza did Madeeha get. - Adeline

Adeline helped her mother make 7/9 liters of lemonade to treat their guests. She poured the lemonade into cups. Each cup had a capacity of 1/6 liters. She filled some cups entirely except for 1 cup. How much was lemonade in the cup that was not filled? - Akpan

Akpan spent 3/8 of his time in school during the week. What fraction of his time does he spend at home during the week? - Balloons 2

One balloon is 3 7/10 meters above the ground. A second balloon 2 3/5 meters higher. How far above the ground is the second balloon? Complete the addition equation and a related subtraction equation to model the problem. Use x to represent the height of t

- The recipe 2

The recipe needs 3/4 cups of flour. How many cups of flour will be left if you have 4 cups of flour in the container? - Blank number

5/2 + blank =1/3 What is the blank number? - One large

One large pizza is cut into 12 pieces. The pizza has sausage, mushrooms, and cheese on it. Michelle ate 1/6 of the pizza, Natalie ate 1/4 of the pizza, Bridgette ate 1/8 of the pizza, and Brenda ate 1/3 of the pizza. How much of the whole pizza is left, a - Calculation 7316

The king divided part of his lands between his three sons. To the first, he gave one-fifth. To the second, he gave 40 ha less than the first, and to the third, he gave 30% of the whole. Write down what part of the land was left to the king. Calculation us - Mixed numbers

Rewrite mixed numbers so the fractions have the same denominator: 5 1/5 - 2 2/3

- A rope

From a rope of length 18 3/4 m, two smaller pieces of lengths 5 m and 7 1/2 m are cut out. Find the length of the remaining piece of rope. - Twenty-minute 6665

The truck driver left Prague at 7:20 a.m., took a twenty-minute break in Poděbrady, and reached Hradec Kralové at 8:55 a.m. How long did the whole journey take (including a break)? How long was the ride itself? - A baker 4

A baker has 20 cups of flour. If a loaf of bread requires 3 1/3 cups of flour and the baker made 4 loaves, how many cups of the flower were left over? - Musa worked

Musa worked for 44 hours during one five days a week. His hours are from Monday through Thursday: 3 3/4, 6 7/12, 11 5/16, and 6 5/6. Calculate the number of hours he worked on Friday. - Tree planting

The trapezoidal garden has bases 44 m and 16 m long. Their distance is 25 m. How many square meters of its area will remain for tree planting if we use 1/5 of the entire site to construct a cottage, backyard, and road? Is it possible to find the length of

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