# 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:

### 1 3/4 + 2/3 = 29/12 = 2 5/12 ≅ 2.4166667

The spelled result in words is twenty-nine twelfths (or two and five twelfths).### How do we solve fractions step by step?

- Conversion a mixed number 1 3/4 to a improper fraction: 1 3/4 = 1 3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

To find a new numerator:

a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4

b) Add the answer from the previous step 4 to the numerator 3. New numerator is 4 + 3 = 7

c) Write a previous answer (new numerator 7) over the denominator 4.

One and three quarters is seven quarters. - Add: 7/4 + 2/3 = 7 · 3/4 · 3 + 2 · 4/3 · 4 = 21/12 + 8/12 = 21 + 8/12 = 29/12

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 - seven quarters plus two thirds is twenty-nine 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:

- Adding denominators

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

Type an expression to match, and then evaluate. Type your answer as a mixed number. 4 times as much as the sum of 1/5 and 2/3 - Add two fractions

What is 1/2 added to 2/3? * 1 point A. 1 3/12 B. 1 5/6 C. 1 1/6 D.1 1/4 - Medical facility

Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal today, she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 o

- Joe had

Joe had a full tank of petrol in his car. His car consumed 2/9 of the tank of petrol on Saturday and 1/3 of it on Sunday. What fraction of the tank of petrol was left after the weekend? - Three cakes

There are three cakes an ice cream cake, chocolate, and a sponge cake. We ate 3/4 of the ice cream cake. We cut the chocolate cake into twelve equal pieces, of which We ate nine. The sponge cake was divided into eight equal pieces, with only one remaining - Sytiel

Sytiel used 3/10 of the water in his tank to wash his car. He used 1/10 to water his plants. Now he is using 5/10 for his laundry. How many parts of water in the tank did he use up? - Sum of 18

The sum of two fractions is 4 3/7. If one of the fractions is 2 1/5, find the other one. - Circular garden

Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante

- Berry Smoothie

Rory has 5/8 cups of milk. How much milk does she have left after she doubles the recipe for the smoothie? Berry Smoothie: 2 cups strawberries 1 cup blueberries 1/4 cup milk 1 tbsp (tablespoon) sugar 1/2 tsp (teaspoon) lemon juice 1/8 tsp (teaspoon) vanil - Granddaughter 5489

Grandma wrapped two-fifths of the cake for her granddaughter, Mary, and Eme wrapped one-quarter of the cake. What part did Grandma pack in the science, and what part remained with Grandma? - The sum 42

The sum of two fractions is 6 5/6. If the bigger fraction is subtracted by 3/4, the difference is 4 7/12. What is the smaller fraction? - Complex expr with fractions

Find 1½ of 16 ÷2⅓+(2¼ of ⅑). Use the correct order of operations. The order is PEMDAS: Parentheses, Exponents, Multiplication, Division (from left to right), addition, and Subtraction (from left to right). - Plus minus mixed numbers

If possible, perform the indicated operation/s and reduce your answer to the lowest term. 1. 3 1/8 + 3/5= 2. 6 3/7 + 4/9= 3. 9 6/13 + 1 3/7= 4. 10 4/5 - 2/3= 5. 13 6/7 - 3/11=

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