# 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:

### 2/5 + 6 3/7 - 2 2/3 = 437/105 = 4 17/105 ≅ 4.1619048

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

- Conversion a mixed number 6 3/7 to a improper fraction: 6 3/7 = 6 3/7 = 6 · 7 + 3/7 = 42 + 3/7 = 45/7

To find a new numerator:

a) Multiply the whole number 6 by the denominator 7. Whole number 6 equally 6 * 7/7 = 42/7

b) Add the answer from the previous step 42 to the numerator 3. New numerator is 42 + 3 = 45

c) Write a previous answer (new numerator 45) over the denominator 7.

Six and three sevenths is forty-five sevenths. - Add: 2/5 + 45/7 = 2 · 7/5 · 7 + 45 · 5/7 · 5 = 14/35 + 225/35 = 14 + 225/35 = 239/35

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(5, 7) = 35. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 7 = 35. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - two fifths plus forty-five sevenths is two hundred thirty-nine thirty-fifths. - 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. - Subtract: the result of step No. 2 - 8/3 = 239/35 - 8/3 = 239 · 3/35 · 3 - 8 · 35/3 · 35 = 717/105 - 280/105 = 717 - 280/105 = 437/105

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(35, 3) = 105. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 35 × 3 = 105. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - two hundred thirty-nine thirty-fifths minus eight thirds is four hundred thirty-seven one-hundred fifths.

### 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 cake 2

Karen sliced a cake into 10 slices. She ate 2/10 of it and after some time she ate another 4/10 of it. How much of the cake did Karen 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? - 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? - 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?

- Numbers 5256

What is 4/5 of the sum of numbers (-4.95) and (-11.05)? - The bucket

Anna and Joey share an 18-ounce bucket of clay. By the end of the week, Anna has used 1/3 of the bucket, and Joey has used 2/3 of the bucket of clay. How many ounces are left in the bucket? - Two mixed adding

What is 1 and 1/6 + 1 and 3/6? - Negative fractions

I am a number that is equal to -3/4 subtracted from the sum of 3/5 and -1/3. What number am I? - The sum 34

The sum of two fractions is 5/6. One of the fractions is 1/2. What is the other fraction?

- 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 - Rica has

Rica has 3 pieces of lace, each measuring 1/7 meter, 5/14 meter, and 3/7 meter. How long are the pieces of lace together? - 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 - Chocolate buyer

Peter bought 1/2 a pound of chocolate at rocky mountain chocolate factory. Later, he went to the sweet shop and bought 6/9 of a pound more chocolate. How much chocolate did he buy that day? - 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

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