# Fraction calculator

The calculator performs basic and advanced operations with fractions, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. Solve problems with two, three, or more fractions and numbers in one expression.

## Result:

### 1 3/4 + 1 3/4 = 7/2 = 3 1/2 = 3.5

Spelled result in words is seven halfs (or three and one half).### How do you 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 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 + 7/4 = 7 + 7/4 = 14/4 = 2 · 7/2 · 2 = 7/2

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(4, 4) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 4 = 16. In the following intermediate step, cancel by a common factor of 2 gives 7/2.

In other words - seven quarters plus seven quarters = seven halfs.

#### Rules for expressions with fractions:

**Fractions**- simply use a forward slash between the numerator and denominator, i.e., for five-hundredths, enter

**5/100**. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.

The slash separates the numerator (number above a fraction line) and denominator (number below).

**Mixed numerals**(mixed fractions or mixed numbers) write as integer separated by one space and fraction i.e.,

**1 2/3**(having the same sign). An example of a negative mixed fraction:

**-5 1/2**.

Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e.,

**1/2 : 3**.

Decimals (decimal numbers) enter with a decimal point

**.**and they are automatically converted to fractions - i.e.

**1.45**.

The colon

**:**and slash

**/**is the symbol of division. Can be used to divide mixed numbers

**1 2/3 : 4 3/8**or can be used for write complex fractions i.e.

**1/2 : 1/3**.

An asterisk

*****or

**×**is the symbol for multiplication.

Plus

**+**is addition, minus sign

**-**is subtraction and

**()[]**is mathematical parentheses.

The exponentiation/power symbol is

**^**- for example:

**(7/8-4/5)^2**= (7/8-4/5)

^{2}

#### 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

• exponentiation of fraction: 3/5^3

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

• 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 /) has the same priority and then must evaluate from left to right.

## Fractions in word problems:

- Expressions

Let k represent an unknown number, express the following expressions: 1. The sum of the number 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 - Fe metal sheet

For one product, 5/8 of the metal sheet are consumed, to the second 5/6 of remains. What part of the sheet metal is consumed for both products together? - Simplify 3

Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution. - Gross profit

Joseph sold the following quantities of kerosene of gallons: 3/4, 5/8, 7/8, and 9/10. How many gallons of kerosene did Joseph sell? If gallon costs P28.00 and he sold it at P32.00, how much was his gross profit? - Add two fractions

What is the sum of 2/3 and 3/10? - Adding mixed fractions

Add this two mixed numbers: 1 5/6 + 2 2/11= - One evening

One evening, a restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread. How many loaves were served in all? - Adding mixed numbers

Add this two mixed numbers: 1 5/6 + 2 2/11= - An orchard

During a visit to an orchard, Greg picked 3/5 of a bag of delicious golden apples, 4/5 of a bag of Macintosh apples, 2/5 of a bag of Cortland apples, 1/5 of a bag of Bartlett pears, and 4/5 of a bag of Bosch pears. How many bags of fruit to Greg pick in t - A market

A market vendor was able to sell all the mangoes, papayas, and star apples. 1/5 of the fruits were mangoes, 2/3 of them were papayas and the rest were star apples. How many parts of the fruits sold are star apples? - The movie

Barry watched 1/3 of a movie in the morning, and he watched some more at night. By the end of the day, he still had 1/4 of the movie left to watch. How much of the movie did Barry watch at night? - Adding mixed 4

2 and 1/8th plus 1 and 1/3rd = - Roses and tulips

At the florist are 50 tulips and 5 times fewer roses. How many flowers are in the flower shop?

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