# 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 - 2/9 = 1/9 ≅ 0.1111111

Spelled result in words is one ninth.### How do you solve fractions step by step?

- Subtract: 1/3 - 2/9 = 1 · 3/3 · 3 - 2/9 = 3/9 - 2/9 = 3 - 2/9 = 1/9

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(3, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 9 = 27. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - one third minus two ninths = one ninth.

#### 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

**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.

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:

- Samuel

Samuel has 1/3 of a bag of rice and Isabella has a 1/2 bag of rice. What fraction of are bag of rice do they have altogether? - Kelly

Kelly and Dan are collecting clothes for a clothing drive. Dan collected 1/2 as many clothes as Kelly did. If Kelly collected 3 bags of clothes, how many bags of clothes did Dan collect? - Paper clips

Mrs. Bright is organizing her office supplies. There are 5 open boxes of paper clips in her desk drawer. Each box has 1/2 of the paper clips remaining. How many boxes of paper clips are left? - Juan is

Juan is making cookies. He makes 2 batches on Monday and 4 batches on Tuesday. He uses 3/4 cup of flour in each batch. How much flour does juan use? - Third of an hour

How many minutes is a third of an hour? Do you know to determine a third of the lesson hour (45min)? - Grandmother and grandfather

Grandmother baked cakes. Grandfather ate half, then quarter of the rest ate Peter and Paul ate half of rest. For parents left 6 cakes. How many cakes maked the grandmother? - Inquality

Solve inequality: 3x + 6 > 14 - School library

The school library contains 6300 books. With this constitutes 7% of professional books for teachers 18% interest books and encyclopedias for pupils and the rest of the fairy tales. How much are which books? - Obtuse angle

Which obtuse angle is creating clocks at 17:00? - Gingerbread house

Janka and Marienka calculated that there are 210 gingerbreads on the gingerbread house. Janko ate one-seventh of all gingerbreads, and Marienka ate a third less than Janko. How many gingerbreads remained in the gingerbread house? - Unit rate

Find unit rate: 6,840 customers in 45 days - Mrs Perry

Mrs Perry shares out 25 biscuits between Gemma and Zak in the ratio 1:4. How many biscuits has each? - A sum

A sum of money is shared between Peter, John and Henry in the ratio 2:3:5. a) express Henry's share as fraction of John's share. b) what fraction of the whole sum of money is John's share?

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