# 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:

### 5/2 - 1/3 = 13/6 = 2 1/6 ≅ 2.1666667

Spelled result in words is thirteen sixths (or two and one sixth).### How do you solve fractions step by step?

- Subtract: 5/2 - 1/3 = 5 · 3/2 · 3 - 1 · 2/3 · 2 = 15/6 - 2/6 = 15 - 2/6 = 13/6

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(2, 3) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 3 = 6. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - five halfs minus one third = thirteen sixths.

#### 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:

- Brick weight

Half the weight of a brick plus 20 pounds is equal to 1/3 the weight of the brick plus 30 pounds. How much does the brick weigh? - Sum of fractions

What is the sum of 2/3+3/5? - Dividends

The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least? - Playing

How long have we trained on the pitch when we know that the warm-up took 10 minutes, we trained passes for one-third of the time and we played football half the time? - Series and sequences

Find a fraction equivalent to the recurring decimal? 0.435643564356 - PC disks

Peter has 45 disks in three colors. One-fifth of the disks are blue, red are twice more than the white. How much is blue, red and white disks? - The perimeter 2

The perimeter of the quadrilateral a = 1m b = 14/5m c = 2 3/10m d = 1 4/5m? - Pocket

Mirka spent on a trip for gifts half pocket. For the third remain money bought a bagel. Six euros left her. How many euros had Mirka in pocket? - Walking

Lucie can walk about 3 4/5 miles each hour. How far can she walk in 2 hours 45 minutes? - Dried apples

How many kilograms of fresh apples id needed to 120 kg of dried apples when from 0.4 tons of fresh apples we get 75 kg of dried apples? - Equilateral triangle ABC

In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont - A class IV.A

In a class there are 15 girls and 30 boys. What fraction of the class represents the boys? - One Saturday

One Saturday evening there are 40 girls 25 boys 18 women and 17 men at a cinema. What fraction are girls?

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