# 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:

### 3/5 - 1/10 = 1/2 = 0.5

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

- Subtract: 3/5 - 1/10 = 3 · 2/5 · 2 - 1/10 = 6/10 - 1/10 = 6 - 1/10 = 5/10 = 5 · 1/5 · 2 = 1/2

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(5, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 10 = 50. In the next intermediate step, , cancel by a common factor of 5 gives 1/2.

In words - three fifths minus one tenth = one half.

#### Rules for expressions with fractions:

**Fractions**- use the 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 non-zero 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:

- Ratio 11

Simplify this ratio 10 : 1/4 - Andre

Andre, Thomas, and Ivan split 88 postage stamps in a 2:5:4 ratio. How much did Thomas get? - Equation with x

Solve the following equation: 2x- (8x + 1) - (x + 2) / 5 = 9 - Fraction of a fraction

What is two-quarters of twelve? - Red diplomas

The numbers of students with honors in 2013 and 2014 are in ratio 40:49. How big is the year-on-year percentage increase? - Percent calculation

Calculate 8% if 44% is 32. - Fractions mul add sum

To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get? - Dice and coin

A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is head? - The perimeter 2

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

There are girls and 30 boys in the class. Boys prospering 28, girls all. How many girls are in the class and how many boys are there, if all the prospering students are 95%? - Average speed

When the bus stops at a bus stop driving average speed is 45 km/h. If it did not stop, it would drive at a speed of 54 km/h. How many minutes of every hour does it spend at stops? - Day

What part of the day are 23 hours 22 minutes? Express as a decimal number. - Family party

Anna has 5 €, Anezka has 4,60 € and for all the money they want to buy desserts for a family party. They decide between cakes and pinwheel: The pinwheel is € 0.40 more expensive than the cake, and the cakes can be bought for all the money by a third more

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