# 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:

### 2.5 5/2 = 2 1/2

Spelled result in words is five halfs (or two and one half). =### How do you solve fractions step by step?

- Conversion a decimal number to a fraction: 2.5 = 25/10 = 5/2

a) Write down the decimal 2.5 divided by 1: 2.5 = 2.5/1

b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

2.5/1 = 25/10

Note: 25/10 is called a*decimal fraction*.

c) Simplify and reduce the fraction

25/10 = 5 * 5/2 * 5 = 5~~* 5~~/2~~* 5~~= 5/2

#### 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:

- Write 3

Write a real-world problem involving the multiplication of a fraction and a whole number with a product that is between 8 and 10, then solve the problem. - 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? - Trees

3/5 trees are apples, cherries are 1/3. 5 trees are pear. How many is the total number of trees? - Equation

Find x: x + 1/2 = 1/3 - Vehicle tank

A vehicle tank was 3/5 full of petrol. When 21 liters of fuel was added it was 5/6 full. How many liters of petrol can the tank hold? - Series and sequences

Find a fraction equivalent to the recurring decimal? 0.435643564356 - Denominator

Calculate the missing denominator x: (264)/(96) = (11)/(x) - Trip

On the trip drank 3/10 of pupils tea, 2/5 cola, 1/4 mineral water and remaining 3 juice. How many students were on the trip? - Buing

Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK? - Divide

Divide area of rectangles with dimensions 32m and 10m by the ratio 7: 9. What area corresponds to a smaller section? - Savings

Eva borrowed 1/3 of her savings to her brother, 1/2 of savings spent in the store and 7 euros left. How much did she save? - LCD 2

The least common denominator of 2/5, 1/2, and 3/4 - Scale of the map

Determine the map's scale, which is the actual distance of 120 km l represented by a segment long 6 cm.

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