# 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:

### 0.9 9/10

Spelled result in words is nine tenths. =### How do you solve fractions step by step?

- Conversion a decimal number to a fraction: 0.9 = 9/10 = 9/10

a) Write down the decimal 0.9 divided by 1: 0.9 = 0.9/1

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.)

0.9/1 = 9/10

Note: 9/10 is called a*decimal fraction*.

c) Simplify and reduce the fraction

9/10 = 9 * 1/10 * 1 = 9~~* 1~~/10~~* 1~~

#### 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:

- Someone

Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake that is left, how much of a whole cake will you have eaten? - A baker

A baker has 5 1/4 pies in her shop. She cut the pies in pieces that are each 1/8 of a whole pie. How many pieces of pie does she have? - Tailor

Tailor bought 2 3/4 meters of textile and paid 638 CZK. Determine the price per 1 m of the textile. - Cookies

Mom bake cookies. Rolo took 2/9 of all cookies, Michal 3/9. How many cookies ate Rolo if Michal had 9. - Cakes

1/3 poppy cake, 1/3 apple, 15 pieces of cheese. How many are totally cakes? - Bricklayers

8 bricklayers build a house for 630 days. How many bricklayers have to add after 150 days to complete the whole building in (next) 320 days? - Adding mixed 4

2 and 1/8th plus 1 and 1/3rd = - Unknown number 23

Find 2/3 of unknown number, which is two-thirds of the 99. - Roses

On the large rosary was a third white, half red, yellow quarter and six pink. How many roses was in the rosary? - From a 2

From a rope that is 11 m long, two pieces of lengths 13/5 m and 33/10 m are cut off. What is the length of the remaining rope? - Doug biked

Doug biked 5 1/4 miles in 3/4 of an hour. What is his average speed? - Pupil

I'm a primary school pupil. I attended the parents' exercises with children 1/4 of my age, 1/3 for drawing, and 1/6 for flute. For the first three years of my life, I had no ring, and I never went to two rings simultaneously. How old am I? - Pizza fractions

Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?

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