# Fraction calculator

## Result:

### 0.125 = 18

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

- Conversion a decimal number to a fraction: 0.125 = 1251000 = 18

a) Write down the decimal 0.125 divided by 1: 0.125 = 0.1251

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.)

0.1251 = 1.2510 = 12.5100 = 1251000

Note: 1251000 is called a*decimal fraction*.

c) Simplify and reduce the fraction

1251000 = 1 * 1258 * 125 = 1~~* 125~~8~~* 125~~= 18

#### 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 number 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 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**.

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

Calculator follows well-known rules for

**order of operations**. 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:

- New bridge

Thanks to the new bridge, the road between A and B has been cut to one third and is now 10km long. How much did the road between A and B measure before? - Rolls

Mom bought 13 rolls. Dad ate 3.5 rolls. How many rolls left when Peter yet put two at dinner? - Equation with x

Solve the following equation: 2x- (8x + 1) - (x + 2) / 5 = 9 - Fruits

Amy bought a basket of fruits 1/5 of them were apples,1/4 were oranges, and the rest were 33 bananas. How many fruits did she buy in all? - 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)? - Homework

In the crate are 18 plums, 27 apricot and 36 nuts. How many pieces of fruit left in the crate when Peter took 8 ninth: 1. nuts 2. apricots 3. fruit 4. drupe - Cancel fractions

Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)! - The rod

The rod is painted in four colors. 55% of the bar is painted in blue, green 0.2 of rod, 1/8 is brown and the remaining 45 cm of white. How long is rod? - Copper parts

From copper cast were made 3 parts. At first consumed one third of casting, the second 2/3 of rest and the third weighed 18 kg. What is the weight of original copper cast? - Unknown number

Determine the unknown number that is equal to a quarter of the fifth of number, which is by 152 more than unknown number. - Mr. Happy

Mr. Happy planted 36.6 meters square gardens grass; It's a third of the garden more than half of the garden. What is square area of this garden? - Divide

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

Three divisions of nature protectors participated in the collection of chestnut trees.1. the division harvested 1250 kg, the 2nd division by a fifth more than the 1st division and the 3rd division by a sixth more than the second division. How many tons of

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