# Fraction calculator

#### 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:

- Inquality

Solve inequality: 3x + 6 > 14 - 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? - School library

The school library contains 6300 books. With this constitutes 7% of professional books for teachers 18% interest books and encyclopedias for pupils and the rest of the fairy tales. How much are which books? - Obtuse angle

Which obtuse angle is creating clocks at 17:00? - Gingerbread house

Janka and Marienka calculated that there are 210 gingerbreads on the gingerbread house. Janko ate one-seventh of all gingerbreads, and Marienka ate a third less than Janko. How many gingerbreads remained in the gingerbread house? - 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)? - Unit rate

Find unit rate: 6,840 customers in 45 days - Warehouses

To four warehouses is going cement in 25 kg bags. To first one third, to second quarter of the total. The third store got two thirds of the rest, and the last 310 tons came to fourth. How many cement is in all warehouses and how much got every one? - Blueberries

5 children collect 4 liters of blueberries in 1.5 hours. a) How many minutes do 3 children take 2 liters of blueberries? b) How many liters of blueberries will be taken by 8 children in 3 hours? - 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 - Lunch for free

Gastro ticket are "free" and therefore they should be retained. This think many employees in Slovakia. Calculate how much money employee yearly earn if he get 201 gastro tickets of 2.8 € and you know that the company issuing gastro tickets get 4.9% fee o - Kilo candy

One kilogram of chocolate candy cost 10 euros. Kate buys 250 grams and had the 8 pack of candy. How much does cost one bonbon? - Grandmother's clocks

Grandmother's clock is late every hour by half a minute. Grandmother it by set exactly at 8.00 am. How many hours will show after 24 hours.?

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