# 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:

### 2/3 * 2/5 = 4/15 ≅ 0.2666667

Spelled result in words is four fifteenths.### How do you solve fractions step by step?

- Multiple: 2/3 * 2/5 = 2 · 2/3 · 5 = 4/15

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(4, 15) = 1. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - two thirds multiplied by two fifths = four fifteenths.

#### 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:

- Equation 25

Solve following simple equation: 3/4(x+5)=1/2(x+9) - Slices of pizza

Maria ate 1/4 of a pizza. If there were 20 slices of pizza, how many slices did Maria eat? - Ms. Sheppard

Ms. Sheppard cuts ½ of a piece of construction paper. She uses ⅙ of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower? - Dividends

The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least? - The ketchup

If 3 1/4 of tomatoes are needed to make 1 bottle of ketchup. Find the number of tomatoes required to make 4 1/5 bottles - Cris had

Cris had 15000 . He spent 1/3 of his money on a table and the remaining on 5 similar chairs that cost the same. How much did one chair cost? - Tallest and shortest

Jenn is the tallest on the team. He is 1 1/2 times as tall as the shortest girl whom is 4 1/4 feet tall. How tall is Jebb? - Brick weight

Half the weight of a brick plus 20 pounds is equal to 1/3 the weight of the brick plus 30 pounds. How much does the brick weigh? - Points

Gryffindor won 437 points. How many points obtained by each of the faculties if they were split at a ratio of 5: 7: 3: 4? - Sum of fractions

What is the sum of 2/3+3/5? - 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)? - Breads

Several pieces of bread were in the store. Half of them plus half of the bread bought a cookbook. Of the remaining bread, half of it plus half of the bread was bought by Mr. Novák. Ms. Small bought the last bread. How many breads were in the store at the - Max has

Max has a 1/3 of a pound of pretzels and wants to share equal parts between himself and a friend. How much pretzels will Max's friend receive?

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