# 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:

### (1/2) : 5 = 1/10 = 0.1

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

- Divide: 1/2 : 5 = 1/2 · 1/5 = 1 · 1/2 · 5 = 1/10

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 5/1 is 1/5) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - one half divided by five = one tenth.

#### 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:

- Product of two fractions

Product of two fractions is 9 3/5 . If one of the fraction is 9 3/7. Find the other fraction. - Four people

Four people want waffles for breakfast. There are 6 waffles left. How can 6 waffles be shared equally among 4 people? How much does each person get? Draw a picture and write a division expression to model the problem. - 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? - Candy bars

Sheldon has 4 candy bars and wants to split them among his five friends. If each person gets the same amount, what part of the candy bar will each friend get? Show your work. - Pizza 5

You have 2/4 of a pizza, and you want to share it equally between 2 people. How much pizza does each person get? - The bread

There are 12 slices of bread and each person gets 3/4 of a slice of bread. How many people get bread? - Larry 2

Larry spends half of his workday teaching piano lessons. If he sees 6 students, each for the same amount of time, what fraction of his workday is spent with each student? - One fourth

One fourth of an apple pie is left for 2 family members to share equally. What fraction of the original pie will each member get? - A quotient

What is the quotient of 3/10 divided by 2/4 as a fraction? - Mrs. Glover

Mrs. Glover is making brownies for the girls’ tennis team. She took 1/5 of the leftover brownies to school to give to her 3 friends. How much did each friend get? - Fractions 4

How many 2/3s are in 6? - Barbara 2

Barbara get 6 pizzas to divide equally among 4 people. How much of a pizza can each person have? - Divide 13

Divide. Simplify your answer and write as an improper fraction or whole number. 14÷8/3

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