# 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:

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

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

- Divide: 5 : 1/2 = 5/1 · 2/1 = 5 · 2/1 · 1 = 10/1 = 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 1/2 is 2/1) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators.

In words - five divided by one half = ten.

#### 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:

- Barbara 2

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

Find the quotient of 3/4 and 1/4. - 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. - Cake 7

1/3 of a cake shared with 4 people. What share of the whole cake has each people? - Minutes

Write as fraction in basic form which part of the week is 980 minutes. - The physical

The physical therapist asks Mr. Smith to walk 20 minutes in one hour to improve his ambulation. What fractional part of an hour is Mr. Smith to exercise? - Rose spends

Rose spends 2 1/3 hours studying Math, 1 3/4 hours studying English, and 2 1/4 hours studying Science. Find her average time studying the three subjects. - Ornamental shrubs

Children committed to planting 240 ornamental shrubs. Their commitment, however, exceeded by 48 shrubs. Write the ratio of actually planted shrubs and commitment by lowest possible integers a/b. - The quotient

The quotient of g and 55 is the same as 279. What is g? - Reciprocal

Calculate the reciprocal numbers for the given real numbers. - Quotient and division

What is the quotient of 2/9 and 1/8? - Lemonade 4

Six friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get? - Cutting wire

If you cut a 3 ½ ft length wire into pieces that are 2 inches long, how many pieces of wire will you have?

next math problems »