# 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:

### 5/6 : 5/9 = 3/2 = 1 1/2 = 1.5

Spelled result in words is three halfs (or one and one half).### How do you solve fractions step by step?

- Divide: 5/6 : 5/9 = 5/6 · 9/5 = 5 · 9/6 · 5 = 45/30 = 15 · 3 /15 · 2 = 3/2

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 5/9 is 9/5) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 15 gives 3/2.

In words - five sixths divided by five ninths = three halfs.

#### 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:

- Scale of the map

Determine the map's scale, which is the actual distance of 120 km l represented by a segment long 6 cm. - Strawberry-rhubarb pie

Larry had 3/7 of a strawberry-rhubarb pie left over. He split the leftover pie evenly between his 3 children. What fraction of a pie did each child get? - Unit rate

Find unit rate: 6,840 customers in 45 days - Division by zero

Fraction 5 by 2. if 3 is added to numerator and 2 is subtracted from the denominator then the new fraction is: - Cathy

Cathy has 5 cups of peanuts to share with her family. If each family member gets 1/2 cup of peanuts, how many family members can have some? - A pizza 2

A pizza is cut into slices that are each 1/6 of the whole. John is going to eat 1/2 of the whole pizza. How many slices will John eat? - Erik

Three friends Peter, Erik and Milan shared 420 euros in a ratio of 1: 2: 3. How many euros did Erik get? - Divide 13

Divide. Simplify your answer and write as an improper fraction or whole number. 14÷8/3 - Evaluate 12

Evaluate and simplify 9 divided by 7/6. - Sally

Sally is making 15 individual blueberry cheesecakes. How many pounds of blueberries will be in each cheesecake if 5 1/4 pounds of blueberries are divided equally among them? - Francesca

Francesca is growing 1/2 inch each year. How many years will it take for her to grow 6 inches? - Penny coins

One 2p coin is 1/8 inch thick. A pile of 2p is 1 1/2 inch high. How many coin are there in the pile - Summerjobs

The agency give summerjobs for 2352 students in 2018. The eighth was high-school students, the rest was undergraduates. How many undergraduates works via agency in 2018?

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