# 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 + 5/6 = 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?

- Add: 2/3 + 5/6 = 2 · 2/3 · 2 + 5/6 = 4/6 + 5/6 = 4 + 5/6 = 9/6 = 3 · 3/3 · 2 = 3/2

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 6) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 6 = 18. In the following intermediate step, cancel by a common factor of 3 gives 3/2.

In other words - two thirds plus five sixths = 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:

- Add two fractions

What is the sum of 2/3 and 3/10? - There 13

There are 7 cows 3 sheeps and 4 chickens on a field . What fraction of the animals are sheep? - Write 3

Write a real-world problem involving the multiplication of a fraction and a whole number with a product that is between 8 and 10, then solve the problem. - Equation

Find x: x + 1/2 = 1/3 - A shopkeeper

A shopkeeper cuts a wheel of cheese into 10 equal wedges. A customer buys one-fifth of the wheel. How many wedges does the customer buy? Use the number line to help find the solution. - Red Riding Hood

Red Riding Hood is making her special banana pudding recipe. She is looking for her cup measure, but can only find her quarter cup measure. How many quarter cups does she need for 2 cups of sour cream? - 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? - Trees

3/5 trees are apples, cherries are 1/3. 5 trees are pear. How many is the total number of trees? - A small

A small book took one-sixth of a ream of paper to make. The team said they could make nine books from 3 whole reams of paper. Are they correct? - Class 9.C

Professor collects money in the 9. C for a school trip. 2/3 of the collected amount was from girls and 1/4 from boys. The rest of 410 CZK went from the class fund. How much will the school trip cost in total? - Product and sum

What is the product of two fourths and the sum of three halves and four? - A basket 2

A basket contains three types of fruits weighing 87/4 kg in all. If 23/4 kilograms of these are oranges, 48/7 kg are mangoes, and the rest are apples. What is the weight of the apples in the basket? - Earning 2

Rahul earns 5000 Rs, he saves 500 Rs . What's percentage of his earnings does he save? *

next math problems »