# 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:

### 3/5 + 7/10 - 1/2 = 4/5 = 0.8

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

- Add: 3/5 + 7/10 = 3 · 2/5 · 2 + 7/10 = 6/10 + 7/10 = 6 + 7/10 = 13/10

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(5, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 10 = 50. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - three fifths plus seven tenths = thirteen tenths. - Subtract: the result of step No. 1 - 1/2 = 13/10 - 1/2 = 13/10 - 1 · 5/2 · 5 = 13/10 - 5/10 = 13 - 5/10 = 8/10 = 2 · 4/2 · 5 = 4/5

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(10, 2) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 2 = 20. In the following intermediate step, cancel by a common factor of 2 gives 4/5.

In other words - thirteen tenths minus one half = four fifths.

#### 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:

- Pears

There were pears in the basket, I took two-fifths of them, and left six in the basket. How many pears did I take? - The tap

For one day flows 148 l of water out of the tap. How much water will flow out for 3/4 day? - UN 1

If we add to an unknown number his quarter, we get 210. Identify unknown number. - Shade

Shade the area on the grid that shows 5/8 x 2/4 - Fruits

Amy bought a basket of fruits 1/5 of them were apples,1/4 were oranges, and the rest were 33 bananas. How many fruits did she buy in all? - Trees

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

I think the number. If I add to its third seven I get same as when to its quarter add 8. Which is the number? - Expressions

Let k represent an unknown number, express the following expressions: 1. The sum of the number n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n - Vehicle tank

A vehicle tank was 3/5 full of petrol. When 21 liters of fuel was added it was 5/6 full. How many liters of petrol can the tank hold? - Red diplomas

The numbers of students with honors in 2013 and 2014 are in ratio 40:49. How big is the year-on-year percentage increase? - Calories 2

Ben eats approximately 2400 calories per day. His wife Sarah eats 5/8 as much. How many calories does Sarah eat per day? - The cube

The cube has an edge of 12 dm. The second cube has an edge exactly 20% longer. How many % is more water in the second cube than in the first cube, if the first cube is full to 3/4 and the second to 3/8? - Excavation

Excavation for the base of the cottage has dimensions 4.5 m x 3.24 m x 60 cm. The excavated soil will increase its volume by one-quarter. Calculate the volume of excavated soil.

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