# 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:

### 1/4 + 3/5 - 3/10 = 11/20 = 0.55

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

- Add: 1/4 + 3/5 = 1 · 5/4 · 5 + 3 · 4/5 · 4 = 5/20 + 12/20 = 5 + 12/20 = 17/20

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(4, 5) = 20. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - one quarter plus three fifths = seventeen twentieths. - Subtract: the result of step No. 1 - 3/10 = 17/20 - 3/10 = 17/20 - 3 · 2/10 · 2 = 17/20 - 6/20 = 17 - 6/20 = 11/20

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(20, 10) = 20. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 20 × 10 = 200. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - seventeen twentieths minus three tenths = eleven twentieths.

#### Rules for expressions with fractions:

**Fractions**- simply use a forward 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 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:

- UN 1

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

Write ten fractions between 1/3 and 2/3 - Cyclo trip

Eighth-graders took a full-day trip on a cycling course. They took 1/7 of the route to the first break and added another 3/7 of the route to lunch. They had 18 km left to the finish. How many kilometers did the trip route measure? - 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? - Divide

Divide the number 72 in the ratio 7: 2 and calculate the ratio of the numbers found in this order and write down as decimal. - Parking

At a building parking, 245 spaces are for cars, 56 are for vans and the rest are for buses. If 14% of all parking spaces are for buses, how many parking spaces are there in the building? How many spaces are for buses? - Kilo candy

One kilogram of chocolate candy cost 10 euros. Kate buys 250 grams and had the 8 pack of candy. How much does cost one bonbon? - Youth track

Youth track from Hronská Dúbrava to Banská Štiavnica which announced cancellation attracted considerable media attention and public opposition, has cost 6.3 euro per capita and revenue 13 cents per capita. Calculate the size of subsidies to a trip group o - A class IV.A

In a class there are 15 girls and 30 boys. What fraction of the class represents the boys? - Difference of two fractions

What is the difference between 1/2 and 1/6? (Write the answer as a fraction in lowest terms. ) - Pie division

5/8 of a pie divide 6 pieces. Each friend got 1/6. What fraction of the whole pie does each person receive? - Fraction eq

2/3x + 5/7 = 1/2x + 22/21 - Find unknown

Find unknown numerator: 4/8 + _/8 = 1

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