# 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 3/4 + 2 1/8 = 47/8 = 5 7/8 = 5.875

Spelled result in words is forty-seven eighths (or five and seven eighths).### How do you solve fractions step by step?

- Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4

To find new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4

b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15

c) Write a previous answer (new numerator 15) over the denominator 4.

Three and three quarters is fifteen quarters - Conversion a mixed number 2 1/8 to a improper fraction: 2 1/8 = 2 1/8 = 2 · 8 + 1/8 = 16 + 1/8 = 17/8

To find new numerator:

a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/8 = 16/8

b) Add the answer from previous step 16 to the numerator 1. New numerator is 16 + 1 = 17

c) Write a previous answer (new numerator 17) over the denominator 8.

Two and one eighth is seventeen eighths - Add: 15/4 + 17/8 = 15 · 2/4 · 2 + 17/8 = 30/8 + 17/8 = 30 + 17/8 = 47/8

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, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 8 = 32. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - fifteen quarters plus seventeen eighths = forty-seven eighths.

#### 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:

- Fractions mul add sum

To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get? - Weigh in total

I put 3/5 kg of grapes into a box which is 1/4kg in weight. How many kilograms do the grapes and the box weigh in total? - Math homework

It took Jose two-thirds of an hour to complete his math homework on Monday, three-fourths of an hour on Tuesday, any two- fifths of an hour on Wednesday. How many hours did it take Jose to complete his homework altogether? - Interior designer

To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies? - An orchard

During a visit to an orchard Greg picked 3/5 of a bag of golden delicious apples, 4/5 of a bag of Macintosh apples, 2/5 of a bag of Cortland apples, 1/5 of a bag of Bartlett pears, and 4/5 of a bag of Bosch pears. How many bags of fruit to Greg pick in to - Addition of mixed numerals

Add two mixed fractions: 2 4/6 + 1 3/6 - Adding mixed numerals

3 3/4 + 2 3/5 + 5 1/2 Show your solution. - Ali bought 2

Ali bought 5/6 litre of milk. He drank 1/2 litre and his brother drank 1/6 litre. How much litre of milk left? - Playing Cards

Kara has 2 times more cards than Dana, Dana has 4× less than Mary. Together they have 728 cards. How many cards has each of them? - Carrie

Carrie picked 2/5 of the raspberries from the garden, and Robin picked some too. When they were finished, 1/3 of the raspberries still needed to be picked. What fraction of the raspberries did Robin pick? Use pictures, numbers or words and write your fi - Pupils

Two classes want to collect money. Boys are four-seventh pupils. In time did not pay a quarter of the boys and a sixth of girls, which mean 12 sinners. How many pupils attend these two classes? - Master and apprentice

Master painted the roof in 3 hours and apprentice for 4 hours. How many of roof they painted in hour and how many in three quarters of an hour? - Chestnuts

Three divisions of nature protectors participated in the collection of chestnut trees.1. the division harvested 1250 kg, the 2nd division by a fifth more than the 1st division and the 3rd division by a sixth more than the second division. How many tons of

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