# 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:

### 7 3/15 + 9 12/15 = 17/1 = 17

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

- Conversion a mixed number 7 3/15 to a improper fraction: 7 3/15 = 7 3/15 = 7 · 15 + 3/15 = 105 + 3/15 = 108/15

To find new numerator:

a) Multiply the whole number 7 by the denominator 15. Whole number 7 equally 7 * 15/15 = 105/15

b) Add the answer from previous step 105 to the numerator 3. New numerator is 105 + 3 = 108

c) Write a previous answer (new numerator 108) over the denominator 15.

Seven and three fifteenths is one hundred eight fifteenths - Conversion a mixed number 9 12/15 to a improper fraction: 9 12/15 = 9 12/15 = 9 · 15 + 12/15 = 135 + 12/15 = 147/15

To find new numerator:

a) Multiply the whole number 9 by the denominator 15. Whole number 9 equally 9 * 15/15 = 135/15

b) Add the answer from previous step 135 to the numerator 12. New numerator is 135 + 12 = 147

c) Write a previous answer (new numerator 147) over the denominator 15.

Nine and twelve fifteenths is one hundred forty-seven fifteenths - Add: 108/15 + 147/15 = 108 + 147/15 = 255/15 = 15 · 17/15 · 1 = 17

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(15, 15) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 15 = 225. In the next intermediate step, , cancel by a common factor of 15 gives 17/1.

In words - one hundred eight fifteenths plus one hundred forty-seven fifteenths = seventeen.

#### 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? - Evaluate fractions

The difference of 5 1/2 and 2/3 is added to the product of 5/6 and 1/2 - 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? - Area and perimeter 2

Find the area and the perimeter of a rectangle of length 45 1/2 cm and breadth 16 2/3 cm. - An orchard

During a visit to an orchard, Greg picked 3/5 of a bag of delicious golden 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 t - Addition of mixed numerals

Add two mixed fractions: 2 4/6 + 1 3/6 - Team run

The first team member in a 926-person relay race must run 2 1/4 laps, the second team member must run 1 1/2 laps, and the third team member must run 3 1/4 laps. How many laps in all must each team run? - 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? - Two numbers 11

The sum of two rational numbers is (-2). If one of them is 3/5, find the other.

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