# 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:

### 4/20 + 7/15 = 2/3 ≅ 0.6666667

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

- Add: 4/20 + 7/15 = 4 · 3/20 · 3 + 7 · 4/15 · 4 = 12/60 + 28/60 = 12 + 28/60 = 40/60 = 20 · 2/20 · 3 = 2/3

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, 15) = 60. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 20 × 15 = 300. In the next intermediate step, , cancel by a common factor of 20 gives 2/3.

In words - four twentieths plus seven fifteenths = two thirds.

#### 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:

- Fraction and a decimal

Write as a fraction and a decimal. One and two plus three and five hundredths - One third 2

One third of all students in class live in a house. If here are 42 students in a class, how many of them live in house? - Rolls

Mom bought 13 rolls. Dad ate 3.5 rolls. How many rolls left when Peter yet put two at dinner? - Missing number

Blank +1/6 =3/2 find the missing number - Akpan

Akpan spent 3/8 of his time in school during the week. What fraction of his time does he spend at home during the week? - The book 4

Mr. Kinion read 3 3/4 chapters in his book on Monday. He then read 2 4/6 more chapters on Tuesday. How many chapters has he read so far? - A class IV.C

In a class 2/5 were boys. 30 were girls. How many more girls than boys are there? - Mixed numbers

Rewrite mixed numbers, so the fractions have the same denominator: 5 1/5 - 2 2/3 - Two thirds

Two thirds of the unknown number is 8/7. What is 7/3 of this number? - Fruits

For the price of one pineapple, I will buy two oranges. For the price of three oranges, I will buy four apples. I will buy 6 bananas for the price of three apples. What is the price of one banana if I pay 1 euro for one pineapple? - A pizza 2

A pizza is cut into slices that are each 1/6 of the whole. John is going to eat 1/2 of the whole pizza. How many slices will John eat? - Land area

The land area of Asia and Africa are in a 3: 2 ratio, the European and African are is 1:3. What are the proportions of Asia, Africa, and Europe? - Max has

Max has a 1/3 of a pound of pretzels and wants to share equal parts between himself and a friend. How much pretzels will Max's friend receive?

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