# 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:

### 2/3 + 4/5 = 22/15 = 1 7/15 ≅ 1.4666667

Spelled result in words is twenty-two fifteenths (or one and seven fifteenths).### How do you solve fractions step by step?

- Add: 2/3 + 4/5 = 2 · 5/3 · 5 + 4 · 3/5 · 3 = 10/15 + 12/15 = 10 + 12/15 = 22/15

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(3, 5) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - two thirds plus four fifths = twenty-two fifteenths.

#### 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:

- Adding denominators

Max is working out 2/3+7/9. He says the answer is 9/12. What mistake have Max made? - Berry Smoothie

Rory has 5/8 cup of milk. How much milk does she have left after she doubles the recipe of the smoothie? Berry Smoothie: 2 cups strawberries 1 cup blueberries 1/4 cup milk 1 tbsp (tablespoon) sugar 1/2 tsp (teaspoon) lemon juice 1/8 tsp (teaspoon) vanilla - Sum of 18

Sum of two fractions is 4 3/7. If one of the fractions is 2 1/5 find the other one . - Circular garden

Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante - Adding mixed 3

Why does 1 3/4 + 2 9/10 equal 4.65? How do you solve this? - Salad

We need two tenths kg of a carrot, one tenth of peas and three tenths of of tomatoes to make salad. Express the fraction of the weight of the vegetables to be salad. Convert the result to grams. - Baxter

Baxter ate 1/12 of a box of dog food. Now the box is 3/4 full. What fraction of the full of a full box was there before Baxter? - Two pizzas

Jacobs mom bought two whole pizzas. He ate 2/10 of the pizza and his dad ate 1 1/5. How much is left. - 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? - Eight pipes

Eight pipes are each 2¼m long. What is the total length of the eight pipes? - Evaluate 17

Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form. - 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? - All tasks - taskman

Skilled workshop master washes client car 1/5 hour, cleaned the client's car in 5/4 hour, and painted small defects on car 1 1/3 hour. How long did it take him to do all the necessary work tasks?

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