# 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 1/5 - 1 4/5 = 7/5 = 1 2/5 = 1.4

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

- Conversion a mixed number 3 1/5 to a improper fraction: 3 1/5 = 3 1/5 = 3 · 5 + 1/5 = 15 + 1/5 = 16/5

To find new numerator:

a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5

b) Add the answer from previous step 15 to the numerator 1. New numerator is 15 + 1 = 16

c) Write a previous answer (new numerator 16) over the denominator 5.

Three and one fifth is sixteen fifths - Conversion a mixed number 1 4/5 to a improper fraction: 1 4/5 = 1 4/5 = 1 · 5 + 4/5 = 5 + 4/5 = 9/5

To find new numerator:

a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5

b) Add the answer from previous step 5 to the numerator 4. New numerator is 5 + 4 = 9

c) Write a previous answer (new numerator 9) over the denominator 5.

One and four fifths is nine fifths - Subtract: 16/5 - 9/5 = 16 - 9/5 = 7/5

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(5, 5) = 5. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 5 = 25. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - sixteen fifths minus nine fifths = seven fifths.

#### 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:

- The recipe

The recipe they are following requires 7/8 cups of milk, Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe? - Difference of two fractions

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

King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers? - Package

The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package? - From a

From a 1 meter ribbon, Ericka cut 2/4 meter for her hat and another 1/4 meter for her bag. How long was the remaining piece? - Evaluate - lowest terms

Evaluate: 16/25 - 11/25 (Express answer as a fraction reduced to lowest terms. ) - Shopper

Eva spent 1/4 in one store and 1/3 in another. What fraction is left? - Sadie

Sadie practiced her spelling words for 3/4 of an hour, and Max practiced his spelling words for 5/12 of an hour. In the simplest form, how much longer did Sadie practice than Max? - Sum of 18

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

Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first orange, 3/10 cups from the second orange, StartFraction 9 over 20 E - Michael

Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left? - Pizza

Three siblings ordered one pizza. Miška ate a quarter of the whole pizza. Lenka ate a third of the rest and Patrik ate half of what Lenka had left. They had the rest packed up. How much of the pizza did they pack? Write the result as a fraction. - You leave

You leave school and the end of the day and walk 3/8 of a mile away before realizing that you left your backpack and immediately turn around you then walk 1/6 of a mile back towards school at this point assuming you walked in a straight line how many mile

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