# 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 1/8 - 1 1/2 = 13/8 = 1 5/8 = 1.625

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

- Conversion a mixed number 3 1/8 to a improper fraction: 3 1/8 = 3 1/8 = 3 · 8 + 1/8 = 24 + 1/8 = 25/8

To find new numerator:

a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8

b) Add the answer from previous step 24 to the numerator 1. New numerator is 24 + 1 = 25

c) Write a previous answer (new numerator 25) over the denominator 8.

Three and one eighth is twenty-five eighths - Conversion a mixed number 1 1/2 to a improper fraction: 1 1/2 = 1 1/2 = 1 · 2 + 1/2 = 2 + 1/2 = 3/2

To find new numerator:

a) Multiply the whole number 1 by the denominator 2. Whole number 1 equally 1 * 2/2 = 2/2

b) Add the answer from previous step 2 to the numerator 1. New numerator is 2 + 1 = 3

c) Write a previous answer (new numerator 3) over the denominator 2.

One and one half is three halfs - Subtract: 25/8 - 3/2 = 25/8 - 3 · 4/2 · 4 = 25/8 - 12/8 = 25 - 12/8 = 13/8

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(8, 2) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 2 = 16. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - twenty-five eighths minus three halfs = thirteen 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:

- Square metal sheet

We cut out four squares of 300 mm side from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet. - In bucket

In bucket of 87 oranges 1/3 are spoiled ones and the remaining are eaten by the member of a family. How many oranges are eaten by the member of family? - Erika admin

Erika’s career consists of filing, typing and answering phones. She spends 1/6 of her time filing and 5/8 of her time typing. What fraction of her time does she spend answering phone calls? - 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 - Lunch time

In a cafeteria, 3/10 of the students are eating salads, and 3/5 are eating sandwiches. There are 30 students in the cafeteria. How many students are eating lunches other than salads or sandwiches? - Sugar 8

Heather has 2 cups of powdered sugar. She sprinkles 3/5 of the sugar onto a plate of brownies and sprinkles the rest into a plate of lemon cookies. How much sugar does Heather sprinkle on the brownies? How much sugar does Heather sprinkle on the lemon coo - Mike buys

Mike buys flowers to plant around his trees. 3/8 of the flowers are red. 1/3 of the flowers are pink. The rest of the flowers are white. Find the fraction of flowers that are white. - Monica’s

Monica's lawnmower had 1/8 of a gallon of gasoline in the tank. Monica started mowing and used all of the gasoline. She put 6/10 of a gallon of gasoline in the tank. After she mowed, 1/4 of a gallon was left in the tank. What was the total amount of gasol - A farmer 3

A farmer sells 9.3 kg of pears and apples at the farmers market.3/4 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmers market. - Cereals

Ari and Joey share a 30-ounce box of cereal. By the end of the week, Ari has eaten 3/10 of the box, and Joey has eaten 3/5 of the box of cereal. How many ounces are left in the box? - Two cakes

Two cakes were each cut into 8 slices. Maria ate 1/8 of the chocolate cake and 1 slice of carrot cake. Julia ate 1/2 of the carrot cake. Mark ate 1 slice of each. Thomas ate 3 slices of chocolate cake. How many slices were left? - Farmer Peter

Farmer Peter paints 12 chicken coop. He started painting this day morning. Now he only has 1/4 of the chicken coop left to paint this afternoon. How many chicken coops did farmer Peter paint this morning? - Claire and book

After Claire has read the first 5/8 of the book, there are 120 pages left to read. What is the total number of pages of the book?

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