# 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:

### 9 1/8 - 3 5/6 = 127/24 = 5 7/24 ≅ 5.2916667

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

- Conversion a mixed number 9 1/8 to a improper fraction: 9 1/8 = 9 1/8 = 9 · 8 + 1/8 = 72 + 1/8 = 73/8

To find new numerator:

a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/8 = 72/8

b) Add the answer from previous step 72 to the numerator 1. New numerator is 72 + 1 = 73

c) Write a previous answer (new numerator 73) over the denominator 8.

Nine and one eighth is seventy-three eighths - Conversion a mixed number 3 5/6 to a improper fraction: 3 5/6 = 3 5/6 = 3 · 6 + 5/6 = 18 + 5/6 = 23/6

To find new numerator:

a) Multiply the whole number 3 by the denominator 6. Whole number 3 equally 3 * 6/6 = 18/6

b) Add the answer from previous step 18 to the numerator 5. New numerator is 18 + 5 = 23

c) Write a previous answer (new numerator 23) over the denominator 6.

Three and five sixths is twenty-three sixths - Subtract: 73/8 - 23/6 = 73 · 3/8 · 3 - 23 · 4/6 · 4 = 219/24 - 92/24 = 219 - 92/24 = 127/24

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, 6) = 24. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 6 = 48. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - seventy-three eighths minus twenty-three sixths = one hundred twenty-seven twenty-fourths.

#### 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. - 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? - Animal species

Of 100 types of animals, 9/100 were discovered in ancient times, and 2/100 were discovered in the Middle Ages. Another 3/10 were discovered in the 1800s. What fraction of the 100 types of animals was discovered after the 1800s? Explain. - Equation with mixed 2

A number, X, is subtracted from 8 1/4. The result is 12 3/5. What is the value of X? - 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? - A laundry

Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed? - A market

A market vendor was able to sell all the mangoes, papayas, and star apples. 1/5 of the fruits were mangoes, 2/3 of them were papayas and the rest were star apples. How many parts of the fruits sold are star apples? - 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 - Coloured teacups

The teacups in Tea Stop 55 are `2/5` green and `3/10` yellow. What fraction of the teacups are neither green nor yellow? - 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. - The Bakery

At a Bakery, ⅗ of the baked goods are pies, and the rest are cakes. ⅓ of the pies are coconut. ⅙ of the cakes are angel food. What fraction of all the baked goods at the Bakery are coconut pies? What fraction of all the baked goods at the Bakery are are a - Pizzas

Billy ate 1 1/4 pizzas and John ate 1 2/3 pizzas. How much more pizza did John eat than Billy? - 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

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