# 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:

### 12 9/10 + 8 3/5 = 43/2 = 21 1/2 = 21.5

Spelled result in words is forty-three halfs (or twenty-one and one half).### How do you solve fractions step by step?

- Conversion a mixed number 12 9/10 to a improper fraction: 12 9/10 = 12 9/10 = 12 · 10 + 9/10 = 120 + 9/10 = 129/10

To find new numerator:

a) Multiply the whole number 12 by the denominator 10. Whole number 12 equally 12 * 10/10 = 120/10

b) Add the answer from previous step 120 to the numerator 9. New numerator is 120 + 9 = 129

c) Write a previous answer (new numerator 129) over the denominator 10.

Twelve and nine tenths is one hundred twenty-nine tenths - Conversion a mixed number 8 3/5 to a improper fraction: 8 3/5 = 8 3/5 = 8 · 5 + 3/5 = 40 + 3/5 = 43/5

To find new numerator:

a) Multiply the whole number 8 by the denominator 5. Whole number 8 equally 8 * 5/5 = 40/5

b) Add the answer from previous step 40 to the numerator 3. New numerator is 40 + 3 = 43

c) Write a previous answer (new numerator 43) over the denominator 5.

Eight and three fifths is forty-three fifths - Add: 129/10 + 43/5 = 129/10 + 43 · 2/5 · 2 = 129/10 + 86/10 = 129 + 86/10 = 215/10 = 5 · 43/5 · 2 = 43/2

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(10, 5) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 5 = 50. In the next intermediate step, , cancel by a common factor of 5 gives 43/2.

In words - one hundred twenty-nine tenths plus forty-three fifths = forty-three halfs.

#### 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:

- Samuel

Samuel has 1/3 of a bag of rice and Isabella has a 1/2 bag of rice. What fraction of are bag of rice do they have altogether? - A large 2

A large popcorn bag holds four times as much as a small popcorn bag at the end of the party 3 1/3 small bags and 2 1/4 large bags left. How many small bags with the leftover popcorn fill? - Chestnuts

Three divisions of nature protectors participated in the collection of chestnut trees.1. the division harvested 1250 kg, the 2nd division by a fifth more than the 1st division and the 3rd division by a sixth more than the second division. How many tons of - Area and perimeter 2

Find the area and the perimeter of a rectangle of length 45 1/2 cm and breadth 16 2/3 cm. - Recipe ingredients

Monica’s cookie recipe calls for Three-fourths of a cup of flour. Her mother’s recipe calls for Two-thirds as much as Monica’s. How many cups of flour does her mother’s recipe require? - Metal rod

You have a metal rod that’s 51/64 inches long. The rod needs to be trimmed. You cut 1/64 inches from one end and 1/32 inches from the other end. Next, you cut the rod into 6 equal pieces. What will be the final length of each piece? - The pet

Ananya has a bunny. She bought 4 7/8 pounds of carrots. She fed her bunny 1 1/4 pounds of carrots the first week. She fed her bunny 5/6 pounds of carrots the second week. All together, how many pounds of carrots did she feed her bunny? 1. Draw a tape diag - Chocolate buyer

Peter bought 1/2 a pound of chocolate at rocky mountain chocolate factory. Later he went to the sweet shoppie and he bought 6/9 of a pound more chocolate. How much chocolate did he buy that day? - Fe metal sheet

For one product, 5/8 of the metal sheet are consumed, to the second 5/6 of remains. What part of the sheet metal is consumed for both products together? - Rose spends

Rose spends 2 1/3 hours studying Math, 1 3/4 hours studying English, and 2 1/4 hours studying Science. Find her average time studying the three subjects. - Playing Cards

Kara has 2 times more cards than Dana, Dana has 4× less than Mary. Together they have 728 cards. How many cards has each of them? - A 14.5-gallon

A 14.5-gallon gasoline tank is 3/4 full. How many gallons will it take to fill the tank? Write your answer as a mixed number. - Interior designer

To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies?

next math problems »