# 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:

### 4 1/2 + 3 3/4 = 33/4 = 8 1/4 = 8.25

Spelled result in words is thirty-three quarters (or eight and one quarter).### How do you solve fractions step by step?

- Conversion a mixed number 4 1/2 to a improper fraction: 4 1/2 = 4 1/2 = 4 · 2 + 1/2 = 8 + 1/2 = 9/2

To find new numerator:

a) Multiply the whole number 4 by the denominator 2. Whole number 4 equally 4 * 2/2 = 8/2

b) Add the answer from previous step 8 to the numerator 1. New numerator is 8 + 1 = 9

c) Write a previous answer (new numerator 9) over the denominator 2.

Four and one half is nine halfs - Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4

To find new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4

b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15

c) Write a previous answer (new numerator 15) over the denominator 4.

Three and three quarters is fifteen quarters - Add: 9/2 + 15/4 = 9 · 2/2 · 2 + 15/4 = 18/4 + 15/4 = 18 + 15/4 = 33/4

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(2, 4) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - nine halfs plus fifteen quarters = thirty-three quarters.

#### 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:

- Cupcakes

In a bowl was some cupcakes. Janka ate one third and Danka ate one quarter of cupcakes. a) How many of cookies ate together? b) How many cookies remain in a bowl? Write the results as a decimal number and in notepad also as a fraction. - Integer add to fraction

7 is added to the sum of 4/5 and 6/7 - 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? - Sum three fractions

Work out the sum of 1/4, 1/5 and 3/10. - An orchard

During a visit to an orchard Greg picked 3/5 of a bag of golden delicious apples, 4/5 of a bag of Macintosh apples, 2/5 of a bag of Cortland apples, 1/5 of a bag of Bartlett pears, and 4/5 of a bag of Bosch pears. How many bags of fruit to Greg pick in to - Adding mixed numbers

Add this two mixed numbers: 1 5/6 + 2 2/11= - Addition of mixed numerals

Add two mixed fractions: 2 4/6 + 1 3/6 - Team run

The first team member in a 926-person relay race must run 2 1/4 laps, the second team member must run 1 1/2 laps, and the third team member must run 3 1/4 laps. How many laps in all must each team run? - Frank

Frank will be riding his bike to school this year. The distance from his house to the end of the street is ⅜ mile. The distance from the end of the street to the school is ⅚ mile. How far is Frank's house from school? - How many 3

How many hours the Andersons watched TV in all Wednesday 3/1 hr Thursdays 2/3 hr Friday 4/5 hr Saturday 3/4 hr - Adding mixed 4

2 and 1/8th plus 1 and 1/3rd = - Notebooks

Liza, a store owner, buys 560 notebooks. He sold 3/8 of the notebook, and then she adds the stock of a notebook of 1/4 of the number of notebooks she bought. What is the total number of notebooks she purchased? - Cups of flour

Jade was baking cupcakes for her class. She has 4 5/4 cups of flour. For one batch, she used 1 2/3 cups of flour. On another batch, she used 7/9 of a cup of flour. How much flour does Jade have left after making the two batches of cupcakes?

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