# 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 / 3/5 = 15/2 = 7 1/2 = 7.5

Spelled result in words is fifteen halfs (or seven and one half).### 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 a 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 - Divide: 9/2 : 3/5 = 9/2 · 5/3 = 9 · 5/2 · 3 = 45/6 = 3 · 15 /3 · 2 = 15/2

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/5 is 5/3) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 3 gives 15/2.

In other words - nine halfs divided by three fifths = fifteen 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:

- The third

The one-third rod is blue, one-half of the rod is red, the rest of the rod is white and measures 8 cm. How long is the whole rod? - Gear wheels

Two gear wheels, which fit together, have the number of teeth z_{1}=58 and z_{2}=149. Calculate the speed of the first wheel, if the second wheel rotates 1232 revolutions per minute. - Drinking water

A man drinks a keg of water in 40 days, and a woman drinks in 62 days. How many days do they consume a keg together? - Divide 13

Divide. Simplify your answer and write as an improper fraction or whole number. 14÷8/3 - Women

In a company of 1050 employees are 2/3 women. How many women work in the company? - Lauren

Lauren is tutoring students at the library on Saturday. If she is at the library for a total of 6 hours and she helps each student, one at a time, for three-fourths of an hour, how many students does she tutor? - Lemonade

How many 1/4 cup servings are in 2 and 1/3 cups of lemonade? - 6/24 change

6/24 change to a fraction in lowest terms - The rope 2

The rope in the school gym is 10 ½ feet long. To make it easier to climb, Coach Hill tied a knot in the rope every ¾ foot. How many knots are in the rope? - The carpenters

The carpenters cut the beam. Half of the cut pieces were 1 meter long, a quarter of the pieces were two meters long and the remaining 8 meters of the beam were cut into two equal parts. - What was the length of the original beam? - What part of the origin - Jordan

Jordan wants to bring in cookie cakes to share with his 23 classmates for his birthday. His mom is willing to buy no more than 6 cookie cakes and Jordan must share the cakes equally between his classmates (and himself). Answer the questions to help Jordan - Dana helped

Dana helped her dad build a sandbox for her younger sister. The sandbox is shaped like a rectangular prism that is 4 1/2 feet long and 4 feet wide. Dana used bags of sand to fill the sandbox 1/2 of a foot deep. Each bag contained 1/2 of a cubic foot of sa - ŽSR

Calculate fixed annual personnel costs of operating monorail line 118 km long if every 5 km is a station, which serves three people - one dispatcher and two switchmen in 4-shift operation. Consider the average salary of the employee 885 €.

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