# 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:

### 2/3 * 5 = 10/3 = 3 1/3 ≅ 3.3333333

Spelled result in words is ten thirds (or three and one third).### How do you solve fractions step by step?

- Multiple: 2/3 * 5 = 2 · 5/3 · 1 = 10/3

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(10, 3) = 1. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - two thirds multiplied by five = ten thirds.

#### Rules for expressions with fractions:

**Fractions**- simply use a forward 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 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 machine

The machine was in operation for 9 tenths (in a fraction) of eight hours of working time. How long has he been running? - Anne eats

Anne eats 3/4 cup of raisins each day. How many total cups of raisins does Annie eat in 14 days? - Yellow tangs

In an aquarium 2/5 of the fish are surgeonfish. Of these 3/4 are yellow tangs. What fraction of all fish in the aquarium are yellow tangs? - Berry Smoothie

Rory has 5/8 cup of milk. How much milk does she have left after she doubles the recipe of the smoothie? Berry Smoothie: 2 cups strawberries 1 cup blueberries 1/4 cup milk 1 tbsp (tablespoon) sugar 1/2 tsp (teaspoon) lemon juice 1/8 tsp (teaspoon) vanilla - A recipe

A recipe requires 3/4 cups of milk. Paula is making 1/2 of the recipe. How many cups will Paula use? - A basket

A basket is full of 50 different kinds of fruits that has a ratio of 2:3:5. If the fruits are apple, mango, and guava, how many guavas are there? - A supermarket

A supermarket has 3 7/8 pounds of tangerines. Kelsey buys 1/2 of all the tangerines in the supermarket. How many pounds of tangerines did Kelsey buy? - Hungry cat

John is a fully grown cat. He eats 2/3 of a can a day. How many cans of food does Tinker eat in a week? * - Bathtub

Kevin has a bathtub shaped like a block. The bathtub measures 70 cm long, 45 cm wide and 50 cm high. Then the bathtub will be filled with clean water 3/5 of its height. The clean water needed is…. - Father's garden

John's father has a garden in the back yard. The dimensions of the garden are shown here. A green rectangle is shown. The width is labeled as 2 and two-thirds feet. The length is labeled as 7 and three-fourths feet. Calculate the area of the garden. You f - Lengths of the pool

Miguel swam 6 lengths of the pool. Mat swam 3 times as far as Miguel. Lionel swam 1/3 as far as Miguel. How many lengths did Mat swim? - Ratio - proportion

Reduce the number 16 in proportion 3:2 5:4 11:8 - Toilets

Federal law requires that all residential toilets sold in the United States use no more than 1 3/5 gallons of water per flush. Before this legislation, conventional toilets used 3 2/5 gallons of water per flush. Find the amount of water saved in one year

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