# 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:

### 2/5 * 3/5 = 6/25 = 0.24

Spelled result in words is six twenty-fifths.### How do you solve fractions step by step?

- Multiple: 2/5 * 3/5 = 2 · 3/5 · 5 = 6/25

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(6, 25) = 1. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - two fifths multiplied by three fifths = six twenty-fifths.

#### 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:

- Unknown number

I think the number - its sixth is 3 smaller than its third. - Cakes

On the bowl were a few cakes. Jane ate one-third of them, and Dana ate a quarter of those cakes that remained. a) What part (of the original number of cakes) Dana ate? b) At least how many cakes could be (initially) on the bowl? - Larry 2

Larry spends half of his workday teaching piano lessons. If he sees 6 students, each for the same amount of time, what fraction of his workday is spent with each student? - Cups of punch

Cyka made 6 19/20 cups of punch punch at two different types of juice in it. If the punch had 4 1/5 cups of one type of juice how many cups of the other type of juice did it have? - Athletic race

Before a race, you start 4 5/8 feet behind your friend. At the halfway point, you are 3 2/3 feet ahead of your friend. What is the change in distance between you and your friend from the beginning of the race? - Almonds

Rudi has 4 cups of almonds. His trail mix recipe calls for 2/3 cup of almonds. How many batches of trail mix can he make? - Farmer Peter

Farmer Peter paints 12 chicken coop. He started painting this day morning. Now he only has 1/4 of the chicken coop left to paint this afternoon. How many chicken coops did farmer Peter paint this morning? - Cakes

1/3 poppy cake, 1/3 apple, 15 pieces of cheese. How many are totally cakes? - Two divided

Two divided by nine-tenths. - 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? - Jam cakes

Mom baked a third of plum jam cakes, one third cheesecakes and 18 poppy. How many cakes she had bake? - Missing number

Blank +1/6 =3/2 find the missing number - In bucket

In bucket of 87 oranges 1/3 are spoiled ones and the remaining are eaten by the member of a family. How many oranges are eaten by the member of family?

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