# 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:

### 3/5 - 1/8 = 19/40 = 0.475

Spelled result in words is nineteen fortieths.### How do you solve fractions step by step?

- Subtract: 3/5 - 1/8 = 3 · 8/5 · 8 - 1 · 5/8 · 5 = 24/40 - 5/40 = 24 - 5/40 = 19/40

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(5, 8) = 40. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 8 = 40. In the next intermediate step, the fraction result cannot be further simplified by canceling.

In words - three fifths minus one eighth = nineteen fortieths.

#### 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:

- 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? - Unknown number

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

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

Two divided by nine-tenths. - 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 - Cleaning windows

Cleaning company has to wash all the windows of the school. The first day washes one-sixth of the windows of the school, the next day three more windows than the first day and the remaining 18 windows washes on the third day. Calculate how many windows ha - Discount sale

At Christmas Sale after a 20% discount, the cosmetic package was priced for 5 euros and 60 cents; later it went to 3 euros and 80 cents. How much percentage is the total discount? - Brick

Isosceles scale has on one side all brick and second weight 1 kg and 1/4 of brick. The balance is in equilibrium. What is the weight of a brick? - 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? - 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?

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