# 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:

### 3/4 ÷ 1/8 = 6/1 = 6

Spelled result in words is six.

### How do you solve fractions step by step?

1. Divide: 3/4 : 1/8 = 3/4 · 8/1 = 3 · 8/4 · 1 = 24/4 = 4 · 6 /4 · 1 = 6
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 1/8 is 8/1) 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 4 gives 6/1.
In other words - three quarters divided by one eighth = six.

#### 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:

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:

• Simple equation 5 Solve equation with fractions: X × 3/8 = 1/2
• Equation 20 In given equation: 8/9-4/5=2/9+x, find x
• Spending Peter spends 1/5 of his earnings on his rent, and he saves 2/7. What fraction of his earnings is left?
• Mixed to improper Change the given mixed numbers to improper fraction: five-and-four-over-nine (5 4/9)
• Ratio 11 Simplify this ratio 10 : 1/4
• Seeds Of the 72 wet seeds, 7/8 germinated. How many seeds germinate?
• 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? Cris had 15000 . He spent 1/3 of his money on a table and the remaining on 5 similar chairs that cost the same. How much did one chair cost? Two cakes were each cut into 8 slices. Maria ate 1/8 of the chocolate cake and 1 slice of carrot cake. Julia ate 1/2 of the carrot cake. Mark ate 1 slice of each. Thomas ate 3 slices of chocolate cake. How many slices were left? Solve equation and check the result: 1.4x - 3/2 + x - 9,8 = x + 0,4/3 - 7 + 1,6/6 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 The land area of Asia and Africa are in a 3: 2 ratio, the European and African are is 1:3. What are the proportions of Asia, Africa, and Europe? How tall is a poplar by the river if we know that 1/5 of its total height is a trunk, 1/10th of the height is the root, and 35m from the trunk to the top of the poplar?