# 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:

### 1/3 * 3/5 * 21/4 = 9/20 = 0.45

Spelled result in words is nine twentieths.

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

1. Multiple: 1/3 * 3/5 = 1 · 3/3 · 5 = 3/15 = 1 · 3/5 · 3 = 1/5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 15) = 3. In the next intermediate step, , cancel by a common factor of 3 gives 1/5.
In words - one third multiplied by three fifths = one fifth.
2. Conversion a mixed number 2 1/4 to a improper fraction: 2 1/4 = 2 1/4 = 2 · 4 + 1/4 = 8 + 1/4 = 9/4

To find new numerator:
a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/4 = 8/4
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 4.

Two and one quarter is nine quarters
3. Multiple: the result of step No. 1 * 9/4 = 1/5 * 9/4 = 1 · 9/5 · 4 = 9/20
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(9, 20) = 1. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - one fifth multiplied by nine quarters = nine twentieths.

#### 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:

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:

• Giraffes to monkeys
The ratio of the number of giraffes to the number of monkeys in a zoo is 2 to 5. Which statement about the giraffes and monkeys could be true? A. For every 10 monkeys in the zoo, there are 4 giraffes. B. For every  giraffe in the zoo, there are 3 monkeys.
• Fraction
Find for what x fraction (-4x -6)/(x) equals:
• A laundry
Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
• Sandy
Sandy, John and Marg baked pies for the Bake Sale. Sandy cut his pies into 6ths, John but his into 8ths and Marg cut hers into quarters. Sandy sold 11/6, John sold  1 3/8 pies and Marg sold 9/4 pies. Who sold the most pies? Who sold the fewest?
• Fractions
Sort fractions z1 = (6)/(11); z2 = (10)/(21); z3 = (19)/(22) by its size. Result write as three serial numbers 1,2,3.
• Ten fractions
Write ten fractions between 1/3 and 2/3
• Stones in aquarium
In an aquarium with a length of 2 m, 1.5 m wide, and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes)
• Equivalent fractions
Are these two fractions equivalent -4/9 and 11/15?
• Arrange
Arrange the following in descending order: 0.32, 2on5, 27%, 1 on 3
• Evaluate mixed expressions
Which of the following is equal to 4 and 2 over 3 divided by 3 and 1 over 2? A. 4 and 2 over 3 times 3 and 2 over 1 B. 14 over 3 times 2 over 7 C. 14 over 3 times 7 over 2 D. 42 over 3 times 2 over 31
• Sayavong
Sayavong is making cookies for the class. He has a recipe that calls for 3 and 1/2 cups of flour. He has 7/8 of a cup of wheat flour, and 2 and 1/2 cups of white flour. Does Mr. Sayavong have enough flour to make the cookies?
• Torque
Torque and Mari each multiplied 1/8 inch times 5/8 inch. Tartaric 5/8 squares point inches. And Marie got 5/64 squared thought inches tall. Which student found a corrupt area?
• Engineer Kažimír
The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri