# 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:

### - 3/8 * -4/9 = 1/6 ≅ 0.1666667

Spelled result in words is one sixth.

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

1. Unary minus: -3/8 = -3/8
2. Multiple: the result of step No. 1 * (-4) = -3/8 * (-4) = -3 · (-4)/8 · 1 = 12/8 = 3 · 4/2 · 4 = 3/2
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(12, 8) = 4. In the next intermediate step, , cancel by a common factor of 4 gives 3/2.
In words - minus three eighths multiplied by minus four = three halfs.
3. Divide: the result of step No. 2 : 9 = 3/2 : 9 = 3/2 · 1/9 = 3 · 1/2 · 9 = 3/18 = 3 · 1 /3 · 6 = 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 9/1 is 1/9) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 3 gives 1/6.
In words - three halfs divided by nine = one sixth.

#### 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:

• Difference of two fractions
What is the difference between 1/2 and 1/6? (Write the answer as a fraction in lowest terms. )
• Pounds
3 pounds subtract 1/3 of a pound.
• Emily
Emily had 20 minutes to do a three-problem quiz. She spent 11 3/4 minutes on question A and 5 1/2 minutes on question B. How much time did she have left for question C?
• Pupils 7
There are 40 pupils in a certain class. 3/5 of the class are boys. How many are girls?
• Plums
In the bag was to total 136 plums. Igor took 3 plums and Mary took 4/7 from the rest. How many plums remained in the bag?
• The pet
Ananya has a bunny. She bought 4 7/8 pounds of carrots. She fed her bunny 1 1/4 pounds of carrots the first week. She fed her bunny 5/6 pounds of carrots the second week. All together, how many pounds of carrots did she feed her bunny? 1. Draw a tape diag
• A 14.5-gallon
A 14.5-gallon gasoline tank is 3/4 full. How many gallons will it take to fill the tank? Write your answer as a mixed number.
• Evaluate 17
Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form.
• Pizzas
Billy ate 1 1/4 pizzas and John ate 1 2/3 pizzas. How much more pizza did John eat than Billy?
• Magic bag
Each time the prince crossed the bridge, the number of tolars in the magic bag doubled. But then the devil always conjured 300 tolars for him. When this happened for the third time, the prince had twice as much as he had in the beginning. How many tolars
• Players - baseball
There are 20 players on each of two baseball teams. If 2/5 of the players on team 1 miss practice and 1/4 of the players on team two miss practice, how many more players from team 1 missed practice then team 2?
• Seven up
Peter barman is making 8 gallons of Tropical trip punch. He has already poured in 1 3/4 gal of pineapple juice and 2 1/2 gal of orange juice. The only other ingredient us 7-Up. How much does 7-Up does Peter need?
• Honey 2
The baker has 3/4 liter of honey and decided to bake a few honeycombs and biscuits from it. 1/6 liter of honey was needed for honeycombs and 1/4 liter for biscuits. How much honey did she have left after baking honeycombs and biscuits?