# 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:

### 54/5 + 81/3 - 23/4 = 503/60 = 8 23/60 ≅ 8.3833333

Spelled result in words is five hundred three sixtieths (or eight and twenty-three sixtieths).

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

1. Conversion a mixed number 5 4/5 to a improper fraction: 5 4/5 = 5 4/5 = 5 · 5 + 4/5 = 25 + 4/5 = 29/5

To find a new numerator:
a) Multiply the whole number 5 by the denominator 5. Whole number 5 equally 5 * 5/5 = 25/5
b) Add the answer from previous step 25 to the numerator 4. New numerator is 25 + 4 = 29
c) Write a previous answer (new numerator 29) over the denominator 5.

Five and four fifths is twenty-nine fifths
2. Conversion a mixed number 8 1/3 to a improper fraction: 8 1/3 = 8 1/3 = 8 · 3 + 1/3 = 24 + 1/3 = 25/3

To find a new numerator:
a) Multiply the whole number 8 by the denominator 3. Whole number 8 equally 8 * 3/3 = 24/3
b) Add the answer from previous step 24 to the numerator 1. New numerator is 24 + 1 = 25
c) Write a previous answer (new numerator 25) over the denominator 3.

Eight and one third is twenty-five thirds
3. Add: 29/5 + 25/3 = 29 · 3/5 · 3 + 25 · 5/3 · 5 = 87/15 + 125/15 = 87 + 125/15 = 212/15
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, 3) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 3 = 15. In the following intermediate step, the fraction result cannot be further simplified by canceling.
In other words - twenty-nine fifths plus twenty-five thirds = two hundred twelve fifteenths.
4. Subtract: the result of step No. 3 - 23/4 = 212/15 - 23/4 = 212 · 4/15 · 4 - 23 · 15/4 · 15 = 848/60 - 345/60 = 848 - 345/60 = 503/60
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(15, 4) = 60. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 4 = 60. In the following intermediate step, the fraction result cannot be further simplified by canceling.
In other words - two hundred twelve fifteenths minus twenty-three quarters = five hundred three sixtieths.

#### 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: 7 is added to the sum of 4/5 and 6/7 3 3/4 + 2 3/5 + 5 1/2 Show your solution.
• 30 eggs There are 30 eggs in a tray. If 1/2 of the tray used 1/5 of it cooked,1/3 kept the refrigerator, how many eggs were left?
• Candies There are 150 candies in the bowl. Ivan took 7 thirtieths, Charles 6 fifteenths, and Thomas 3 tenths. How many sweets are left in the bowl?
• Of the 2 Of the shapes,1/6 are triangles and 5/12 are pentagons. What fraction of the shapes are either triangles or pentagons?
• 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.
• Simplify 3 Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
• Two numbers The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number.
• Bus vs train Milada took the bus and the journey took 55 minutes. Jarmila was 1h 20 min by train. They arrived in Prague at the same time 10h45 min. At what time did each have to go out?
• Length subtracting Express in mm: 5 3/10 cm - 2/5 mm
• Martin Martin is making a model of a Native American canoe. He has 5 1/2 feet of wood. He uses 2 3/4 feet for the hull and 1 1/4 feet for a paddle. How much wood does he have left? Martin has feet of wood left.
• Barrels Peter has 42 barrels. One-sixth of them are filled with lemonade, one third is filled with wine and half is empty. Calculate how many barrels are with each filling.
• The book 4 Mr. Kinion read 3 3/4 chapters in his book on Monday. He then read 2 4/6 more chapters on Tuesday. How many chapters has he read so far?