# 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:

### 32/3 + 23/5 = 94/15 = 6 4/15 ≅ 6.2666667

Spelled result in words is ninety-four fifteenths (or six and four fifteenths).

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

1. Conversion a mixed number 3 2/3 to a improper fraction: 3 2/3 = 3 2/3 = 3 · 3 + 2/3 = 9 + 2/3 = 11/3

To find new numerator:
a) Multiply the whole number 3 by the denominator 3. Whole number 3 equally 3 * 3/3 = 9/3
b) Add the answer from previous step 9 to the numerator 2. New numerator is 9 + 2 = 11
c) Write a previous answer (new numerator 11) over the denominator 3.

Three and two thirds is eleven thirds
2. Conversion a mixed number 2 3/5 to a improper fraction: 2 3/5 = 2 3/5 = 2 · 5 + 3/5 = 10 + 3/5 = 13/5

To find new numerator:
a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/5 = 10/5
b) Add the answer from previous step 10 to the numerator 3. New numerator is 10 + 3 = 13
c) Write a previous answer (new numerator 13) over the denominator 5.

Two and three fifths is thirteen fifths
3. Add: 11/3 + 13/5 = 11 · 5/3 · 5 + 13 · 3/5 · 3 = 55/15 + 39/15 = 55 + 39/15 = 94/15
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(3, 5) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - eleven thirds plus thirteen fifths = ninety-four fifteenths.

#### 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:

• Expressions with variable
This is algebra. Let n represent an unknown number and write the following expressions: 1. 4 times the sum of 7 and the number x 2. 4 times 7 plus the number x 3. 7 less than the product of 4 and the number x 4. 7 times the quantity 4 more than the number
• Lengths of the pool
Miguel swam 6 lengths of the pool. Mat swam 3 times as far as Miguel. Lionel swam 1/3 as far as Miguel. How many lengths did Mat swim?
• Fitness center
Every Wednesday, Monica works out for 3/4  of an hour at the fitness center. Every Saturday, he goes to the fitness center again and exercises for 3 times as long. How much time does Wayne spend at the fitness center in all each week?
Divide number 135 into two additions so that one adds 30 more than 2/5 of the other add. Write the bigger one.
• Recipe ingredients
Monica’s cookie recipe calls for Three-fourths of a cup of flour. Her mother’s recipe calls for Two-thirds as much as Monica’s. How many cups of flour does her mother’s recipe require?
• Metal rod
You have a metal rod that’s 51/64 inches long. The rod needs to be trimmed. You cut 1/64 inches from one end and 1/32 inches from the other end. Next, you cut the rod into 6 equal pieces. What will be the final length of each piece?
• 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)
• Walk for exercise
Anya, Jose, Cali, and Stephan walk for exercise. Anya's route is 2 1/4 kilometers long. Jose's route is 1 1/2 fewer km. Cali's route is 1 1/2  times as long as Jose's route, and 2 fewer km than Stephan's route. What distance (S) is Stephan's route?
• Farmer 5
Farmer Joe ordered 3 bags of soil last month. Each bag weighed 4 ⅖ kilograms. He used the first bag in a week. At the end of this month, there were 2 ¾ kilograms of soil left in the second bag and ⅞ kilograms of soil left in the third bag. How much soil w
• Three friends
John, Peter, and Pablo each carried a 24 liters bucket full of water down the hill. After they reached the bottom, John's bucket was only 3/4 full, Peter's bucket was 2/3 full, and Pablo's was 1/6 full. How much liters of water did they spill altogether o
• Rose spends
Rose spends 2 1/3 hours studying Math, 1 3/4 hours studying English, and 2 1/4 hours studying Science. Find her average time studying the three subjects.
• Sum three fractions
Work out the sum of 1/4, 1/5 and 3/10.
• Notebooks
Liza, a store owner, buys 560 notebooks. He sold 3/8 of the notebook, and then she adds the stock of a notebook of 1/4 of the number of notebooks she bought. What is the total number of notebooks she purchased?