# 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:

### 72/3 + 93/4 = 209/12 = 17 5/12 ≅ 17.4166667

Spelled result in words is two hundred nine twelfths (or seventeen and five twelfths).

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

1. Conversion a mixed number 7 2/3 to a improper fraction: 7 2/3 = 7 2/3 = 7 · 3 + 2/3 = 21 + 2/3 = 23/3

To find new numerator:
a) Multiply the whole number 7 by the denominator 3. Whole number 7 equally 7 * 3/3 = 21/3
b) Add the answer from previous step 21 to the numerator 2. New numerator is 21 + 2 = 23
c) Write a previous answer (new numerator 23) over the denominator 3.

Seven and two thirds is twenty-three thirds
2. Conversion a mixed number 9 3/4 to a improper fraction: 9 3/4 = 9 3/4 = 9 · 4 + 3/4 = 36 + 3/4 = 39/4

To find new numerator:
a) Multiply the whole number 9 by the denominator 4. Whole number 9 equally 9 * 4/4 = 36/4
b) Add the answer from previous step 36 to the numerator 3. New numerator is 36 + 3 = 39
c) Write a previous answer (new numerator 39) over the denominator 4.

Nine and three quarters is thirty-nine quarters
3. Add: 23/3 + 39/4 = 23 · 4/3 · 4 + 39 · 3/4 · 3 = 92/12 + 117/12 = 92 + 117/12 = 209/12
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, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - twenty-three thirds plus thirty-nine quarters = two hundred nine twelfths.

#### 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:

adding fractions: 2/4 + 3/4
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:

• Berry Smoothie
Rory has 5/8 cup of milk. How much milk does she have left after she doubles the recipe of the smoothie? Berry Smoothie: 2 cups strawberries 1 cup blueberries 1/4 cup milk 1 tbsp (tablespoon) sugar 1/2 tsp (teaspoon) lemon juice 1/8 tsp (teaspoon) vanilla
• Sum of 18
Sum of two fractions is 4 3/7. If one of the fractions is 2 1/5 find the other one .
• Circular garden
Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante
• Adding mixed 3
Why does 1 3/4 + 2 9/10 equal 4.65? How do you solve this?
• Salad
We need two tenths kg of a carrot, one tenth of peas and three tenths of of tomatoes to make salad. Express the fraction of the weight of the vegetables to be salad. Convert the result to grams.
• Baxter
Baxter ate 1/12 of a box of dog food. Now the box is 3/4 full. What fraction of the full of a full box was there before Baxter?
• Two pizzas
Jacobs mom bought two whole pizzas. He ate 2/10 of the pizza and his dad ate 1 1/5. How much is left.
• 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?
• Fractions mul add sum
To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
• All tasks - taskman
Skilled workshop master washes client car 1/5 hour, cleaned the client's car in 5/4 hour, and painted small defects on car 1 1/3 hour. How long did it take him to do all the necessary work tasks?
• Quotient and product
If the quotient of [8/5 divided by 8/10] is added to the product of [8/14 x 7/12 x 3/8], what is the sum?
• Eight pipes
Eight pipes are each 2¼m long . what is the total length of the eight pipes?
• 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.