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:

2 1/4 + 1 2/5 = 73/20 = 3 13/20 = 3.65

Spelled result in words is seventy-three twentieths (or three and thirteen twentieths).

How do you solve fractions step by step?

  1. 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
  2. Conversion a mixed number 1 2/5 to a improper fraction: 1 2/5 = 1 2/5 = 1 · 5 + 2/5 = 5 + 2/5 = 7/5

    To find new numerator:
    a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5
    b) Add the answer from previous step 5 to the numerator 2. New numerator is 5 + 2 = 7
    c) Write a previous answer (new numerator 7) over the denominator 5.

    One and two fifths is seven fifths
  3. Add: 9/4 + 7/5 = 9 · 5/4 · 5 + 7 · 4/5 · 4 = 45/20 + 28/20 = 45 + 28/20 = 73/20
    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(4, 5) = 20. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - nine quarters plus seven fifths = seventy-three 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:

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:

  • Food weight
    vaha Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal, today she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 o
  • Tom has
    water2 Tom has a water tank that holds 5 gallons of water. Tom uses water from a full tank to fill 6 bottles that each hold 16 ounces and a pitcher that holds 1/2 gallon. How many ounces of water are left in the water tank?
  • Evaluate
    calculator The division of numbers $a and $b increase by-product of the numbers $c and $d
  • Complicated sum minus product
    plusminus What must be subtracted from the sum of 3/8 and 5/16 to get difference equal to the product of 5/8 and 3/16?
  • Expressions with variable
    plusminus 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
  • Conversion of units
    meter Complete the following length data
  • Of the 2
    pentagon Of the shapes,1/6 are triangles and 5/12 are pentagons. What fraction of the shapes are either triangles or pentagons?
  • Mac painter
    painter Mac is mixing red and white paint to make pink for his candy painting. He uses 1/4 ounce of red paint and 2/3 ounce of white paint. How many ounces of paint did he use?
  • Marbles
    ball_f Dave had 40 marbles. Junjun has 2 1/5 more than Dave’s marbles. How many marbles do they have altogether?
  • Patel
    juice Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first orange, 3/10 cups from the second orange, StartFraction 9 over 20 E
  • An orchard
    apples During a visit to an orchard, Greg picked 3/5 of a bag of delicious golden apples, 4/5 of a bag of Macintosh apples, 2/5 of a bag of Cortland apples, 1/5 of a bag of Bartlett pears, and 4/5 of a bag of Bosch pears. How many bags of fruit to Greg pick in t
  • Walk for exercise
    runners 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?
  • Area and perimeter 2
    rectangle_diagonals Find the area and the perimeter of a rectangle of length 45 1/2 cm and breadth 16 2/3 cm.


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