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 9/15 + 3 10/15 = 94/15 = 6 4/156.2666667

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 2 9/15 to a improper fraction: 2 9/15 = 2 9/15 = 2 · 15 + 9/15 = 30 + 9/15 = 39/15

    To find a new numerator:
    a) Multiply the whole number 2 by the denominator 15. Whole number 2 equally 2 * 15/15 = 30/15
    b) Add the answer from previous step 30 to the numerator 9. New numerator is 30 + 9 = 39
    c) Write a previous answer (new numerator 39) over the denominator 15.

    Two and nine fifteenths is thirty-nine fifteenths
  2. Conversion a mixed number 3 10/15 to a improper fraction: 3 10/15 = 3 10/15 = 3 · 15 + 10/15 = 45 + 10/15 = 55/15

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 15. Whole number 3 equally 3 * 15/15 = 45/15
    b) Add the answer from previous step 45 to the numerator 10. New numerator is 45 + 10 = 55
    c) Write a previous answer (new numerator 55) over the denominator 15.

    Three and ten fifteenths is fifty-five fifteenths
  3. Add: 39/15 + 55/15 = 39 + 55/15 = 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(15, 15) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 15 = 225. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - thirty-nine fifteenths plus fifty-five fifteenths = ninety-four fifteenths.

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:

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:

  • Expressions
    Let k represent an unknown number, express the following expressions: 1. The sum of the number n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n
  • Simplify 3
    Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
  • 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
  • An orchard
    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
  • 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?
  • Math test
    Brayden was solving some math problems for the math team. He answered 2 math problems. Matthew answered 3, John answered 1 reasoning. Matthew 1/2 times as many. Brayden said that 2/6. Is he correct? Why or why not? Be sure to explain your answer.
  • Product and sum
    What is the product of two fourths  and the sum of three halves and four?
  • Weigh in total
    I put 3/5 kg of grapes into a box which is 1/4kg in weight. How many kilograms do the grapes and the box weigh in total?
  • Honey 3
    Honey jogged 1 3/4 km on Monday,1 1/2 km on Wednesday and 1  2/3 km on Friday . how far did he jog?
  • 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.
  • Length subtracting
    Express in mm: 5 3/10 cm - 2/5 mm
  • Interior designer
    To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies?
  • Submerging
    Monika dove 9 meters below the ocean's surface. She then dove 13 meters deeper. Then she rose 19 and one-fourth meters. What was her position concerning the water's surface (the water surface = 0, minus values = above water level, plus = above water level


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