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 3/4 + 1 1/2 = 17/4 = 4 1/4 = 4.25

Spelled result in words is seventeen quarters (or four and one quarter).

How do you solve fractions step by step?

  1. Conversion a mixed number 2 3/4 to a improper fraction: 2 3/4 = 2 3/4 = 2 · 4 + 3/4 = 8 + 3/4 = 11/4

    To find a 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 3. New numerator is 8 + 3 = 11
    c) Write a previous answer (new numerator 11) over the denominator 4.

    Two and three quarters is eleven quarters
  2. Conversion a mixed number 1 1/2 to a improper fraction: 1 1/2 = 1 1/2 = 1 · 2 + 1/2 = 2 + 1/2 = 3/2

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 2. Whole number 1 equally 1 * 2/2 = 2/2
    b) Add the answer from previous step 2 to the numerator 1. New numerator is 2 + 1 = 3
    c) Write a previous answer (new numerator 3) over the denominator 2.

    One and one half is three halfs
  3. Add: 11/4 + 3/2 = 11/4 + 3 · 2/2 · 2 = 11/4 + 6/4 = 11 + 6/4 = 17/4
    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, 2) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 2 = 8. In the following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - eleven quarters plus three halfs = seventeen quarters.

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:

  • Adding denominators
    plusminus Max is working out 2/3+7/9. He says the answer is 9/12. What mistake have Max made?
  • Berry Smoothie
    milk 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
    mixed_fractions Sum of two fractions is 4 3/7. If one of the fractions is 2 1/5 find the other one .
  • Circular garden
    seed 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
    mixed_fractions Why does 1 3/4 + 2 9/10 equal 4.65? How do you solve this?
  • Salad
    salát 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
    dog 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
    pizza 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
    books 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
    fractions 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
    clocks 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
    plusminus 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
    pipe1 Eight pipes are each 2¼m long. What is the total length of the eight pipes?


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