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:

5 4/7 - 2 1/2 = 43/14 = 3 1/143.0714286

Spelled result in words is forty-three fourteenths (or three and one fourteenth).

How do you solve fractions step by step?

  1. Conversion a mixed number 5 4/7 to a improper fraction: 5 4/7 = 5 4/7 = 5 · 7 + 4/7 = 35 + 4/7 = 39/7

    To find new numerator:
    a) Multiply the whole number 5 by the denominator 7. Whole number 5 equally 5 * 7/7 = 35/7
    b) Add the answer from previous step 35 to the numerator 4. New numerator is 35 + 4 = 39
    c) Write a previous answer (new numerator 39) over the denominator 7.

    Five and four sevenths is thirty-nine sevenths
  2. Conversion a mixed number 2 1/2 to a improper fraction: 2 1/2 = 2 1/2 = 2 · 2 + 1/2 = 4 + 1/2 = 5/2

    To find new numerator:
    a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/2 = 4/2
    b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
    c) Write a previous answer (new numerator 5) over the denominator 2.

    Two and one half is five halfs
  3. Subtract: 39/7 - 5/2 = 39 · 2/7 · 2 - 5 · 7/2 · 7 = 78/14 - 35/14 = 78 - 35/14 = 43/14
    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(7, 2) = 14. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 2 = 14. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - thirty-nine sevenths minus five halfs = forty-three fourteenths.

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:

  • School
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  • Hussein
    penize Hussein owns 450000 crowns (local currency). He spent at the bookstore 2 over 9 to buy some books and tales. He paid 3 over 5 of his money to buy his math book. a. Calculate the remaining amount of money with Hussein? b. Hussein lost 3 over 4 of the remai
  • Simplify 3
    fractal Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
  • Equation with mixed 2
    mixed A number, X, is subtracted from 8 1/4. The result is 12 3/5. What is the value of X?
  • 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
  • Visit to grandfather
    family Shane's family traveled 3/10 of the distance to his grandfather’s house on Saturday. They traveled 4/7 of the remaining distance on Sunday. What fraction of the total distance to his grandfather’s house was traveled on Sunday?
  • Lunch time
    skola In a cafeteria, 3/10 of the students are eating salads, and 3/5 are eating sandwiches. There are 30 students in the cafeteria. How many students are eating lunches other than salads or sandwiches?
  • Cookies
    cookies In a cookie jar, 1/4 of the cookies are chocolate chip and 1/2 of the rest are peanut butter. What fraction of all the cookies are peanut butter?
  • Math test
    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.
  • The boy
    time The boy scouts spent 10/12 hour doing their daily exercises. They only used 1/4 hour in hiking. How much time did they use for other body exercises?
  • Kenneth
    painter Kenneth is painting his kitchen and bathroom. He bought 5 gallons of paint to paint the two rooms. He uses 1/4 of that amount to paint the bathroom and the rest to paint the kitchen. How many gallons of paint did Kenneth use to paint the kitchen?
  • Cereals
    kombajn Ari and Joey share a 30-ounce box of cereal. By the end of the week, Ari has eaten 3/10 of the box, and Joey has eaten 3/5 of the box of cereal. How many ounces are left in the box?
  • Evaluate 17
    fractions Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form.


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