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:

1/2 + 2/5 + 6 2/7 = 503/70 = 7 13/70 ≅ 7.1857143

Spelled result in words is five hundred three seventieths (or seven and thirteen seventieths).

How do you solve fractions step by step?

  1. Add: 1/2 + 2/5 = 1 · 5/2 · 5 + 2 · 2/5 · 2 = 5/10 + 4/10 = 5 + 4/10 = 9/10
    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(2, 5) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 5 = 10. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - one half plus two fifths = nine tenths.
  2. Conversion a mixed number 6 2/7 to a improper fraction: 6 2/7 = 6 2/7 = 6 · 7 + 2/7 = 42 + 2/7 = 44/7

    To find new numerator:
    a) Multiply the whole number 6 by the denominator 7. Whole number 6 equally 6 * 7/7 = 42/7
    b) Add the answer from previous step 42 to the numerator 2. New numerator is 42 + 2 = 44
    c) Write a previous answer (new numerator 44) over the denominator 7.

    Six and two sevenths is forty-four sevenths
  3. Add: the result of step No. 1 + 44/7 = 9/10 + 44/7 = 9 · 7/10 · 7 + 44 · 10/7 · 10 = 63/70 + 440/70 = 63 + 440/70 = 503/70
    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(10, 7) = 70. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 7 = 70. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - nine tenths plus forty-four sevenths = five hundred three seventieths.

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:

  • Dividends
    money The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least?
  • Paper collecting
    sber At the paper collecting contest gathered Franta 2/9 ton, Karel 1/4 ton, and Patrick 19/36 tons of paper. Who has gathered the most and the least?
  • A laundry
    prasok Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
  • Pizza palace
    pizza Josh is at Enzo's pizza palace. He can sit at a table with 5 of his friends or at a different table with seven of his friends. The same size pizza is shared equally among the people at each table. At which table should Josh sit to get more pizza? (write a
  • 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.
  • Arrange
    compare Arrange the following in descending order: 0.32, 2on5, 27%, 1 on 3
  • Evaluate mixed expressions
    mixed Which of the following is equal to 4 and 2 over 3 divided by 3 and 1 over 2? A. 4 and 2 over 3 times 3 and 2 over 1 B. 14 over 3 times 2 over 7 C. 14 over 3 times 7 over 2 D. 42 over 3 times 2 over 31
  • Sandy
    kolac Sandy, John and Marg baked pies for the Bake Sale. Sandy cut his pies into 6ths, John but his into 8ths and Marg cut hers into quarters. Sandy sold 11/6, John sold  1 3/8 pies and Marg sold 9/4 pies. Who sold the most pies? Who sold the fewest?
  • Torque
    rectangles Torque and Mari each multiplied 1/8 inch times 5/8 inch. Tartaric 5/8 squares point inches. And Marie got 5/64 squared thought inches tall. Which student found a corrupt area?
  • Sayavong
    vaha2 Sayavong is making cookies for the class. He has a recipe that calls for 3 and 1/2 cups of flour. He has 7/8 of a cup of wheat flour, and 2 and 1/2 cups of white flour. Does Mr. Sayavong have enough flour to make the cookies?
  • Pumpkin pie
    pumpkin pie Have some pumpkin pie. One half of the pie is cut into 4 equal slices, the other half is cut into 3 equal slices. After eating one of the larger slices (on the 3 piece side), I wonder if I will eat more if I have one more from the 3 side, or two from the
  • How many
    zlomky How many integers are greater than 547/3 and less than 931/4?
  • Engineer Kažimír
    demagog_smer The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri


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