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:

(3/5) : (2 1/2) = 6/25 = 0.24

Spelled result in words is six twenty-fifths.

How do you solve fractions step by step?

  1. 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 a 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
  2. Divide: 3/5 : 5/2 = 3/5 · 2/5 = 3 · 2/5 · 5 = 6/25
    Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 5/2 is 2/5) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - three fifths divided by five halfs = six twenty-fifths.

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:

  • Larry 2
    piano Larry spends half of his workday teaching piano lessons. If he sees 6 students, each for the same amount of time, what fraction of his workday is spent with each student?
  • I have
    water2 I have 1/5 of an ounce of water left. I separate the water equally into two cups. How many ounces of water are in each cup?
  • Two divided
    fractions14 Two divided by nine-tenths.
  • Evaluate expression
    mixed_fractions Evaluate expression using BODMAS rule: 1 1/4+1 1/5÷3/5-5/8
  • The third
    meter The one-third rod is blue, one-half of the rod is red, the rest of the rod is white and measures 8 cm. How long is the whole rod?
  • Ornamental shrubs
    delnik Children committed to planting 240 ornamental shrubs. Their commitment, however, exceeded by 48 shrubs. Write the ratio of actually planted shrubs and commitment by lowest possible integers a/b.
  • Pediatrician
    doctor Pediatrician this month of 20 working days takes 8 days holidays. What is the probability that on Monday it will be at work?
  • TV fail
    old_tv The TV has after 10,000 hours average 35 failures. Determine the probability of TV failure after 400 hours of operation.
  • Lemonade 4
    lemonade Six friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
  • How many 15
    fractions How many six-eights are there in 18? Which of the following would you choose to solve this question? 18 x 6/8 or 18 : 6/8
  • If Ben
    age If Ben is ⅕ the age of his father, ¼ the age of his mother, and twice the age of his sister, how old are his parents and sister if he is 8 years old?
  • A glass
    cups A glass holds 3/4 cups. A jug holds 12 cups. How many glasses can be filled?
  • Camp
    skauti In the camp are children. 1/2 went on a trip, 1/4 went to bathe, and 38 children remained in the room. How many children are in the camp?


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