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 5/10 - 1 3/5 = 19/10 = 1 9/10 = 1.9

Spelled result in words is nineteen tenths (or one and nine tenths).

How do you solve fractions step by step?

  1. Conversion a mixed number 3 5/10 to a improper fraction: 3 5/10 = 3 5/10 = 3 · 10 + 5/10 = 30 + 5/10 = 35/10

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 10. Whole number 3 equally 3 * 10/10 = 30/10
    b) Add the answer from previous step 30 to the numerator 5. New numerator is 30 + 5 = 35
    c) Write a previous answer (new numerator 35) over the denominator 10.

    Three and five tenths is thirty-five tenths
  2. Conversion a mixed number 1 3/5 to a improper fraction: 1 3/5 = 1 3/5 = 1 · 5 + 3/5 = 5 + 3/5 = 8/5

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5
    b) Add the answer from previous step 5 to the numerator 3. New numerator is 5 + 3 = 8
    c) Write a previous answer (new numerator 8) over the denominator 5.

    One and three fifths is eight fifths
  3. Subtract: 35/10 - 8/5 = 35/10 - 8 · 2/5 · 2 = 35/10 - 16/10 = 35 - 16/10 = 19/10
    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(10, 5) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 5 = 50. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - thirty-five tenths minus eight fifths = nineteen tenths.

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:

  • Difference of two fractions
    subaru1 What is the difference between 1/2 and 1/6? (Write the answer as a fraction in lowest terms. )
  • Michael
    chocholate Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?
  • Mrs. Susan
    textiles Mrs. Susan bought 1/8 m of curtain cloth. She used 3/5 m to make a curtain for the living room window. How many meters of cloth were not used?
  • Issac
    pizza Issac eats 1/6 of the pizza. Maya then eats 3/5 of the remaining pizza. What fraction of the original pizza is left?
  • Antonio
    mixed Antonio is thinking of an improper fraction and a mixed fraction which have a sum of 5 5/12. The improper fraction is 8/3. What is the mixed number?
  • On day
    vylet On day one of the trip they drove 1/4 of the total distance. On day two they drove 1/2 of the total distance. What fraction of the total distance is left to travel?
  • Karina
    textiles Karina has 5 4/7 meters of cloth. She needs 3 1/6 meters of it in making a curtain for her window. How many meters of cloth were left to her after making the curtain?
  • Bucket of clay
    sand Tina and Bill share a 12-ounce bucket of clay. By the end of the week, Tina has used 1/6 of the bucket, and Bill has used 2/3 of the bucket of clay. How many ounces are left in the bucket?
  • Magic bag
    mince Each time the prince crossed the bridge, the number of tolars in the magic bag doubled. But then the devil always conjured 300 tolars for him. When this happened for the third time, the prince had twice as much as he had in the beginning. How many tolars
  • Farmer 5
    bagSoil Farmer Joe ordered 3 bags of soil last month. Each bag weighed 4 ⅖ kilograms. He used the first bag in a week. At the end of this month, there were 2 ¾ kilograms of soil left in the second bag and ⅞ kilograms of soil left in the third bag. How much soil w
  • Benhur
    water2 Benhur boiled 1 1/4 liters of water in a kettle. After 10 1/2 minutes he measured the water again. It had 3/4 liters left in the kettle. What is the amount of water that evaporates every minutes?
  • Pizza cover
    pizza 5/8 of the pizza is covered in mushrooms, 1/4 of the pizza is covered with pineapples, and the rest of the pizza is covered with only cheese. What fraction of the pizza is covered with only cheese?
  • 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?


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