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:

15 - 10 5/12 = 55/12 = 4 7/124.5833333

Spelled result in words is fifty-five twelfths (or four and seven twelfths).

How do you solve fractions step by step?

  1. Conversion a mixed number 10 5/12 to a improper fraction: 10 5/12 = 10 5/12 = 10 · 12 + 5/12 = 120 + 5/12 = 125/12

    To find a new numerator:
    a) Multiply the whole number 10 by the denominator 12. Whole number 10 equally 10 * 12/12 = 120/12
    b) Add the answer from previous step 120 to the numerator 5. New numerator is 120 + 5 = 125
    c) Write a previous answer (new numerator 125) over the denominator 12.

    Ten and five twelfths is one hundred twenty-five twelfths
  2. Subtract: 15 - 125/12 = 15/1 - 125/12 = 15 · 12/1 · 12 - 125/12 = 180/12 - 125/12 = 180 - 125/12 = 55/12
    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(1, 12) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 12 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - fifteen minus one hundred twenty-five twelfths = fifty-five twelfths.

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:

  • Farmer Peter
    chicken Farmer Peter paints 12 chicken coop. He started painting this day morning. Now he only has 1/4 of the chicken coop left to paint this afternoon. How many chicken coops did farmer Peter paint this morning?
  • Wood 11
    wood Father has 12 1/5 meters long wood. Then I cut the wood into two pieces. One part is 7 3/5 meters long. Calculate the length of the other wood?
  • Pupils 7
    skola There are 40 pupils in a certain class. 3/5 of the class are boys. How many are girls?
  • Curtain
    textiles Mrs. Lazo bought 9 1/8 m curtain cloth. She used 3 5/6 m to make a curtain for their bedroom. How many meters of cloth were not used?
  • 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?
  • Toilets
    toilet Federal law requires that all residential toilets sold in the United States use no more than 1 3/5 gallons of water per flush. Before this legislation, conventional toilets used 3 2/5 gallons of water per flush. Find the amount of water saved in one year
  • Sugar 8
    sugar Heather has 2 cups of powdered sugar. She sprinkles 3/5 of the sugar onto a plate of brownies and sprinkles the rest into a plate of lemon cookies. How much sugar does Heather sprinkle on the brownies? How much sugar does Heather sprinkle on the lemon coo
  • Maria 3
    clocks Maria spent two eighths of her holiday in Town A, two fifth in Town B and the rest on travelling. What fraction of her holiday did she spend on travelling?
  • 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?
  • Package
    latky The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
  • Forty
    skola Forty five of the 80 students were girls. What is the ratio of girls to boys?
  • King
    kral King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers?
  • Add sub fractions
    fractions What is 4 1/2+2/7-213/14?


next math problems »