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:

3/4 / 5/6 = 9/10 = 0.9

Spelled result in words is nine tenths.

How do you solve fractions step by step?

  1. Divide: 3/4 : 5/6 = 3/4 · 6/5 = 3 · 6/4 · 5 = 18/20 = 2 · 9 /2 · 10 = 9/10
    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 5/6 is 6/5) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 2 gives 9/10.
    In other words - three quarters divided by five sixths = nine 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:

  • 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?
  • Gear wheels
    gear Two gear wheels, which fit together, have the number of teeth z1=58 and z2=149. Calculate the speed of the first wheel, if the second wheel rotates 1232 revolutions per minute.
  • Drinking water
    blue-barrel A man drinks a keg of water in 40 days, and a woman drinks in 62 days. How many days do they consume a keg together?
  • Divide 13
    delnik Divide. Simplify your answer and write as an improper fraction or whole number. 14÷8/3
  • Women
    smajlik In a company of 1050 employees are 2/3 women. How many women work in the company?
  • Lauren
    clocks Lauren is tutoring students at the library on Saturday. If she is at the library for a total of 6 hours and she helps each student, one at a time, for three-fourths of an hour, how many students does she tutor?
  • Lemonade
    lemonade How many 1/4 cup servings are in 2 and 1/3 cups of lemonade?
  • 6/24 change
    numbers 6/24 change to a fraction in lowest terms
  • The rope 2
    rope The rope in the school gym is 10 ½ feet long. To make it easier to climb, Coach Hill tied a knot in the rope every ¾ foot. How many knots are in the rope?
  • The carpenters
    wood The carpenters cut the beam. Half of the cut pieces were 1 meter long, a quarter of the pieces were two meters long and the remaining 8 meters of the beam were cut into two equal parts. - What was the length of the original beam? - What part of the origin
  • Jordan
    cake Jordan wants to bring in cookie cakes to share with his 23 classmates for his birthday. His mom is willing to buy no more than 6 cookie cakes and Jordan must share the cakes equally between his classmates (and himself). Answer the questions to help Jordan
  • Dana helped
    sand Dana helped her dad build a sandbox for her younger sister. The sandbox is shaped like a rectangular prism that is 4 1/2 feet long and 4 feet wide. Dana used bags of sand to fill the sandbox 1/2 of a foot deep. Each bag contained 1/2 of a cubic foot of sa
  • ŽSR
    luzianky Calculate fixed annual personnel costs of operating monorail line 118 km long if every 5 km is a station, which serves three people - one dispatcher and two switchmen in 4-shift operation. Consider the average salary of the employee 885 €.


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