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 * 2/3 = 1/2 = 0.5

Spelled result in words is one half.

How do you solve fractions step by step?

  1. Multiple: 3/4 * 2/3 = 3 · 2/4 · 3 = 6/12 = 1 · 6/2 · 6 = 1/2
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(6, 12) = 6. In the following intermediate step, cancel by a common factor of 6 gives 1/2.
    In other words - three quarters multiplied by two thirds = one half.

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:

  • Jeff rode
    Jeff rode his bike around a bike trail that was 1/3 of a mile long. He rode around the trail 9 times. Write a fraction greater than 1 for the distance. How many miles did Jeff ride?
  • The kennel
    20 dogs. Ratio dogs to cats is 3:2  how many cats?
  • Sixth graders
    About 6/9 of the sixth- grade pupils will be going to the parents' seminar. If 1/6 of the participants are girls, what part of the portion of sixth graders are boys?
  • In bucket
    In bucket of 87 oranges 1/3 are spoiled ones and the remaining are eaten by the member of a family. How many oranges are eaten by the member of family?
  • Yellow tangs
    In an aquarium 2/5 of the fish are surgeonfish.  Of these 3/4 are yellow tangs.  What fraction of all fish in the aquarium are yellow tangs?
  • Lunch time
    In a cafeteria, 3/10 of the students are eating salads, and 3/5 are eating sandwiches. There are 30 students in the cafeteria. How many students are eating lunches other than salads or sandwiches?
  • Sugar 8
    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
  • Twelve eggs
    A dozen eggs cost 80 cents . how much will 3½ dozen eggs cost?
  • Enrollees
    The enrolment for this school year in Villahermosa integrated school is 276. If 1/3 are grade ten and are 1/4 grade seven, how many are grade eight and grade nine enrollees?
  • Sally
    Sally is making 15 individual blueberry cheesecakes. How many pounds of blueberries will be in each cheesecake if 5 1/4 pounds of blueberries are divided equally among them?
  • A farmer 3
    A farmer sells 9.3 kg of pears and apples at the farmers market.3/4 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmers market.
  • Cereals
    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?
  • The elevation
    The elevation of a sunken ship is -120 feet. Your elevation is 5/8 of the ship’s elevation. What is your elevation?


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