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:

2/5 * 15/4 = 3/2 = 1 1/2 = 1.5

Spelled result in words is three halfs (or one and one half).

How do you solve fractions step by step?

  1. Multiple: 2/5 * 15/4 = 2 · 15/5 · 4 = 30/20 = 3 · 10/2 · 10 = 3/2
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(30, 20) = 10. In the following intermediate step, cancel by a common factor of 10 gives 3/2.
    In other words - two fifths multiplied by fifteen quarters = three halfs.

Rules for expressions with fractions:

Fractions - use the 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 non-zero 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:

  • Lengths of the pool
    bazen2 Miguel swam 6 lengths of the pool. Mat swam 3 times as far as Miguel. Lionel swam 1/3 as far as Miguel. How many lengths did Mat swim?
  • Expressions with variable
    plusminus This is algebra. Let n represent an unknown number and write the following expressions: 1. 4 times the sum of 7 and the number x 2. 4 times 7 plus the number x 3. 7 less than the product of 4 and the number x 4. 7 times the quantity 4 more than the number
  • Youth track
    tunel Youth track from Hronská Dúbrava to Banská Štiavnica which announced cancellation attracted considerable media attention and public opposition, has cost 6.3 euro per capita and revenue 13 cents per capita. Calculate the size of subsidies to a trip group o
  • The machine
    clocks2 The machine was in operation for 9 tenths (in a fraction) of eight hours of working time. How long has he been running?
  • Brownies
    cukr Mrs. Merritt made brownies, the recipe had to be cut in 1/2. The recipe called for 2 5/8 cups of sugar. How much sugar did she use?
  • Fitness center
    time Every Wednesday, Monica works out for 3/4  of an hour at the fitness center. Every Saturday, he goes to the fitness center again and exercises for 3 times as long. How much time does Wayne spend at the fitness center in all each week?
  • 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?
  • Caroline
    flasa Caroline collected 3 ¼ bags of recycling to take to the recycling center. ⅓ of the bags are glass bottles. How many bags will be filled with glass bottles?
  • Golf balls
    balls2 Of the 28 golf balls, 1/7 are yellow. How many golf balls are yellow? Use the model to help you. Enter your answer in the box.
  • DIY press
    typewriter Under socialism regime was in some socialist countries to own a typewriter requires special permission. That has hindered the spread of DIY literature (manually transcribed through carbon copy paper for typewriters). Calculate how many typewriters today c
  • A basket
    mangoes A basket is full of 50 different kinds of fruits that has a ratio of 2:3:5. If the fruits are apple, mango, and guava, how many guavas are there?
  • Grocery store
    clocks You spend 4/5 of an hour at the mall. You spend 1/3 of that time in the food court. How many minutes are you in the food court?
  • Ray
    luc-slnka Light ray loses 1/19 of brightness passing through glass plate. What is the brightness of the ray after passing through 7 identical plates?


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