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 + 1/3 = 11/150.7333333

Spelled result in words is eleven fifteenths.

How do you solve fractions step by step?

  1. Add: 2/5 + 1/3 = 2 · 3/5 · 3 + 1 · 5/3 · 5 = 6/15 + 5/15 = 6 + 5/15 = 11/15
    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(5, 3) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 3 = 15. In the following intermediate step, the fraction result cannot be further simplified by canceling.
    In other words - two fifths plus one third = eleven fifteenths.

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:

  • Write 2
    fractions Write 791 thousandths as fraction in expanded form.
  • Divide 13
    delnik Divide. Simplify your answer and write as an improper fraction or whole number. 14÷8/3
  • A quotient
    fractions What is the quotient of 3/10 divided by 2/4 as a fraction?
  • Pie division
    kolac 5/8 of a pie divide 6 pieces. Each friend got 1/6.  What fraction  of the whole pie does each person receive?
  • Sadie 2
    jablka Sadie picked up fallen apples from an apple tree in her yard. She picked up 14 green ones, 16 that were changing from green to red, and 18 that were red. What fraction in simplest form names the green apples?
  • Eqn
    fractal Solve equation with fractions: 2x/3-50=40+x/4
  • Frac equation v2
    eq1 3.80 is two fifths of a quarter sum of money. How much money is there?
  • Adding denominators
    plusminus Max is working out 2/3+7/9. He says the answer is 9/12. What mistake have Max made?
  • Ratio 11
    zlomky Simplify this ratio 10 : 1/4
  • Equation with x
    eq2 Solve the following equation: 2x- (8x + 1) - (x + 2) / 5 = 9
  • Andre
    stamp Andre, Thomas, and Ivan split 88 postage stamps in a 2:5:4 ratio. How much did Thomas get?
  • Lemonade 4
    lemonade Six friends are sharing 8 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?
  • Berry Smoothie
    milk Rory has 5/8 cup of milk. How much milk does she have left after she doubles the recipe of the smoothie? Berry Smoothie: 2 cups strawberries 1 cup blueberries 1/4 cup milk 1 tbsp (tablespoon) sugar 1/2 tsp (teaspoon) lemon juice 1/8 tsp (teaspoon) vanilla


next math problems »