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:

2/3 + 3/8 = 25/24 = 1 1/241.0416667

Spelled result in words is twenty-five twenty-fourths (or one and one twenty-fourth).

How do you solve fractions step by step?

  1. Add: 2/3 + 3/8 = 2 · 8/3 · 8 + 3 · 3/8 · 3 = 16/24 + 9/24 = 16 + 9/24 = 25/24
    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(3, 8) = 24. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 8 = 24. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - two thirds plus three eighths = twenty-five twenty-fourths.

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:

  • How many 3
    tv How many hours the Andersons watched TV in all Wednesday 3/1 hr Thursdays 2/3 hr Friday 4/5 hr Saturday 3/4 hr
  • Evaluate expression
    mixed_fractions Evaluate expression using BODMAS rule: 1 1/4+1 1/5÷3/5-5/8
  • Complicated sum minus product
    plusminus What must be subtracted from the sum of 3/8 and 5/16 to get difference equal to the product of 5/8 and 3/16?
  • A large 2
    cinema2 A large popcorn bag holds four times as much as a small popcorn bag at the end of the party 3 1/3 small bags and 2 1/4 large bags left. How many small bags with the leftover popcorn fill?
  • Evaluate 17
    fractions Evaluate 2x+6y when x=- 4/5 and y=1/3. Write your answer as a fraction or mixed number in simplest form.
  • Metal rod
    meter You have a metal rod that’s 51/64 inches long. The rod needs to be trimmed. You cut 1/64 inches from one end and 1/32 inches from the other end. Next, you cut the rod into 6 equal pieces. What will be the final length of each piece?
  • The cost 2
    apples The cost of 5 apples is $3.45  and 5 oranges is $1.23. If Rachel buys one apple and one orange, then how much must she pay?
  • Baxter
    dog Baxter ate 1/12 of a box of dog food. Now the box is 3/4 full. What fraction of the full of a full box was there before Baxter?
  • Marvin
    meter Marvin buys a hose that is 27 ¾ feet long. He already owns a hose at home that is ⅔ the length of the new hose. How many total yards of hose does Marvin have now?
  • A 14.5-gallon
    fuel A 14.5-gallon gasoline tank is 3/4 full. How many gallons will it take to fill the tank? Write your answer as a mixed number.
  • Stock market 2
    nyse For the week of July 22, the following day to day changes in the stock market was recorded a certain stock: -2 on Monday; +4 Tuesday; -8 Wednesday; + 2 1/2 Thursday; - 3 1/4 Friday. The stock began the week at 78 points. How many points did it finish with
  • Sayavong
    vaha2 Sayavong is making cookies for the class. He has a recipe that calls for 3 and 1/2 cups of flour. He has 7/8 of a cup of wheat flour, and 2 and 1/2 cups of white flour. Does Mr. Sayavong have enough flour to make the cookies?
  • Food weight
    vaha Stacie is a resident at the medical facility where you work. You are asked to chart the amount of solid food that she consumes. For the noon meal, today she ate 1/2 of a 3-ounce serving of meatloaf, 3/4 of her 3-ounce serving of mashed potatoes, and 1/3 o


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