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 5/12 + 3 8/12 = 73/12 = 6 1/126.0833333

Spelled result in words is seventy-three twelfths (or six and one twelfth).

How do you solve fractions step by step?

  1. Conversion a mixed number 2 5/12 to a improper fraction: 2 5/12 = 2 5/12 = 2 · 12 + 5/12 = 24 + 5/12 = 29/12

    To find a new numerator:
    a) Multiply the whole number 2 by the denominator 12. Whole number 2 equally 2 * 12/12 = 24/12
    b) Add the answer from previous step 24 to the numerator 5. New numerator is 24 + 5 = 29
    c) Write a previous answer (new numerator 29) over the denominator 12.

    Two and five twelfths is twenty-nine twelfths
  2. Conversion a mixed number 3 8/12 to a improper fraction: 3 8/12 = 3 8/12 = 3 · 12 + 8/12 = 36 + 8/12 = 44/12

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 12. Whole number 3 equally 3 * 12/12 = 36/12
    b) Add the answer from previous step 36 to the numerator 8. New numerator is 36 + 8 = 44
    c) Write a previous answer (new numerator 44) over the denominator 12.

    Three and eight twelfths is forty-four twelfths
  3. Add: 29/12 + 44/12 = 29 + 44/12 = 73/12
    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(12, 12) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 12 = 144. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - twenty-nine twelfths plus forty-four twelfths = seventy-three twelfths.

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:

  • Expressions
    Let k represent an unknown number, express the following expressions: 1. The sum of the number n and two 2. The quotient of the numbers n and nine 3. Twice the number n 4. The difference between nine and the number n 5. Nine less than the number n
  • Circular garden
    Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden. What fraction represents the remaining unplante
  • Honey 3
    Honey jogged 1 3/4 km on Monday,1 1/2 km on Wednesday and 1  2/3 km on Friday . how far did he jog?
  • Sum of fractions
    What is the sum of 2/3+3/5?
  • Fractions mul add sum
    To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
  • Marvin
    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?
  • Fitness center
    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?
  • Pizza fractions
    Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
  • Flower garden
    In the mr elliots garden 1/8 of the flowers are red 1/4 of them are purple and 1/4 of the remaning flowers are pink. If there is 128 flowers how many of them are pink?
  • 30 eggs
    There are 30 eggs in a tray. If 1/2 of the tray used 1/5 of it cooked,1/3 kept the refrigerator, how many eggs were left?
  • A large 2
    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?
  • Birthday party
    For her youngest son's birthday party, the mother bought 6 3/4 kg of hotdog and 5 1/3 dozens bread rolls. Hotdogs cost 160 per kilogram, and a dozen bread rolls cost 25. How much did she spend in all?
  • Fractions and mixed numerals
    (a) Convert the following mixed numbers to improper fractions. i. 3 5/8 ii. 7 7/6 (b) Convert the following improper fraction to a mixed number. i. 13/4 ii. 78/5 (c) Simplify these fractions to their lowest terms. i. 36/42 ii. 27/45 2. evaluate the follow


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