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:

1/7 + 2/3 = 17/210.8095238

Spelled result in words is seventeen twenty-firsts.

How do you solve fractions step by step?

  1. Add: 1/7 + 2/3 = 1 · 3/7 · 3 + 2 · 7/3 · 7 = 3/21 + 14/21 = 3 + 14/21 = 17/21
    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(7, 3) = 21. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 3 = 21. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - one seventh plus two thirds = seventeen twenty-firsts.

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:

  • Cupcakes 2
    cake Susi has 25 cupcakes. She gives 4/5. How much does she have left?
  • Unknown number
    fractions I think the number - its sixth is 3 smaller than its third.
  • Equation with x
    eq2 Solve the following equation: 2x- (8x + 1) - (x + 2) / 5 = 9
  • Fruits
    jablka Amy bought a basket of fruits 1/5 of them were apples,1/4 were oranges, and the rest were 33 bananas. How many fruits did she buy in all?
  • Trees
    jablone From the total number of trees in the orchard, there are two-fifths pearls and apples are three eighty. The rest of the trees are 9 ceremonial. How many trees are in the set?
  • Brick
    balance_scale Isosceles scale has on one side all brick and second weight 1 kg and 1/4 of brick. The balance is in equilibrium. What is the weight of a brick?
  • Cookies
    kolac Mom bake cookies. Rolo took 2/9 of all cookies, Michal 3/9. How many cookies ate Rolo if Michal had 9.
  • One sixth
    one_sixth How many sixths are two thirds?
  • Class 8.A
    trieda Three quarters of class 8.A went skiing. Of those who remained at home one third was ill and the remaining six were on math olympic. How many students have class 8.A?
  • Expressions
    plusminus 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
  • Sales tax
    penize A sales tax on a Php 10,800 appliance is Php.1,620. What is the rate of sales tax?
  • PC disks
    diskette Peter has 45 disks in three colors. One-fifth of the disks are blue, red are twice more than the white. How much is blue, red and white disks?
  • The quotient
    12466 The quotient of g and 55 is the same as 279. What is g?


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