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:

1/2 + 1/2 + 1/2 = 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. Add: 1/2 + 1/2 = 1 + 1/2 = 2/2 = 2 · 1/2 · 1 = 1
    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(2, 2) = 2. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 2 = 4. In the next intermediate step, , cancel by a common factor of 2 gives 1/1.
    In words - one half plus one half = one.
  2. Add: the result of step No. 1 + 1/2 = 1 + 1/2 = 1/1 + 1/2 = 1 · 2/1 · 2 + 1/2 = 2/2 + 1/2 = 2 + 1/2 = 3/2
    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(1, 2) = 2. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 2 = 2. In the next intermediate step, the fraction result cannot be further simplified by canceling.
    In words - one plus one half = 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:

  • Integer add to fraction
    fractions 7 is added to the sum of 4/5 and 6/7
  • Teacher
    cake Teacher Rem bought 360 pieces of cupcakes for the outreach program of their school. 5/9 of the cupcakes were chocolate flavor and 1/4 wete pandan flavor and the rest were a vanilla flavor. How much more pandan flavor cupcakes than vanilla flavor?
  • The recipe
    milk The recipe they are following requires 7/8 cups of milk, Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe?
  • Paper clips
    paper Mrs. Bright is organizing her office supplies. There are 5 open boxes of paper clips in her desk drawer. Each box has 1/2 of the paper clips remaining. How many boxes of paper clips are left?
  • King
    kral King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers?
  • Bricklayers
    murari 8 bricklayers build a house for 630 days. How many bricklayers have to add after 150 days to complete the whole building in (next) 320 days?
  • 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?
  • Dividends
    money The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least?
  • Michael
    chocholate Michael had a bar of chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?
  • Boys and girls
    children There are 28 girls in the hall. 5/7 of all children are boys. How many children and how many boys are there?
  • A shopkeeper
    cheese A shopkeeper cuts a wheel of cheese into 10 equal wedges. A customer buys one-fifth of the wheel. How many wedges does the customer buy? Use the number line to help find the solution.
  • Chocolate buyer
    cokolada Peter bought 1/2 a pound of chocolate at rocky mountain chocolate factory. Later he went to the sweet shoppie and he bought 6/9 of a pound more chocolate. How much chocolate did he buy that day?
  • Obtuse angle
    UholZSobr2 Which obtuse angle is creating clocks at 17:00?


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