Work with fractions

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This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

The result:

1 + 1/2 = 3/2 = 1 1/2 = 1.5

Spelled result in words is three halfs (or one and one half).

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How bởi we solve fractions step by step?

  1. Add: 1 + 1/2 = 1/1 + 1/2 = 1 · 2/1 · 2 + 1/2 = 2/2 + 1/2 = 2 + 1/2 = 3/2
    It is suitable to tướng adjust both fractions to tướng a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(1, 2) = 2. It is enough to tướng find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 2 = 2. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - one plus one half is three halfs.

Rules for expressions with fractions:

Fractions - use a forward slash to tướng divide the numerator by the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.

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Mixed numerals (mixed numbers or fractions) keep one space between the integer and
fraction and use a forward slash to tướng input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to tướng fractions - i.e. 1.45.

Math Symbols

SymbolSymbol nameSymbol MeaningExample
+plus signaddition 1/2 + 1/3
-minus signsubtraction 1 50% - 2/3
*asteriskmultiplication 2/3 * 3/4
×times signmultiplication 2/3 × 5/6
:division signdivision 1/2 : 3
/division slashdivision 1/3 / 5
:coloncomplex fraction 1/2 : 1/3
^caretexponentiation / power 1/4^3
()parenthesescalculate expression inside first-3/5 - (-1/4)

The calculator follows well-known rules for the 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.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always bởi multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to tướng right.

Fractions in word problems:

  • A class IV.A
    In a class, there are 15 girls and 30 boys.  What fraction of the class represents the boys?
  • A quarter
    A quarter of the number 72 is:
  • Fractions 80134
    There are 420 pupils in the school. Two hundred fifty-two pupils go to tướng the 1st level. Write as a fraction what part of the pupils goes to tướng the 1st grade and what part to tướng the 2nd grade. Shorten both fractions to tướng their basic size.
  • Someone
    Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake left, how much of a whole cake will you have eaten?
  • Simplify 12
    Simplify {1/3 + 1/12} ÷ {2/3 - 5/8}
  • Brown or black
    Max has 13 pairs of socks. From this, six pairs are xanh lơ, three pairs are brown, two are đen ngòm, and two are white. What fraction of Max's socks are either brown or black?
  • Lowest terms 2
    We can write the expression 4/12 in its lowest term as 1/3. What is 3/15 expressed in its lowest term?
  • Samantha
    Samantha took 72 pictures on her beach vacation. 3/4 of those pictures are on the beach. How many pictures from her vacation are on the beach?
  • In fractions
    An ant climbs 2/5 of the pole in the first hour and climbs 1/4 of the pole in the next hour. What part of the pole does the ant climb in two hours?
  • A company
    A company has 860 employees, of which 500 are female. Write a fraction to tướng represent the female employees in the company.
  • Evaluate expression
    Calculate the value of the expression z/3 - 2 z/9 + 1/6, for z = 2
  • A farm 6
    A farm has đôi mươi animals. There are four chickens. What fraction of the animals are chickens? Express your answer as a fraction in the simplest size.
  • Fruit basket
    If there are seven apples and five oranges in the basket, what fraction of oranges are in the fruit basket?
  • Reduce 9
    Reduce the fraction 16/24 to tướng the lowest terms.
  • Value of Z
    For x = -9, what is the value of Z, where Z equals fraction numerator x minus 17 over denominator 6.5 kết thúc fraction. Give your answer to tướng 2 decimal places.

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