Calculator expression with brackets



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.

1/3 * (1/2 - 3 3/8) = -23/24 ≅ -0.9583333

Spelled result in words is minus twenty-three twenty-fourths.

How do we solve fractions step by step?

  1. Conversion a mixed number 3 3/8 to a improper fraction: 3 3/8 = 3 3/8 = 3 · 8 + 3/8 = 24 + 3/8 = 27/8

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8
    b) Add the answer from the previous step 24 to the numerator 3. New numerator is 24 + 3 = 27
    c) Write a previous answer (new numerator 27) over the denominator 8.

    Three and three eighths is twenty-seven eighths.
  2. Subtract: 1/2 - 27/8 = 1 · 4/2 · 4 - 27/8 = 4/8 - 27/8 = 4 - 27/8 = -23/8
    It is suitable to adjust both fractions to 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(2, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - one half minus twenty-seven eighths is minus twenty-three eighths.
  3. Multiple: 1/3 * the result of step No. 2 = 1/3 * (-23/8) = 1 · (-23)/3 · 8 = -23/24
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-23, 24) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - one third multiplied by minus twenty-three eighths is minus twenty-three twenty-fourths.

Rules for expressions with fractions:

Fractions - use a forward slash to 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.

Mixed numerals (mixed numbers or fractions) keep one space between the integer and
fraction and use a forward slash to 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 fractions - i.e. 1.45.

Math Symbols


SymbolSymbol nameSymbol MeaningExample
+plus signaddition 1/2 + 1/3
-minus signsubtraction 1 1/2 - 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 do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must evaluate from left to right.

Fractions in word problems:



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