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  2. Missing dollar riddle - Wikipedia

    en.wikipedia.org/wiki/Missing_dollar_riddle

    The misdirection in this riddle is in the second half of the description, where unrelated amounts are added together and the person to whom the riddle is posed assumes those amounts should add up to 30, and is then surprised when they do not ⁠— ⁠there is, in fact, no reason why the (10 ⁠− ⁠1) ⁠× ⁠3 ⁠ + ⁠2 ⁠ = ⁠29 sum should add up to 30.

  3. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction ⁠ 5 / 7 ⁠ when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...

  4. Division (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Division_(mathematics)

    Sometimes this remainder is added to the quotient as a fractional part, so 10 / 3 is equal to ⁠3 + 1 / 3 ⁠ or 3.33..., but in the context of integer division, where numbers have no fractional part, the remainder is kept separately (or exceptionally, discarded or rounded). [5] When the remainder is kept as a fraction, it leads to a rational ...

  5. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    [2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of ...

  6. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    For instance, the numeral for 10,405 uses one time the symbol for 10,000, four times the symbol for 100, and five times the symbol for 1. A similar well-known framework is the Roman numeral system . It has the symbols I, V, X, L, C, D, M as its basic numerals to represent the numbers 1, 5, 10, 50, 100, 500, and 1000.

  7. Cube (algebra) - Wikipedia

    en.wikipedia.org/wiki/Cube_(algebra)

    y = x 3 for values of 1 ≤ x ≤ 25. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number n is denoted n 3, using a superscript 3, [a] for example 2 3 = 8. The cube operation can also be defined for any other mathematical expression, for ...

  8. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12). Multiplication can also be thought of as scaling. Here, 2 is being multiplied by 3 using scaling, giving 6 as a result. Animation for the multiplication 2 × 3 = 6 4 × 5 = 20. The large rectangle is made up of 20 squares, each 1 unit by 1 unit.

  9. Algebraic operation - Wikipedia

    en.wikipedia.org/wiki/Algebraic_operation

    The plusminus sign, ±, is used as a shorthand notation for two expressions written as one, representing one expression with a plus sign, the other with a minus sign. For example, y = x ± 1 represents the two equations y = x + 1 and y = x − 1. Sometimes, it is used for denoting a positive-or-negative term such as ±x.