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  2. Mental calculation - Wikipedia

    en.wikipedia.org/wiki/Mental_calculation

    For any 2-digit by 2-digit multiplication problem, if both numbers end in five, the following algorithm can be used to quickly multiply them together: [1] E x : 35 × 75 {\displaystyle \mathrm {Ex} :35\times 75}

  3. Algebraic operation - Wikipedia

    en.wikipedia.org/wiki/Algebraic_operation

    Multiplication symbols are usually omitted, and implied, when there is no operator between two variables or terms, or when a coefficient is used. For example, 3 × x 2 is written as 3x 2, and 2 × x × y is written as 2xy. [5] Sometimes, multiplication symbols are replaced with either a dot or center-dot, so that x × y is written as either x ...

  4. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    For example, taking the statement x + 1 = 0, if x is substituted with 1, this implies 1 + 1 = 2 = 0, which is false, which implies that if x + 1 = 0 then x cannot be 1. If x and y are integers, rationals, or real numbers, then xy = 0 implies x = 0 or y = 0. Consider abc = 0. Then, substituting a for x and bc for y, we learn a = 0 or bc = 0.

  5. Cross-multiplication - Wikipedia

    en.wikipedia.org/wiki/Cross-multiplication

    The rule of three [1] was a historical shorthand version for a particular form of cross-multiplication that could be taught to students by rote. It was considered the height of Colonial maths education [2] and still figures in the French national curriculum for secondary education, [3] and in the primary education curriculum of Spain. [4]

  6. Extraneous and missing solutions - Wikipedia

    en.wikipedia.org/wiki/Extraneous_and_missing...

    The problem is that multiplication by zero is not invertible: if we multiply by any nonzero value, we can reverse the step by dividing by the same value, but division by zero is not defined, so multiplication by zero cannot be reversed. More subtly, suppose we take the same equation and multiply both sides by . We get

  7. 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 ...

  8. Multiplication - Wikipedia

    en.wikipedia.org/wiki/Multiplication

    Area of a cloth 4.5m × 2.5m = 11.25m 2; 4 ⁠ 1 / 2 ⁠ × 21 / 2 ⁠ = 11 ⁠ 1 / 4 ⁠ Multiplication (often denoted by the cross symbol × , by the mid-line dot operator ⋅ , by juxtaposition, or, on computers, by an asterisk * ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition ...

  9. Algebra tile - Wikipedia

    en.wikipedia.org/wiki/Algebra_tile

    For instance, if one had x×x, the only algebra tile that would complete the rectangle would be x 2, which is the answer. Multiplication of binomials is similar to multiplication of monomials when using the algebra tiles . Multiplication of binomials can also be thought of as creating a rectangle where the factors are the length and width. [2]