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MULTIPLIERS SOME BASICS In its simplest conceptual form, an analog multiplier is a three-terminal (plus common) device that will perform the mathematical operations of multiplication and division, by appropriate terminal connections Figure 1 shows the conceptual block representing a multiplier Vx OUT E = VxVy o ER Vy Figure 1
2 Solve problems of multiplication of whole numbers up to five digits by using the multiplication table up to 9 x 9 3 Solve problems of short division by two-digit whole numbers and long division by whole numbers up to five digits 4 Solve problems of addition and subtraction of fractions and mixed numbers
multiplication and division work should be done by means of practical tasks involving children themselves, ‘real’ objects or mathematical apparatus in which the context is entirely apparent Similarly, recording of multiplication and division work should also, for the most part, contain
Here’s a typical example Consider the equation y2 = x3 +1 In an algebra or high school class, we might graph this equation in the plane; there’s little challenge
Definition Subset S of vector space (V, +, ·) Closed under addition (+) and scalar multiplication ( ·) Examples Subspaces of ?3: origin (0, 0, 0), line through the origin, plane containing origin, ?3itself For vector v, { v ?} is a subspace (why?) Affine Subspace
addition or multiplication mod n for us) with some nice properties A RING is a set equipped with two operations, called addition and multiplication A RING is a GROUP under addition and satis?es some of the properties of a group for multiplication A FIELD is a GROUP under both addition and multiplication De?nition 1