Vimala Education Centre

  Theorem 1:   Euclid’s Division Lemma Let a and b (a>b)   be any two positive integers.   Then, there exist unique integers q and r such that   a=bq+r, 0≤r<b.     Example   2.1             We have 34 cakes.   Each box can hold 5 cakes only.   How many boxes we need to pack and how many cakes are unpacked?     34 = 5 x 6 + 4 Total number of cakes = Number of cakes in each box x Number of boxes + Number of cakes left over a = b x q + r                           i)      Number of boxes =6                       ii)   ...

    TAMIL NADU 10TH MATHS EM CH-2 EXAMPLE 2.2 Example 2.2              Find the quotient and remainder when a is divided by b in the following cases          (i) a= -12, b= 5     (ii) a= 17, b= -3     (iii)  a= -19,  b= -4   Solutions (i)                    a= -12, b= 5             By Euclid’s division lemma a=bq+r,        0≤r<|b|. -12 = 5 X (-3) +3              0≤r<|5|                Quotient q = -3 ,      Remainder r = 3   (ii)         ...