Q. 109 A5.0( 2 Votes )

Observe the following patterns and fill in the blanks to make the statements true:

–5 × 4 = – 20

–5 × 3 = – 15 = –20 – (–5)

–5 × 2 = _______ = – 15 – (–5)

– 5 × 1 = _______ = _______

– 5 × 0 = 0 = _______

– 5 × – 1 = 5 = _______

– 5 × – 2 = _______ = _______

Answer :

Given is,

-5 × 4 = -20


Now, note the equation in second line:


-5 × 3 = -15 = -20 – (-5) ...(i)


Now, note the equation in third line:


-5 × 2 = _____________ = -15 – (-5)


Compare the equation of second and third line,


In second line -5 × 3 = -15


So, in third line -5 × 2 = -10


[This was not a pattern but just simple multiplication of -5 with 2 as was of -5 with 3]


So, we can re-write the equation as:


-5 × 2 = = -15 – (-5) ...(ii)


Now, note the equation in fourth line:


-5 × 1 = _____________ = ____________


Note the pattern in the bolded equation of (i) and (ii),


(-5) remains same, but 20 and 15 are basically factors of 5 in descending order.


…(iii)


Now, note the equation in fifth line:


-5 × 0 = 0 = _______


Note the pattern in the bolded equation of (i), (ii) and (iii),


(-5) remains same, but 20, 15 and 10 are factors of 5 in descending order.


-5 × 0 = 0 = (iv)


Now, note the equation in sixth line:


-5 × -1 = 5 = ________


Note the pattern in the bolded equation of (i), (ii), (iii) and (iv),


(-5) remains same, but 20, 15, 10 and 5 are factors of 5 in descending order.


…(v)


Now, note the equation in seventh line:


-5 × -2 = ____ = ____


The first blank has got to do with multiplication of -5 and -2.


(-5 × -2 = 10)


For the second blank, (-5) remains same, but 20, 15, 10, 5, 0 are factors of 5 in descending order in bolded equation of (i), (ii), (iii), (iv) and (v). ...(vi)


Thus, we have


-5 × 4 = -20


-5 × 3 = -15 = -20 – (-5)


-5 × 2 = = -15 – (-5)



-5 × 0 = 0 =




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