Q. 109 B

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

7 × 4 = 28

7 × 3 = _______ = 28 – 7

7 × 2 = __ __ = _______– 7

7 × 1 = 7 = _______ – 7

7 × 0 = ______ = ______ –_______

7 × – 1 = –7 = ______ – _______

7 × – 2 = _____ = _____ – ______

7 × – 3 ______ = ______ – _______

Answer :

In order to fill these blanks, you need to identify the pattern.

Given is,


7 × 4 = 28


This can also be written as:


7 × 4 = 28 = 35 – 7


7 × 4 = 28 = (7 × 5) – 7 …(i)


Now, note the equation in second line:


7 × 3 = ___ = 28 - 7


Here, the blank can be filled by simple multiplication of 7 by 3.



7 × 3 = 21 = (7 × 4) – 7 ...(ii)


Now, note the equation in third line:


7 × 2 = ___ = _____ - 7


Here, the blank can be filled by simple multiplication of 7 by 2.


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


(7) remains same, but (7 × 5) and (7 × 4) are in series.



...(iii)


Now, note the equation in fourth line:


7 × 1 = 7 = ____ - 7


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


(7) remains same, but (7 × 5), (7 × 4) and (7 × 3) are in series.



…(iv)


Now, note the equation in fifth line:


7 × 0 = ___ = ___ - ___


Here, the first blank can be filled by simple multiplication of 7 by 0.


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


(7) remains same in the third blank, but (7 × 5), (7 × 4), (7 × 3) and (7 × 2) are in series.



…(v)


Now, note the equation in sixth line:


7 × -1 = -7 = ___ - ___


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


(7) remains same in the third blank, but (7 × 5), (7 × 4), (7 × 3), (7 × 2) and (7 × 1) are in series.



...(vi)


Now, note the equation in seventh line:


7 × -2 = ___ = ___ - ___


Here, the first blank can be filled by simple multiplication of 7 by -2.


Note the pattern in the bolded equations of (i), (ii), (iii), (iv), (v) and (vi),


(7) remains same in the third blank, but (7 × 5), (7 × 4), (7 × 3), (7 × 2) and (7 × 0) are in series.



…(vii)


Now, note the equation in eighth line:


7 × -3 = ___ = ___ - ___


Here, the first blank can be filled by simple multiplication of 7 by -3.


Note the pattern in the bolded equations of (i), (ii), (iii), (iv), (v), (vi) and (vii),


(7) remains same in the third blank, but (7 × 5), (7 × 4), (7 × 3), (7 × 2), (7 × 0) and (7 × -1) are in series.



…(viii)


Thus, we have


7 × 4 = 28








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