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 ______ = ______ – _______

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