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 = _______ = _______

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 =