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4. Multiplication and division of more than 2 integers

Multiplication:

When more than

$2$ numbers are multiplied, depending upon the number of negative numbers involved, the sign of the answer varies.

We know that,

$(-1) × (1) = -1$

$(-1) × (-1) = +1$

Now,

$(-1) × (-2) × (-3) = -6$

$(-1) × (-2) × (-3) × (-4) = +24$

$(-1) × (-2) × (-3) × (-4) × (-5) = -120$

Inference:

When

$2$ negative numbers are multiplied, the result will be a positive number.

When

$3$ negative numbers are multiplied, the result will be a negative number.

When

$4$ negative numbers are multiplied, the result will be a positive number.

Conclusion:

From the above, we can conclude that,

Number of negative integers in multiplication	Sign of the result
Even	$+$
odd	$-$

Division:

Let's learn, how to deal with the division of more than

$2$ numbers,

$a,b,c$ are three numbers,

$a/b/c$ should be evaluated as

$(a×c)/b$ .

Example:

$\begin{array}{l} 1. \frac{1 / 2}{3} = \frac{1 \times 3}{2} = \frac{3}{2} \\ 2. \frac{2 / 6}{5} = \frac{2 \times 5}{6} = \frac{10}{6} \end{array}$

$a,b,c,d$ are four numbers, a/b/c/d should be evaluated as

$(a×d)/(b×c)$

Example:

$\begin{array}{l} 1. \frac{5 / 2}{3 / 6} = \frac{5 \times 6}{3 \times 2} = \frac{30}{6} \\ 2. \frac{2 / 6}{5 / 2} = \frac{2 \times 2}{5 \times 6} = \frac{4}{30} \\ 3. \frac{2 / 4}{6 / 2} = \frac{2 \times 2}{6 \times 4} = \frac{4}{24} \end{array}$

Similar to multiplication, when more than

$2$ numbers are involved, depending upon the number of negative numbers involved, the sign of the answer varies.

Number of negative integers in division	Sign of the result
Even	$+$
odd	$-$

Example:

$\begin{array}{l} 1. \frac{- 5 / - 2}{- 2 / 8} = \frac{- 5 \times 8}{- 2 \times - 2} = \frac{- 40}{4} \\ 2. \frac{- 8 / - 6}{2 / 4} = \frac{- 8 \times 4}{- 6 \times 2} = \frac{- 32}{- 12} = \frac{32}{12} \\ 3. \frac{- 9 / 1}{- 1 / 6} = \frac{- 9 \times 6}{- 1 \times 1} = \frac{- 54}{- 1} = \frac{54}{1} \\ 4. \frac{- 1 / 2}{1 / 2} = \frac{- 1 \times 2}{1 \times 2} = \frac{- 2}{2} = - 1 \\ 5. \frac{\frac{- 1}{2}}{2} = \frac{- 1 \times 2}{2 \times 1} = - 1 \end{array}$

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4. Multiplication and division of more than 2 integers

Theory: