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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: