Division of more than 2 integers — lesson. Mathematics State Board, Class 7.

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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 $a/(b×c)$.

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

Let $a,b,c,d$ are four numbers, and $(a/b)/(c/d)$ 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}{2 \times 2} = \frac{- 1}{4} \end{array}

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2. Division of more than 2 integers

Theory: