Answer
given below.
Work Step by Step
(a)
The expression is\[6\times 6,66\times 66,666\times 666\]and \[6666\times 6666\].
Solve this expression by usinga calculator:
\[\begin{align}
& 6\times 6=36 \\
& 66\times 66=4356 \\
& 666\times 666=443,556 \\
& 6666\times 6666=44,435,556
\end{align}\]
(b)
A pattern in the result obtained can be identified as follows:
If an additional digit 6 is attached to the number being multiplied. An additional digit of 4 is attached to the left of the result and an additional digit of 5 is placed between 3 and 6.
(c)
The expression is\[6\times 6,66\times 66,666\times 666\], and \[6666\times 6666\].
Solve these two-next multiplication and product expression by usinga calculator:
\[\begin{align}
& 6\times 6=36 \\
& 66\times 66=4356 \\
& 666\times 666=443,556 \\
& 6666\times 6666=44,435,556
\end{align}\]
That is,
\[66666\times 66666=4,444,355,556\]
\[666666\times 666666=444,443,555,556\]
Verify this result as
\[\begin{align}
& 66666\times 66666=4,444,355,556 \\
& 4,444,355,556=4,444,355,556
\end{align}\]
And,
\[\begin{align}
& 666666\times 666666=444,443,555,556 \\
& 444,443,555,556=444,443,555,556
\end{align}\]
Thus, the result is correct.
(d)
The expression is\[6\times 6,66\times 66,666\times 666\], and \[6666\times 6666\].
Solve this expression by using a calculator,
\[\begin{align}
& 6\times 6=36 \\
& 66\times 66=4356 \\
& 666\times 666=443,556 \\
& 6666\times 6666=44,435,556
\end{align}\]
This is a inductive reasoning, it uses an observed pattern and draws a conclusion from that pattern.A pattern in the number and an additional digit of 6 is attached to the number being multiplied. An additional digit of 4 is attached to the left of the result and an additional digit of 5 is placed between 3 and 6.
