## Thinking Mathematically (6th Edition)

(a) The expression of $3367\times 3,\ 3367\times 6,\ 3367\times 9$, and $3367\times 12$. Solve this expression by using a calculator: \begin{align} & 3367\times 3=10101 \\ & 3367\times 6=20202 \\ & 3367\times 9=30303 \\ & 3367\times 12=40404 \end{align} (b) In the expression, the first multiplier is always 3367 and the second multiplier is a successive multiple of 3. Then, these products are 10101, 20202, 30303, 40404. The pattern in the products is that the first answer is $10101\times 1=10101$, second is $10101\times 2=20202$,and so on. Therefore, theexpression of the value is$3367\times 3=10101$, $3367\times 6=20202$, $3367\times 9=30303$, and$3367\times 12=40404$. (c) The expression of $3367\times 3,3367\times 6,3367\times 9$, and $3367\times 12$. Solve these two-next multiplication and product expression by usinga calculator: \begin{align} & 3367\times 3=10101 \\ & 3367\times 6=20202 \\ & 3367\times 9=30303 \\ & 3367\times 12=40404 \end{align} That is, $3367\times 15=50505$ $3367\times 18=60606$ Verify this result: $3367\times 15=50505$ $10101\times 5=50505$ And, \begin{align} & 3367\times 18=60606 \\ & 10101\times 6=60606 \end{align} Thus, theseresultsare correct and verified. (d) The expression of $3367\times 3,\ 3367\times 6,\ 3367\times 9$, and $3367\times 12$. Solve this expression by using a calculator: \begin{align} & 3367\times 3=10101 \\ & 3367\times 6=20202 \\ & 3367\times 9=30303 \\ & 3367\times 12=40404 \end{align} This is an inductive reasoning, it uses an observed pattern and draws a conclusion from that pattern. In the expression, the first multiplier is always 3367 and the second multiplier isa successive multiple of 3. Then, these products are 10101, 20202, 30303, 40404.