## Exploding Dots

### 3.8 Solutions

As promised, here are my solutions to the questions posed.

1.

$$148+323=4|6|11=471$$

$$567 + 271 = 7|13|8 = 838$$

$$377 + 188 = 4|15|15 = 5|5|15 = 565$$

$$310462872 + 389107123 = 6|9|9|5|6|9|9|9|5 = 699569995$$

$$87263716381 + 18778274824 = 9|15|9|13|11|9|8|10|11|10|5 = \ldots = 106041991205$$

2. We have

$$26417 \times 4 = 8|24|16|4|28 = 10|4|16|4|28 = 1|0|4|16|4|28 = 1|0|5|6|4|28 = 105668$$

$$26417 \times 5 = 10|30|20|5|35 = 10|30|20|8|5 = 10|32|0|8|5 = 13|2|0|8|5 = 132085$$

$$26417 \times 9 = 18|54|36|9|63 = 18|54|36|15|3 = \ldots = 237753$$

$$26417 \times 11 = 22|66|44|11|77 = \ldots = 290587$$

$$26417 \times 12 = 24|72|48|12|84 = \ldots = 317004$$

Read on in the chapter to see why $$26417 \times10$$ is  264170.

3.

a) $$476 \times 10$$ is $$4760$$. Since $$476 \times 100$$ is “$$476$$ times ten times ten” the answer will be $$47600$$.

b) We have that $$9190$$ is the answer to $$919 \times 10$$. This means that $$9190 \div 10$$ must be $$919$$.

And $$3310000$$  is the answer to $$33100 \times 100$$, and so $$3310000 \div 100$$ must be $$33100$$.

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