## 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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