# Answers to Book 1 Problems

1.     [pmath]1/6[/pmath] +  [pmath]3/6[/pmath]  =   [pmath]4/6[/pmath] ,          [pmath]6/6[/pmath] –   [pmath]4/6[/pmath]  =   [pmath]2/6[/pmath]

2.     [pmath]4/8[/pmath] +  [pmath]1/8[/pmath] =   [pmath]5/8[/pmath],          [pmath]8/8[/pmath] –  [pmath]5/8[/pmath] =  [pmath]3/8[/pmath]

3.    [pmath]3/8[/pmath] +  [pmath]4/8[/pmath] =  [pmath]7/8[/pmath] ,        [pmath]8/8[/pmath] –  [pmath]7/8[/pmath] =  [pmath]1/8[/pmath]

4.    [pmath]2/12[/pmath] +  [pmath]4/12[/pmath] +  [pmath]5/12[/pmath] =  [pmath]11/12[/pmath] ,         [pmath]12/12[/pmath] –  [pmath]11/12[/pmath] =  [pmath]1/12[/pmath]

5a.   [pmath]5/8[/pmath]     5b.   [pmath]2/8[/pmath]     5c.   [pmath]3/8[/pmath]     5d.   [pmath]4/12[/pmath]

5e.   [pmath]14/14[/pmath] = 1     5f.   [pmath]6/7[/pmath]    5g.   [pmath]3/5[/pmath]     5h.   [pmath]5/12[/pmath]

5i.   [pmath]9/10[/pmath]     5j.   [pmath]3/12[/pmath]     5k.   [pmath]3/10[/pmath]     5l.   [pmath]4/12[/pmath]

Did you notice that 5b is the inverse of 5a? Inverses “undo” each other. That sounds funny, so let me explain: In 5a, you added two-eighths to three-eighths to get five-eighths. In 5b, you took the answer to 5a (five-eighths) and subtracted one of the things you added (three-eighths) to get the other thing you added (two-eighths). So we can say that 5b “undid” 5a. That’s pretty cool, isn’t it? I’ve got a lot more cool stuff in my other books. Oh, in my next book, you’ll meet my friend, Cleveland. He’s cool, too!

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