Page 102 - ArithBook5thEd ~ BCC

Example 118. What is 3 divided by 6?
7
3 3 6
÷ 6= ÷
7 7 1
3 1
= ·
7 6
3
=
42
1
= (cancelling 3).
14
We can divide mixed numbers, too, by simply converting them into improper fractions first.
8
1
Example 119. Perform the division 2 ÷ 1 . Express the result as a mixed number.
9 2
Solution. Converting mixed numbers to improper fractions, we have
8 1 26 3
2 ÷ 1 = ÷ .
9 2 9 2
3
Now we convert the division into multiplication by the reciprocal of :
2
26 2
= · .
9 3
No pre-cancellation is possible, so
26 · 2 52 25
= =1 ,
9 · 3 27 27
where, at the last step, we converted the improper fraction into a mixed number.

3
Example 120. How many books, each 1 inch thick, can fit on a 35 inch bookshelf?
4
3
Solution. The question calls for division, since we need to know how manytimes 1 “goes into” 35.
4
3 35 7 35 4
35 ÷ 1 = ÷ = · .
4 1 4 1 7
Cancelling 7, we get
5 4 20
· = =20.
1 1 1
So, exactly 20 books will fit on the shelf.

3.10.4 Exercises

Perform the divisions. Reduce to lowest terms, and change improper fractions to mixed numbers.
1 3
1. ÷
5 2
2
2. 15 ÷
3
8 16
3. ÷
15 21

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