Multiplication and division are inverse operations. The rules for dividing integers are discovered through this relationship. Rational numbers can be expressed as fractions or decimals, where the decimals either terminate or repeat. Irrational numbers are non-terminating and non-repeating decimals that cannot be expressed as fractions, such as π.

3. Rational and Irrational

22. Multiplication and division are inverse operations. They “undo”
each other. You can use this fact to discover the rules for
division of integers.
4 · (-2) = -8 -4 · (-2) = 8
-8 ÷ (-2) = 4 8 ÷ (-2) = -4
same sign positive different signs negative
The rule for division is like the rule for multiplication.

23. Fractions and decima

24. a 1 2 3 4 5 …
b
1 1/1 2/1 3/1 4/1 5/1 …
2 1/2 2/2 3/2 4/2 5/2 …
3 1/3 2/3 3/3 4/3 5/3 …
4 1/4 2/4 3/4 4/4 5/4 …
5 1/5 2/5 3/3 4/5 5/5 …
…

26. Rational number
In decimal form
Rational number
In fractional form
0.3 3/10
0.007 7/1000
-5.9 -59/10

27. 6 or 6/1 can also be written as 6.0
-2 or -2/1 can also be written as -2.0
½can also be written as 0.5
-5/4 can also be written as -1.25
2/3 can also be written as .66
2/3 can also be written as 0.666666…
21/55 can also be written as 0.38181818…
53/83 can also be written as 0.62855421687…
the decimals will repeat after 41 digits

30.  An irrational number cannot be expressed
as a fraction.
 Irrational numbers cannot be represented as
terminating or repeating decimals.
 Irrational numbers are non-terminating,
non-repeating decimals.

31. 10
101001000.0

32. π
π
π