1. Exercise
Multiply.
5 • 7
= 35

2. Exercise
Multiply.
5 (– 7)
= – 35

3. Exercise
Multiply.
– 5 (– 7)
= 35

4. Exercise
Simplify.
(– 5)2
= 25

5. Exercise
Simplify.
(– 5)3
= – 125

6. 1 2
shaded
1 2
of shaded
1 3
1 6
shaded

7. 1 2
1 3 x
1 x 1 3 x 2 =
1 6 =

8. Multiplying Rational Numbers
To multiply two rational numbers, multiply the first numerator times the second numerator and the first denominator times the second denominator. Express the product in lowest terms.

9. Multiplying Rational Numbers
For all rational numbers
and (b ≠ 0, d ≠ 0),
x =
a b
c d
a x c b x d

10. Example 1
4 5
7 9
Multiply x
4 5
7 9 x
4 x 7 5 x 9 = =
2845

11. Example 2
4 7
2 5
Multiply – x
4 7
2 5 x –
– 4 x 2 7 x 5 = =
8 35 –

12. Example 3
2 3 3
Evaluate
2 3 3
2 3 x =
2 x 2 x 2 3 x 3 x 3 = =
8 27

13. Example 4 5 2 3 Evaluate . – 5 2 3 – = 5 3 – 5 3 – 5(– 5) 3(3) = =
5 2 3
Evaluate –
5 2 3 – =
5 3 –
5 3
– 5(– 5) 3(3) = =
25 9

14. Example 4 5 3 3 Evaluate . – 5 3 3 – = 5 3 – 5 3 = 25 9 – 5 3 = 125 27
5 3 3
Evaluate –
5 3 3 – =
5 3 –
5 3 =
25 9 –
5 3 =
125 27 –

15. dividing both the numerator and the denominator by the same number
canceling simplifying reducing

16. 5 9
3 4 x
3 x 5 2 x 2 x 3 x 3 =
5 12 =

17. Example 5 3 4 5 9 Multiply . x 1 3 4 5 9 3 4 5 9 x x = 3 1 x 5 4 x 3
5 12

18. Example 6 4 9 2 5 15 16 Multiply . – – – 1 3 = – 4 9 2 5 – 15 16 x 1 2
Multiply – –
– 1 3 =
– 4 9
2 5 – x 1 2
– 4 9
2 5 – x
–1(1)(–1) 3(1)(2) = =
1 6

19. Example 7 1 6 Multiply . 2 x 9 13 6 2 3 9 1 x = 1 6 9 x 2 13 6 9 1 x =
39 2

20. Example
Cancel before multiplying.
5 12
8 25 =
2 15 •

21. Example
Cancel before multiplying.
– 7 8
10 21
– 9 25 =
3 20 • •

22. Example
Cancel before multiplying.
3 2 5 =
4 9 •

23. Example
Multiply the mixed numbers.
5 8
1 3
= 14 2 x 5

24. 753 1,000
35 100 x
0.753 x 0.35
26, ,000 = =

25. Example 8
Multiply x 2.06.
2.06 x
824
618

26. Example
Multiply the decimals.
34,000 x
= 10.2

27. Example
Multiply the decimals.
2.3 x 40 x 0.03
= 2.76

28. Example
Multiply the decimals.
x 0.01 =