Exercise Multiply. 5 • 7 = 35

Exercise Multiply. 5 (– 7) = – 35

Exercise Multiply. – 5 (– 7) = 35

Exercise Simplify. (– 5)2 = 25

Exercise Simplify. (– 5)3 = – 125

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

1 x 1 = 1 3 x 2 6 3 2

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.

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

Example 1 Multiply 4 x 7. 5 9 4 x 7 = 4 x 7 5 9 5 x 9 = 28 45

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

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

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

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

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

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

Example 5 Multiply 3 x 5. 4 9 3 x 5 13 x 5 = 4 93 1 x 5 5 = = 4 x 3 12

Example 6 Multiply – 4 2 – 15. 9 5 16 – 1 1 – 4 x 2 x – 15 = – 4 x 2 x – 15 9 3 51 16 2 9 5 16 – 1(1)(– 1) = 1 = 3(1)(2) 6

Example 7 1 Multiply 2 x 9. 6 3 13 13 9 1 9 2 x 9= x x = 6 62 1 6 1 13 x 3 39 = = 2 x 1 2

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

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

Example Cancel before multiplying. 3 2 • 10 2 = 4 9 5 9

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

0. 753 x 0. 35 753 x 35 1, 000 100 26, 355 = 100, 000 = 0. 26355

Example 8 Multiply 0. 0034 x 2. 06 x 0. 0034 824 618 0. 007004

Example Multiply the decimals. 34, 000 x 0. 0003 = 10. 2

Example Multiply the decimals. 2. 3 x 40 x 0. 03 = 2. 76

Example Multiply the decimals. 138. 01 x 0. 01 = 1. 3801