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 2 shaded 1 2 of shaded 1 3 1 6 shaded

1 2 1 3 x 1 x 1 3 x 2 = 1 6 =

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 and (b ≠ 0, d ≠ 0), x = . a b c d a x c b x d

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

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

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

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

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 –

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

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

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

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

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

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

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

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

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

753 1,000 35 100 x 0.753 x 0.35 26,355 100,000 = = 0.26355

Example 8 Multiply 0.0034 x 2.06. 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