Rational Numbers & Equations Lesson 12 Rational Numbers & Equations Multiplying Integers

Warm-Up A town in Alaska had a low temperature of −14º and a high temperature of 21º. What is the difference between these temperatures? Jan started her hike at an elevation of −120 feet below sea level. She climbed 250 feet in elevation. What was her ending elevation? Alex withdrew $35 from his account on Monday and $16 on Tuesday. What integer represents the total change in his account over those days?

Target: Multiply two integers to find the product. Multiplying Integers Target: Multiply two integers to find the product.

Example 1a Find the product. 5(− 4) “five groups of negative 4” 5(− 4) = − 20

Example 1b Find the product. −2(−3) “the opposite of 2 groups of negative 3” −2(−3) = 6

Multiplying Integers · · · Determine the sign of the answer. The product of two integers with the same sign is positive. The product of two integers with different signs is negative. Find the product of the absolute value of the numbers and use the sign determined above. · · + + = + – – = + · + – = –

Example 2 A submarine descends below the water’s surface at a rate of 50 meters per minute. Find the integer that represents the submarine’s position relative to the surface of the water after 6 minutes. Write the problem. −50(6) The integers have different signs so the answer is negative. −50(6) = −300 The submarine is 300 meters below the surface of the water after 6 minutes.

Example 3 Find the value of 2(−5)(− 4). Multiply the first two integers. 2(−5) = −10 Multiply the product by the last integer. −10(− 4) = 40 2(−5)(− 4) = 40

Exit Problems Find the value of each expression. −8(3) 5(−2) −7(−7) 2(−1)(−4) 5(−5)(3)

Communication Prompt The integer multiplication rules are different than the integer addition rules. How do you remember the rules for each operation?