Sec 4.2B Solve One-Step Multiplication and Division Equations pg. 215 - 219

Definitions The expression 3x means “3 times the value of x” The numerical factor of a multiplication expression like 3x is called a COEFFICENT. What is the coefficient of 4y? 4 What is the coefficient of -5a -5

Division Property of Equality If you divide each side of an equation by the SAME NONZERO NUMBER, the two sides remain equal. If a = b and c ≠ 0, then 𝑎 𝑐 = 𝑏 𝑐 Numbers 9 = 9 9 3 = 9 3 3 = 3 Algebra 3c = -12 3𝑐 3 = −12 3 c = -4

Solve Check! 6x = 24 6𝑥 6 = 24 6 6x = 24 x = 4 6(4) = 24 -2a = 20 6𝑥 6 = 24 6 x = 4 -2a = 20 −2𝑎 −2 = 20 −2 a = -10 6x = 24 6(4) = 24 24 = 24 -2a = 20 -2(-10) = 20 20 = 20

Mulitiplication Property of Equality If you multiply each side of an equation by the SAME NUMBER, the two sides remain equal. Numbers 4 = 4 4(-5) = 4(-5) -20 = -20 Algebra 𝑥 5 =6 𝑥 5 5 =6(5) x = 30

Solve −11= 𝑏 4 −11 4 = 𝑏 4 (4) Check! −11= 𝑏 4 −11= −44 4 -44 = b −11 4 = 𝑏 4 (4) -44 = b −11= 𝑏 4 −11= −44 4 -11 = -11

Formula A formula is an equation that shows the relationship among certain quantities. d = rt is a common one that shows the relationship between distance, rate and time.

Solve The rate, r, driven by Mark can be calculated given that he travels 230 miles in 2.5 hours. d = rt 230 miles = r (2.5 hours) 230 𝑚𝑖𝑙𝑒𝑠 2.5 ℎ𝑜𝑢𝑟𝑠 = (𝑟)(2.5 ℎ𝑜𝑢𝑟𝑠) 2.5 ℎ𝑜𝑢𝑟𝑠 92 miles per hour = r