standard_description: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
problem_activity: Given below are the graphs of two lines,
$${y = 0.5x + 5}$$
and
$${y = -1.25x + 8}$$
, and several regions and points are shown. Note that C is the region that appears completely white in the graph.
[IMG]
For each region and point, write a system of equations or inequalities that has the region or point as its solution set.
Verify that a point that lies in region A satisfies the system of inequalities that you wrote for region A.
Without choosing any specific numbers, explain how you know that all the points in quadrant 3 must satisfy the inequalities for region A.


aligns: no