Properties and Operations in Algebra

The video covers California standards test questions for grade 7 math, focusing on problems 36 to 46. It includes solving equations using variable substitution, understanding operations on nonzero numbers, applying the distributive property, identifying equivalent expressions, illustrating the inverse property of multiplication, and graphing data. Each problem is explained step-by-step, highlighting key mathematical properties and operations.

If m = 3 and n = 5, what is the value of 4m + mn?

• 15

• 27

• 20

• 30

Which operation will change the value of any nonzero number?

• Dividing by 1

• Multiplying by 0

• Multiplying by 1

• Adding 0

What property is used in the equation 12 * (x + 4) = 12x + 48?

• Associative Property

• Commutative Property

• Identity Property

• Distributive Property

Which expression is equivalent to 3x - 3y?

• 3(x - y)

• x - y

• 3x + 3y

• 3(x + y)

Which equation illustrates the inverse property of multiplication?

• 5 + 0 = 5

• 5 * 0 = 0

• 5 * 1 = 5

• 5 * 1/5 = 1

Which equation shows the distributive property?

• 4(3 + 6) = 12 + 24

• 4 + 3 = 7

• 4 * 3 = 12

• 4 - 3 = 1

What property is illustrated by 2 * 3/3 = 2?

• Additive Identity

• Commutative Property

• Distributive Property

• Multiplicative Identity

Which of the following is an example of an inequality?

• 4N - 9

• 4N = 9

• 4N > 9

• 4N + 9

Which graph best represents the pricing of go-kart laps?

• Graph D

• Graph C

• Graph B

• Graph A