Commutative Law
Using the commutative law, write an expression equivalent to each of the following:
1. y + 5
2. 9x
3. 7 + ab
1. 5 + y
2. x ⋅ 9
3. b ⋅ a + 7
1. y + (z + 3)
2. (8x)y
1. (y + z) + 3
2. 8(xy)
Multiply 6(s + 2 + 5w).
6s + 12 + 30w
Identify the main differences in the following equations: 6(5w) and 6(5+ w). Solve for both.
6(5w): only multiplication is involved, uses the associative law, 30w.
6(5+ w): both multiplication and addition involved, uses the distributive law, 30 + 6w.
Use the commutative law of addition to write an equivalent expression:
1. 5(a + 1)
2. 9(x + 5)
1. 5 + 5a
2. 45 + 9x
Using the associative law of addition, write an equivalent expression.
1. (ab + c) + d
2. (m + np) + r
1. ab + (c + d)
2. m + (np + r)
Use the distributive law to get rid of the parantheses in the following equations:
1. 5x + 10
2. 13x + 169
3. 64x + 256
1. 2(x + 5)
2. 13(x + 13)
3. 4(16x + 64)
In 15 seconds or less, explain the important differences between the commutative, associative, and distributive laws.
Commutative --> order changes.
Associative --> group changes.
Distributive --> "share the wealth!"
Use the commutative law of multiplication to write an equivalent expression:
1. 5(a + 1)
2. 9(x + 5)
1. (a + 1) ⋅ 5
2. (x + 5) ⋅ 9
Using the associative law of multiplication, write an equivalent expression.
1. 3[2(a + b)]
2. 5[x(2 + y)]
1. (3 ⋅ 2)(a+b)
2. (5 ⋅ x)(2 + y)
Using the distributive law, factor each of the following:
1. 3x + 3y
2. 7x + 21y + 7
1. 3(x + y)
2. 7(x + 3y + 1)
Choose from the following list of words to complete each statement: associative, factors, commutative, product, distributive, sum, equivalent, terms. Not every word will be used.
1. _________ expressions represent the same
number.
2. Changing the order of multiplication does not
affect the answer. This is an example of a(n) _________ law.
3. The result of addition is called a(n) _______.
4. The numbers in a product are called ________.
1. Equivalent
2. Commutative
3. Sum
4. Factors