4.03 Properties of operations with algebraic terms
Identify whether the commutative property of addition or associative property of addition is demonstrated by each of the following statements:
x + 14 = 14 + x
32 + y = y + 32
a + \left( - b \right) = - b + a
\left(5 + z\right) + 2 = 5 + \left(z + 2\right)
4 + \left(3x + 2\right) = \left(4 + 3x\right) + 2
- m + \left(n + 8\right) = \left( - m + n\right) + 8
\left(x + 2y\right) + 5 = 5 + \left(x + 2y\right)
\left( -m + 4n\right) + 6 = 6 + \left( - m + 4n\right)
x + 8 = 8 + x
\left(2 + x\right) + 3 = 2 + \left(x + 3\right)
Identify whether the commutative property of multiplication or associative property of multiplication is demonstrated by each of the following statements:
5 \left(x + 9\right) = \left(x + 9\right) 5
x \times \left( 9 \times y\right) = \left( x \times 9\right) \times y
a \times \left( b \times c\right) = \left( a \times b\right) \times c
- 9m \times \left( 2n \times 3\right) = \left( - 9m \times 2n \right) \times 3
3c \times \left( d \times 6\right) = \left( 3c \times d \right) \times 6
8a \times 7b = 7b \times 8a
\left( 3 \times y\right) \times 11z = 3 \times \left( y \times 11z\right)
5s \times 6t = 6t \times 5s
Determine whether each number sentence is true or false for all possible values of the variables:
m + 1 = 1 + m
- 5 + n = n - 5
a - 9 = 9 - a
d - 2 = - 2 + d
\left(3 + 7\right) + a = 3 + \left(7 + a\right)
\left( - 2 + f\right) + 3 = - 2 + \left(f + 3\right)
w + p = p + w
\left( a - b \right) - 10 = 10 - \left( a - b \right)
Determine whether each number sentence is true or false for all possible values of the variables:
2 b=b - b + b
g \times 3 = 3 \times g
1 \times 8 a = 18 a
3mv \times 1 = 3mv
b g=g b
0 \times 4fv = 0
9 w \times \dfrac{1}{9}=w
\dfrac{1}{6} b \times 6=b
\left( m \times 7\right) \times 3 = m \times \left( 7 \times 3\right)
v \div 3 = 3 \div v
Consider the expressions x - 5 and 5 - x.
Vanessa substituted x = 5 into each expression to determine whether they are equivalent. Is this a good method to check their equivalence? Explain your answer.
Consider the following statement:
"Using the commutative property of addition, we can rewrite 6 x + 2 as 2 x + 6."
Is this statement true or false? Explain your answer.
Use the commutative property of addition to complete the following:
5 \left(s + 6\right) = ⬚ \left(⬚ + ⬚\right)
8 \left(4 + m\right) = ⬚ (⬚+⬚)
4x \left(7 + 2y\right) = ⬚ \left( ⬚ + ⬚ \right)
\left(3a + 5b\right)c = \left( ⬚ + ⬚ \right) ⬚
For each of the following, find the missing term that would make the number sentence true:
0+⬚=9 m
u + 6=⬚+u
⬚-0=3 d
2 + 4y = 4y + ⬚
⬚ - 3t = -3t
\dfrac{1}{3}b + ⬚ = \dfrac{1}{3}b
d + \dfrac{1}{7} = ⬚ + d
8 + \dfrac{x}{4} = ⬚ + 8
Use the commutative property of multiplication to complete the following:
2 + 8 \times s=⬚+⬚ \times ⬚
4 \times \left(7 + r\right)=⬚ \times ⬚
4x \times 2 + 25= ⬚ \times ⬚ + ⬚
\left(8a + 2b\right) \times 9c =⬚ \times ⬚
For each of the following, find the missing term that would make the number sentence true:
0 \times 8m=⬚
7b \times 1=⬚
1 \times ⬚=4 b
a \times 19=19 \times ⬚
\dfrac{c}{2} \times ⬚ = 0
⬚ \times 3x = 3x
-1 \times 8y= ⬚
\dfrac{a}{3} \times \dfrac{b}{4} = ⬚ \times \dfrac{a}{3}