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Math Problems
Grade 6
Properties of addition
Which equation has no solution?
\newline
5
+
2
(
3
+
2
x
)
=
x
+
3
(
x
+
1
)
5+2(3+2 x)=x+3(x+1)
5
+
2
(
3
+
2
x
)
=
x
+
3
(
x
+
1
)
\newline
5
(
x
+
3
)
+
x
=
4
(
x
+
3
)
+
3
5(x+3)+x=4(x+3)+3
5
(
x
+
3
)
+
x
=
4
(
x
+
3
)
+
3
\newline
4
(
x
+
3
)
+
2
x
=
6
(
x
+
2
)
4(x+3)+2 x=6(x+2)
4
(
x
+
3
)
+
2
x
=
6
(
x
+
2
)
\newline
4
+
6
(
2
+
x
)
=
2
(
3
x
+
8
)
4+6(2+x)=2(3 x+8)
4
+
6
(
2
+
x
)
=
2
(
3
x
+
8
)
Get tutor help
Which property of addition is shown?
\newline
(
q
+
r
)
+
s
=
q
+
(
r
+
s
)
(q + r) + s = q + (r + s)
(
q
+
r
)
+
s
=
q
+
(
r
+
s
)
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which equation shows the commutative property of addition?
\newline
Choices:
\newline
(A)
r
+
s
=
s
+
r
r + s = s + r
r
+
s
=
s
+
r
\newline
(B)
r
=
r
+
0
r = r + 0
r
=
r
+
0
\newline
(C)
0
+
r
=
r
0 + r = r
0
+
r
=
r
\newline
(D)
r
+
(
s
+
t
)
=
(
r
+
s
)
+
t
r + (s + t) = (r + s) + t
r
+
(
s
+
t
)
=
(
r
+
s
)
+
t
Get tutor help
Which property of addition is shown?
\newline
(
r
+
s
)
+
t
=
r
+
(
s
+
t
)
(r + s) + t = r + (s + t)
(
r
+
s
)
+
t
=
r
+
(
s
+
t
)
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which property of addition is shown?
\newline
(
n
+
p
)
+
q
=
n
+
(
p
+
q
)
(n + p) + q = n + (p + q)
(
n
+
p
)
+
q
=
n
+
(
p
+
q
)
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
r
+
(
s
+
t
)
=
(
r
+
s
)
+
t
r + (s + t) = (r + s) + t
r
+
(
s
+
t
)
=
(
r
+
s
)
+
t
\newline
(B)
r
+
0
=
r
r + 0 = r
r
+
0
=
r
\newline
(C)
t
=
r
+
s
t = r + s
t
=
r
+
s
\newline
(D)
s
+
r
=
r
+
s
s + r = r + s
s
+
r
=
r
+
s
Get tutor help
Which equation shows the associative property of addition?
\newline
Choices:
\newline
(A)
q
=
0
+
q
q = 0 + q
q
=
0
+
q
\newline
(B)
q
+
(
r
+
s
)
=
(
q
+
r
)
+
s
q + (r + s) = (q + r) + s
q
+
(
r
+
s
)
=
(
q
+
r
)
+
s
\newline
(C)
q
+
r
=
r
+
q
q + r = r + q
q
+
r
=
r
+
q
\newline
(D)
q
=
r
+
s
+
t
q = r + s + t
q
=
r
+
s
+
t
Get tutor help
Which equation shows the commutative property of addition?
\newline
Choices:
\newline
(A)
k
+
m
=
n
k + m = n
k
+
m
=
n
\newline
(B)
(
k
+
m
)
+
n
=
k
+
(
m
+
n
)
(k + m) + n = k + (m + n)
(
k
+
m
)
+
n
=
k
+
(
m
+
n
)
\newline
(C)
k
+
m
=
m
+
k
k + m = m + k
k
+
m
=
m
+
k
\newline
(D)
k
=
0
+
k
k = 0 + k
k
=
0
+
k
Get tutor help
Which equation shows the commutative property of addition?
\newline
Choices:
\newline
(A)
(
a
+
b
)
+
c
=
a
+
(
b
+
c
)
(a + b) + c = a + (b + c)
(
a
+
b
)
+
c
=
a
+
(
b
+
c
)
\newline
(B)
c
+
d
=
a
+
b
c + d = a + b
c
+
d
=
a
+
b
\newline
(C)
0
+
a
=
a
0 + a = a
0
+
a
=
a
\newline
(D)
b
+
a
=
a
+
b
b + a = a + b
b
+
a
=
a
+
b
Get tutor help
Which property of addition is shown?
\newline
s
+
r
=
r
+
s
s + r = r + s
s
+
r
=
r
+
s
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
Get tutor help
Which property of addition is shown?
\newline
b
+
c
=
c
+
b
b + c = c + b
b
+
c
=
c
+
b
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
Get tutor help
Which property of addition is shown?
\newline
s
+
t
=
t
+
s
s + t = t + s
s
+
t
=
t
+
s
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which equation shows the associative property of addition?
\newline
Choices:
\newline
(A)
a
+
(
b
+
c
)
=
(
a
+
b
)
+
c
a + (b + c) = (a + b) + c
a
+
(
b
+
c
)
=
(
a
+
b
)
+
c
\newline
(B)
c
+
d
=
a
+
b
c + d = a + b
c
+
d
=
a
+
b
\newline
(C)
a
+
b
=
b
+
c
a + b = b + c
a
+
b
=
b
+
c
\newline
(D)
a
=
0
+
a
a = 0 + a
a
=
0
+
a
Get tutor help
Which equation shows the associative property of addition?
\newline
Choices:
\newline
(A)
u
+
v
=
v
+
w
u + v = v + w
u
+
v
=
v
+
w
\newline
(B)
u
+
(
v
+
w
)
=
(
u
+
v
)
+
w
u + (v + w) = (u + v) + w
u
+
(
v
+
w
)
=
(
u
+
v
)
+
w
\newline
(C)
0
+
u
=
u
0 + u = u
0
+
u
=
u
\newline
(D)
u
+
v
=
v
+
u
u + v = v + u
u
+
v
=
v
+
u
Get tutor help
Which equation shows the commutative property of addition?
\newline
Choices:
\newline
(A)
s
=
s
+
0
s = s + 0
s
=
s
+
0
\newline
(B)
t
+
s
=
s
+
t
t + s = s + t
t
+
s
=
s
+
t
\newline
(C)
s
+
t
=
u
+
v
s + t = u + v
s
+
t
=
u
+
v
\newline
(D)
s
+
(
t
+
u
)
=
(
s
+
t
)
+
u
s + (t + u) = (s + t) + u
s
+
(
t
+
u
)
=
(
s
+
t
)
+
u
Get tutor help
Which equation shows the associative property of addition?
\newline
Choices:
\newline
(A)
r
+
0
=
r
r + 0 = r
r
+
0
=
r
\newline
(B)
(
r
+
s
)
+
t
=
r
+
(
s
+
t
)
(r + s) + t = r + (s + t)
(
r
+
s
)
+
t
=
r
+
(
s
+
t
)
\newline
(C)
t
+
u
=
r
+
s
t + u = r + s
t
+
u
=
r
+
s
\newline
(D)
r
=
0
+
r
r = 0 + r
r
=
0
+
r
Get tutor help
Which property of addition is shown?
\newline
v
+
u
=
u
+
v
v + u = u + v
v
+
u
=
u
+
v
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
m
=
n
+
p
+
q
m = n + p + q
m
=
n
+
p
+
q
\newline
(B)
m
+
n
=
n
+
m
m + n = n + m
m
+
n
=
n
+
m
\newline
(C)
m
=
m
+
0
m = m + 0
m
=
m
+
0
\newline
(D)
p
+
q
=
m
+
n
p + q = m + n
p
+
q
=
m
+
n
Get tutor help
Which property of addition is shown?
\newline
(
b
+
c
)
+
d
=
b
+
(
c
+
d
)
(b + c) + d = b + (c + d)
(
b
+
c
)
+
d
=
b
+
(
c
+
d
)
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
Get tutor help
Which property of addition is shown?
\newline
h
+
(
j
+
k
)
=
(
h
+
j
)
+
k
h + (j + k) = (h + j) + k
h
+
(
j
+
k
)
=
(
h
+
j
)
+
k
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
r
=
0
+
r
r = 0 + r
r
=
0
+
r
\newline
(B)
r
=
s
+
t
+
u
r = s + t + u
r
=
s
+
t
+
u
\newline
(C)
r
+
(
s
+
t
)
=
(
r
+
s
)
+
t
r + (s + t) = (r + s) + t
r
+
(
s
+
t
)
=
(
r
+
s
)
+
t
\newline
(D)
s
+
r
=
r
+
s
s + r = r + s
s
+
r
=
r
+
s
Get tutor help
Which property of addition is shown?
\newline
r
+
(
s
+
t
)
=
(
r
+
s
)
+
t
r + (s + t) = (r + s) + t
r
+
(
s
+
t
)
=
(
r
+
s
)
+
t
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which property of addition is shown?
\newline
b
=
b
+
0
b = b + 0
b
=
b
+
0
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
Get tutor help
Which equation shows the associative property of addition?
\newline
Choices:
\newline
(A)
(
s
+
t
)
+
u
=
s
+
(
t
+
u
)
(s + t) + u = s + (t + u)
(
s
+
t
)
+
u
=
s
+
(
t
+
u
)
\newline
(B)
0
+
s
=
s
0 + s = s
0
+
s
=
s
\newline
(C)
s
+
t
=
t
+
s
s + t = t + s
s
+
t
=
t
+
s
\newline
(D)
t
+
u
+
v
=
s
t + u + v = s
t
+
u
+
v
=
s
Get tutor help
Which property of addition is shown?
\newline
m
+
(
n
+
p
)
=
(
m
+
n
)
+
p
m + (n + p) = (m + n) + p
m
+
(
n
+
p
)
=
(
m
+
n
)
+
p
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which property of addition is shown?
\newline
p
+
n
=
n
+
p
p + n = n + p
p
+
n
=
n
+
p
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which property of addition is shown?
\newline
t
+
u
=
u
+
t
t + u = u + t
t
+
u
=
u
+
t
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which property of addition is shown?
\newline
(
m
+
n
)
+
p
=
m
+
(
n
+
p
)
(m + n) + p = m + (n + p)
(
m
+
n
)
+
p
=
m
+
(
n
+
p
)
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
j
=
g
+
h
j = g + h
j
=
g
+
h
\newline
(B)
(
g
+
h
)
+
j
=
g
+
(
h
+
j
)
(g + h) + j = g + (h + j)
(
g
+
h
)
+
j
=
g
+
(
h
+
j
)
\newline
(C)
0
+
g
=
g
0 + g = g
0
+
g
=
g
\newline
(D)
g
+
h
=
h
+
g
g + h = h + g
g
+
h
=
h
+
g
Get tutor help
Which property of addition is shown?
\newline
m
+
n
=
n
+
m
m + n = n + m
m
+
n
=
n
+
m
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which property of addition is shown?
\newline
r
+
q
=
q
+
r
r + q = q + r
r
+
q
=
q
+
r
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which equation shows the associative property of addition?
\newline
Choices:
\newline
(A)
b
+
c
=
d
b + c = d
b
+
c
=
d
\newline
(B)
b
+
c
=
c
+
b
b + c = c + b
b
+
c
=
c
+
b
\newline
(C)
c
+
d
=
b
+
c
c + d = b + c
c
+
d
=
b
+
c
\newline
(D)
(
b
+
c
)
+
d
=
b
+
(
c
+
d
)
(b + c) + d = b + (c + d)
(
b
+
c
)
+
d
=
b
+
(
c
+
d
)
Get tutor help
Which property of addition is shown?
\newline
(
a
+
b
)
+
c
=
a
+
(
b
+
c
)
(a + b) + c = a + (b + c)
(
a
+
b
)
+
c
=
a
+
(
b
+
c
)
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
Get tutor help
Which property of addition is shown?
\newline
u
+
(
v
+
w
)
=
(
u
+
v
)
+
w
u + (v + w) = (u + v) + w
u
+
(
v
+
w
)
=
(
u
+
v
)
+
w
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
n
=
0
+
n
n = 0 + n
n
=
0
+
n
\newline
(B)
n
=
p
+
q
+
r
n = p + q + r
n
=
p
+
q
+
r
\newline
(C)
n
+
(
p
+
q
)
=
(
n
+
p
)
+
q
n + (p + q) = (n + p) + q
n
+
(
p
+
q
)
=
(
n
+
p
)
+
q
\newline
(D)
n
+
p
=
p
+
q
n + p = p + q
n
+
p
=
p
+
q
Get tutor help
Which equation shows the commutative property of addition?
\newline
Choices:
\newline
(A)
j
+
k
=
k
+
j
j + k = k + j
j
+
k
=
k
+
j
\newline
(B)
j
+
k
=
m
j + k = m
j
+
k
=
m
\newline
(C)
(
j
+
k
)
+
m
=
j
+
(
k
+
m
)
(j + k) + m = j + (k + m)
(
j
+
k
)
+
m
=
j
+
(
k
+
m
)
\newline
(D)
k
+
m
+
n
=
j
k + m + n = j
k
+
m
+
n
=
j
Get tutor help
Which property of addition is shown?
\newline
(
t
+
u
)
+
v
=
t
+
(
u
+
v
)
(t + u) + v = t + (u + v)
(
t
+
u
)
+
v
=
t
+
(
u
+
v
)
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
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Which property of addition is shown?
\newline
k
+
j
=
j
+
k
k + j = j + k
k
+
j
=
j
+
k
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
Get tutor help
Which property of addition is shown?
\newline
(
s
+
t
)
+
u
=
s
+
(
t
+
u
)
(s + t) + u = s + (t + u)
(
s
+
t
)
+
u
=
s
+
(
t
+
u
)
\newline
Choices:
\newline
(A)associative
\newline
(B)commutative
\newline
(C)identity
Get tutor help
Which equation shows the commutative property of addition?
\newline
Choices:
\newline
(A)
(
m
+
n
)
+
p
=
m
+
(
n
+
p
)
(m + n) + p = m + (n + p)
(
m
+
n
)
+
p
=
m
+
(
n
+
p
)
\newline
(B)
m
+
0
=
m
m + 0 = m
m
+
0
=
m
\newline
(C)
p
=
m
+
n
p = m + n
p
=
m
+
n
\newline
(D)
n
+
m
=
m
+
n
n + m = m + n
n
+
m
=
m
+
n
Get tutor help
Which equation shows the associative property of addition?
\newline
Choices:
\newline
(A)
b
+
a
=
a
+
b
b + a = a + b
b
+
a
=
a
+
b
\newline
(B)
(
a
+
b
)
+
c
=
a
+
(
b
+
c
)
(a + b) + c = a + (b + c)
(
a
+
b
)
+
c
=
a
+
(
b
+
c
)
\newline
(C)
a
=
0
+
a
a = 0 + a
a
=
0
+
a
\newline
(D)
b
+
c
+
d
=
a
b + c + d = a
b
+
c
+
d
=
a
Get tutor help
Which equation shows the associative property of addition?
\newline
Choices:
\newline
(A)
p
=
p
+
0
p = p + 0
p
=
p
+
0
\newline
(B)
(
p
+
q
)
+
r
=
p
+
(
q
+
r
)
(p + q) + r = p + (q + r)
(
p
+
q
)
+
r
=
p
+
(
q
+
r
)
\newline
(C)
p
+
q
=
q
+
r
p + q = q + r
p
+
q
=
q
+
r
\newline
(D)
q
+
p
=
p
+
q
q + p = p + q
q
+
p
=
p
+
q
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
g
+
h
=
h
+
g
g + h = h + g
g
+
h
=
h
+
g
\newline
(B)
(
g
+
h
)
+
j
=
g
+
(
h
+
j
)
(g + h) + j = g + (h + j)
(
g
+
h
)
+
j
=
g
+
(
h
+
j
)
\newline
(C)
g
=
h
+
j
+
k
g = h + j + k
g
=
h
+
j
+
k
\newline
(D)
g
=
0
+
g
g = 0 + g
g
=
0
+
g
Get tutor help
Which equation shows the associative property of addition?
\newline
Choices:
\newline
(A)
q
=
r
+
s
+
t
q = r + s + t
q
=
r
+
s
+
t
\newline
(B)
q
+
r
=
s
+
t
q + r = s + t
q
+
r
=
s
+
t
\newline
(C)
q
+
(
r
+
s
)
=
(
q
+
r
)
+
s
q + (r + s) = (q + r) + s
q
+
(
r
+
s
)
=
(
q
+
r
)
+
s
\newline
(D)
q
=
0
+
q
q = 0 + q
q
=
0
+
q
Get tutor help
Which equation shows the commutative property of addition?
\newline
Choices:
\newline
(A)
k
+
m
=
m
+
k
k + m = m + k
k
+
m
=
m
+
k
\newline
(B)
k
+
(
m
+
n
)
=
(
k
+
m
)
+
n
k + (m + n) = (k + m) + n
k
+
(
m
+
n
)
=
(
k
+
m
)
+
n
\newline
(C)
k
+
m
=
m
+
n
k + m = m + n
k
+
m
=
m
+
n
\newline
(D)
k
+
0
=
k
k + 0 = k
k
+
0
=
k
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
m
+
n
=
j
+
k
m + n = j + k
m
+
n
=
j
+
k
\newline
(B)
j
+
(
k
+
m
)
=
(
j
+
k
)
+
m
j + (k + m) = (j + k) + m
j
+
(
k
+
m
)
=
(
j
+
k
)
+
m
\newline
(C)
0
+
j
=
j
0 + j = j
0
+
j
=
j
\newline
(D)
k
+
m
+
n
=
j
k + m + n = j
k
+
m
+
n
=
j
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
p
+
q
=
n
+
p
p + q = n + p
p
+
q
=
n
+
p
\newline
(B)
0
+
n
=
n
0 + n = n
0
+
n
=
n
\newline
(C)
n
+
p
=
p
+
n
n + p = p + n
n
+
p
=
p
+
n
\newline
(D)
(
n
+
p
)
+
q
=
n
+
(
p
+
q
)
(n + p) + q = n + (p + q)
(
n
+
p
)
+
q
=
n
+
(
p
+
q
)
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
k
=
0
+
k
k = 0 + k
k
=
0
+
k
\newline
(B)
m
+
n
+
p
=
k
m + n + p = k
m
+
n
+
p
=
k
\newline
(C)
(
k
+
m
)
+
n
=
k
+
(
m
+
n
)
(k + m) + n = k + (m + n)
(
k
+
m
)
+
n
=
k
+
(
m
+
n
)
\newline
(D)
m
+
k
=
k
+
m
m + k = k + m
m
+
k
=
k
+
m
Get tutor help
Which equation shows the identity property of addition?
\newline
Choices:
\newline
(A)
m
=
m
+
0
m = m + 0
m
=
m
+
0
\newline
(B)
(
m
+
n
)
+
p
=
m
+
(
n
+
p
)
(m + n) + p = m + (n + p)
(
m
+
n
)
+
p
=
m
+
(
n
+
p
)
\newline
(C)
n
+
m
=
m
+
n
n + m = m + n
n
+
m
=
m
+
n
\newline
(D)
p
=
m
+
n
p = m + n
p
=
m
+
n
Get tutor help
When solving an equation, Emily's first step is shown below. Which property justifies Emily's first step?
\newline
Original Equation:
\newline
−
1
4
x
=
3
-\frac{1}{4} x=3
−
4
1
x
=
3
\newline
First Step:
\newline
x
=
−
12
x=-12
x
=
−
12
\newline
multiplication property of equality
\newline
addition property of equality
\newline
associative property of addition
\newline
commutative property of addition
Get tutor help
