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Math Problems
Grade 6
Properties of multiplication
Rewrite the function by completing the square.
\newline
f
(
x
)
=
x
2
−
9
x
+
14
f(x) = x^2 - 9x + 14
f
(
x
)
=
x
2
−
9
x
+
14
\newline
f
(
x
)
=
(
x
+
)
2
+
f(x) = (x + )^2 +
f
(
x
)
=
(
x
+
)
2
+
Get tutor help
Which property of multiplication is shown?
\newline
k
⋅
(
m
⋅
n
)
=
(
k
⋅
m
)
⋅
n
k \cdot (m \cdot n) = (k \cdot m) \cdot n
k
⋅
(
m
⋅
n
)
=
(
k
⋅
m
)
⋅
n
Get tutor help
Estimate. Which sign makes the statement true?
\newline
7981
5
÷
2
?
792
\frac{7981}{5} \div 2\;?\;792
5
7981
÷
2
?
792
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
Get tutor help
Estimate. Which sign makes the statement true?
\newline
132
÷
35
8
132 \div \frac{35}{8}
132
÷
8
35
?
?
?
15
15
15
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
Get tutor help
Estimate. Which sign makes the statement true?
\newline
1
,
544
2
3
÷
33
5
1,544\frac{2}{3} \div \frac{33}{5}
1
,
544
3
2
÷
5
33
?
\text{?}
?
893
893
893
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
0
=
_
_
_
_
_
⋅
914
0 = \_\_\_\_\_ \cdot 914
0
=
_____
⋅
914
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
745
⋅
867
=
867
⋅
_
_
_
_
745 \cdot 867 = 867 \cdot \_\_\_\_
745
⋅
867
=
867
⋅
____
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
114
⋅
_
_
_
_
_
=
0
114 \cdot \_\_\_\_\_ = 0
114
⋅
_____
=
0
Get tutor help
What value of
d
d
d
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
56
⋅
d
=
421
⋅
56
56 \cdot d = 421 \cdot 56
56
⋅
d
=
421
⋅
56
\newline
d
=
d =
d
=
_____
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
895
=
895
⋅
895 = 895 \cdot
895
=
895
⋅
_
_
\_\_
__
Get tutor help
What value of
c
c
c
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
(
649
⋅
439
)
⋅
422
=
649
⋅
(
439
⋅
c
)
(649 \cdot 439) \cdot 422 = 649 \cdot (439 \cdot c)
(
649
⋅
439
)
⋅
422
=
649
⋅
(
439
⋅
c
)
\newline
c
=
c =
c
=
_____
Get tutor help
What value of
g
g
g
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
g
⋅
1
=
336
g \cdot 1 = 336
g
⋅
1
=
336
\newline
g
=
g =
g
=
_____
Get tutor help
What value of
t
t
t
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
774
⋅
953
=
953
⋅
t
774 \cdot 953 = 953 \cdot t
774
⋅
953
=
953
⋅
t
\newline
t
=
t =
t
=
_____
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
(
_
_
_
_
_
+
637
)
⋅
223
=
773
⋅
223
+
637
⋅
223
(\_\_\_\_\_ + 637) \cdot 223 = 773 \cdot 223 + 637 \cdot 223
(
_____
+
637
)
⋅
223
=
773
⋅
223
+
637
⋅
223
Get tutor help
What value of
g
g
g
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
g
=
0
⋅
828
g = 0 \cdot 828
g
=
0
⋅
828
\newline
g
=
g =
g
=
_____
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
795
=
795
⋅
795 = 795 \cdot
795
=
795
⋅
_
_
\_\_
__
Get tutor help
What value of
r
r
r
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
307
⋅
0
=
r
307 \cdot 0 = r
307
⋅
0
=
r
\newline
r
=
r =
r
=
_____
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
705
⋅
0
=
705 \cdot 0 =
705
⋅
0
=
_____
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
558
⋅
(
314
+
633
)
=
558
⋅
_
_
_
_
+
558
⋅
633
558 \cdot (314 + 633) = 558 \cdot \_\_\_\_ + 558 \cdot 633
558
⋅
(
314
+
633
)
=
558
⋅
____
+
558
⋅
633
Get tutor help
What value of
p
p
p
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
1
⋅
538
=
p
1 \cdot 538 = p
1
⋅
538
=
p
\newline
p
=
p =
p
=
_____
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
0
=
_
_
_
_
_
⋅
316
0 = \_\_\_\_\_ \cdot 316
0
=
_____
⋅
316
Get tutor help
Type the missing number.
\newline
Hint: Use properties of multiplication.
\newline
_
_
_
_
_
⋅
993
=
0
\_\_\_\_\_ \cdot 993 = 0
_____
⋅
993
=
0
Get tutor help
What value of
w
w
w
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
w
⋅
633
=
633
⋅
832
w \cdot 633 = 633 \cdot 832
w
⋅
633
=
633
⋅
832
\newline
w
=
w =
w
=
_____
Get tutor help
What value of
p
p
p
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
(
p
⋅
36
)
⋅
849
=
107
⋅
(
36
⋅
849
)
(p \cdot 36) \cdot 849 = 107 \cdot (36 \cdot 849)
(
p
⋅
36
)
⋅
849
=
107
⋅
(
36
⋅
849
)
\newline
p
=
p =
p
=
_____
Get tutor help
What value of
c
c
c
makes this multiplication sentence true?
\newline
Hint: Use properties of multiplication.
\newline
954
⋅
c
=
330
⋅
954
954 \cdot c = 330 \cdot 954
954
⋅
c
=
330
⋅
954
\newline
c
=
c =
c
=
_____
Get tutor help
Which property of multiplication is shown?
\newline
1
⋅
s
=
s
1 \cdot s = s
1
⋅
s
=
s
\newline
Choices:
\newline
(A) commutative
\newline
(B) distributive
\newline
(C) identity
\newline
(D) associative
Get tutor help
Which property of multiplication is shown?
\newline
8
⋅
(
5
+
0
)
=
8
⋅
5
+
8
⋅
0
8 \cdot (5 + 0) = 8 \cdot 5 + 8 \cdot 0
8
⋅
(
5
+
0
)
=
8
⋅
5
+
8
⋅
0
\newline
Choices:
\newline
(A) distributive
\newline
(B) associative
\newline
(C) commutative
\newline
(D) identity
Get tutor help
Which property of multiplication is shown?
\newline
0
=
m
⋅
0
0 = m \cdot 0
0
=
m
⋅
0
\newline
Choices:
\newline
(A) associative
\newline
(B) zero
\newline
(C) identity
\newline
(D) distributive
Get tutor help
Which property of multiplication is shown?
\newline
(
6
⋅
4
)
⋅
9
=
6
⋅
(
4
⋅
9
)
(6 \cdot 4) \cdot 9 = 6 \cdot (4 \cdot 9)
(
6
⋅
4
)
⋅
9
=
6
⋅
(
4
⋅
9
)
\newline
Choices:
\newline
(A) identity
\newline
(B) distributive
\newline
(C) commutative
\newline
(D) associative
Get tutor help
Which property of multiplication is shown?
\newline
f
⋅
g
+
f
⋅
h
=
f
⋅
(
g
+
h
)
f \cdot g + f \cdot h = f \cdot (g + h)
f
⋅
g
+
f
⋅
h
=
f
⋅
(
g
+
h
)
\newline
Choices:
\newline
(A) identity
\newline
(B) distributive
\newline
(C) associative
\newline
(D) commutative
Get tutor help
Which property of multiplication is shown?
\newline
(
h
⋅
j
)
⋅
k
=
h
⋅
(
j
⋅
k
)
(h \cdot j) \cdot k = h \cdot (j \cdot k)
(
h
⋅
j
)
⋅
k
=
h
⋅
(
j
⋅
k
)
\newline
Choices:
\newline
(A) distributive
\newline
(B) identity
\newline
(C) commutative
\newline
(D) associative
Get tutor help
Which equation shows the identity property of multiplication?
\newline
Choices:
\newline
(A)
5
⋅
(
8
⋅
6
)
=
(
5
⋅
8
)
⋅
6
5 \cdot (8 \cdot 6) = (5 \cdot 8) \cdot 6
5
⋅
(
8
⋅
6
)
=
(
5
⋅
8
)
⋅
6
\newline
(B)
(
9
⋅
4
)
⋅
2
=
9
⋅
(
4
⋅
2
)
(9 \cdot 4) \cdot 2 = 9 \cdot (4 \cdot 2)
(
9
⋅
4
)
⋅
2
=
9
⋅
(
4
⋅
2
)
\newline
(C)
1
⋅
3
=
3
1 \cdot 3 = 3
1
⋅
3
=
3
\newline
(D)
6
⋅
9
=
6
+
6
+
6
+
6
+
6
+
6
+
6
+
6
+
6
6 \cdot 9 = 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6
6
⋅
9
=
6
+
6
+
6
+
6
+
6
+
6
+
6
+
6
+
6
Get tutor help
Which property of multiplication is shown?
\newline
3
⋅
6
=
6
⋅
3
3 \cdot 6 = 6 \cdot 3
3
⋅
6
=
6
⋅
3
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) zero
\newline
(D) distributive
Get tutor help
Which property of multiplication is shown?
\newline
1
⋅
3
=
3
1 \cdot 3 = 3
1
⋅
3
=
3
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
\newline
(D) zero
Get tutor help
Which property of multiplication is shown?
\newline
7
⋅
1
=
1
⋅
7
7 \cdot 1 = 1 \cdot 7
7
⋅
1
=
1
⋅
7
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
\newline
(D) zero
Get tutor help
Which equation shows the identity property of multiplication?
\newline
Choices:
\newline
(A)
3
⋅
8
=
8
⋅
3
3 \cdot 8 = 8 \cdot 3
3
⋅
8
=
8
⋅
3
\newline
(B)
2
⋅
1
=
2
2 \cdot 1 = 2
2
⋅
1
=
2
\newline
(C)
0
⋅
5
=
0
0 \cdot 5 = 0
0
⋅
5
=
0
\newline
(D)
4
⋅
1
=
1
⋅
4
4 \cdot 1 = 1 \cdot 4
4
⋅
1
=
1
⋅
4
Get tutor help
Which property of multiplication is shown?
\newline
m
=
1
⋅
m
m = 1 \cdot m
m
=
1
⋅
m
\newline
Choices:
\newline
(A)commutative
\newline
(B)identity
\newline
(C)zero
\newline
(D)distributive
Get tutor help
Which property of multiplication is shown?
\newline
0
⋅
3
=
0
0 \cdot 3 = 0
0
⋅
3
=
0
\newline
Choices:
\newline
(A) associative
\newline
(B) commutative
\newline
(C) identity
\newline
(D) zero
\newline
Get tutor help
Which equation shows the zero property of multiplication?
\newline
Choices:
\newline
(A)
4
⋅
6
+
2
=
24
+
2
4 \cdot 6 + 2 = 24 + 2
4
⋅
6
+
2
=
24
+
2
\newline
(B)
7
⋅
6
=
6
⋅
7
7 \cdot 6 = 6 \cdot 7
7
⋅
6
=
6
⋅
7
\newline
(C)
3
⋅
(
4
⋅
7
)
=
(
3
⋅
4
)
⋅
7
3 \cdot (4 \cdot 7) = (3 \cdot 4) \cdot 7
3
⋅
(
4
⋅
7
)
=
(
3
⋅
4
)
⋅
7
\newline
(D)
0
=
9
⋅
0
0 = 9 \cdot 0
0
=
9
⋅
0
Get tutor help
Which property of multiplication is shown?
\newline
4
⋅
1
=
1
⋅
4
4 \cdot 1 = 1 \cdot 4
4
⋅
1
=
1
⋅
4
\newline
Choices:
\newline
(A) associative
\newline
(B) identity
\newline
(C) commutative
\newline
(D) zero
\newline
Get tutor help
Which equation shows the zero property of multiplication?
\newline
Choices:
\newline
(A)
a
⋅
b
=
c
+
d
a \cdot b = c + d
a
⋅
b
=
c
+
d
\newline
(B)
b
⋅
a
=
a
⋅
b
b \cdot a = a \cdot b
b
⋅
a
=
a
⋅
b
\newline
(C)
a
=
1
⋅
a
a = 1 \cdot a
a
=
1
⋅
a
\newline
(D)
0
⋅
a
=
0
0 \cdot a = 0
0
⋅
a
=
0
Get tutor help
Find all the factor pairs for
75
75
75
and complete the equations.
\newline
75
=
_
_
_
×
75
75 = \_\_\_ \times 75
75
=
___
×
75
\newline
75
=
3
×
_
_
_
75 = 3 \times \_\_\_
75
=
3
×
___
\newline
75
=
5
×
_
_
_
75 = 5 \times \_\_\_
75
=
5
×
___
Get tutor help
Marie wants to buy a new car. She saves
25
%
25\%
25%
of her wage and is left with
$
600
\$600
$600
spending money. What is Marie's wage?
\newline
(A)
$
450
\$450
$450
\newline
(B)
$
625
\$625
$625
\newline
(C)
$
750
\$750
$750
\newline
(D)
$
800
\$800
$800
Get tutor help
y
=
−
3
(
x
−
2
)
2
+
12
y=-3(x-2)^{2}+12
y
=
−
3
(
x
−
2
)
2
+
12
\newline
Vertex:
□
\square
□
Get tutor help
1170.16
=
[
C
×
1
⋅
1
(
1
+
0.08
)
5
0.08
]
+
[
0.4
×
(
1000
+
2
C
)
×
1
(
1
+
0.08
)
5
]
+
[
0.6
×
(
C
×
1
−
1
(
1
+
0.12
)
15
0.12
+
1000
(
1
+
0.12
)
15
)
×
1
(
1
+
0.08
)
5
]
\begin{aligned} 1170.16= & {\left[C \times \frac{1 \cdot \frac{1}{(1+0.08)^{5}}}{0.08}\right]+\left[0.4 \times(1000+2 C) \times \frac{1}{(1+0.08)^{5}}\right]+} \\ & {\left[0.6 \times\left(C \times \frac{1-\frac{1}{(1+0.12)^{15}}}{0.12}+\frac{1000}{(1+0.12)^{15}}\right) \times \frac{1}{(1+0.08)^{5}}\right] }\end{aligned}
1170.16
=
[
C
×
0.08
1
⋅
(
1
+
0.08
)
5
1
]
+
[
0.4
×
(
1000
+
2
C
)
×
(
1
+
0.08
)
5
1
]
+
[
0.6
×
(
C
×
0.12
1
−
(
1
+
0.12
)
15
1
+
(
1
+
0.12
)
15
1000
)
×
(
1
+
0.08
)
5
1
]
Get tutor help
Which property of multiplication is shown?
\newline
n
⋅
(
p
−
q
)
=
n
⋅
p
−
n
⋅
q
n \cdot (p - q) = n \cdot p - n \cdot q
n
⋅
(
p
−
q
)
=
n
⋅
p
−
n
⋅
q
\newline
Choices:
\newline
(A) identity
\newline
(B) zero
\newline
(C) commutative
\newline
(D) distributive
Get tutor help
Which equation shows the identity property of multiplication?
\newline
Choices:
\newline
(A)
w
⋅
y
=
u
⋅
v
w \cdot y = u \cdot v
w
⋅
y
=
u
⋅
v
\newline
(B)
0
⋅
u
=
0
0 \cdot u = 0
0
⋅
u
=
0
\newline
(C)
u
⋅
v
−
u
⋅
w
=
u
⋅
(
v
−
w
)
u \cdot v - u \cdot w = u \cdot (v - w)
u
⋅
v
−
u
⋅
w
=
u
⋅
(
v
−
w
)
\newline
(D)
u
=
1
⋅
u
u = 1 \cdot u
u
=
1
⋅
u
Get tutor help
Which equation shows the zero property of multiplication?
\newline
Choices:
\newline
(A)
t
=
1
⋅
t
t = 1 \cdot t
t
=
1
⋅
t
\newline
(B)
(
t
+
u
)
⋅
v
=
t
⋅
v
+
u
⋅
v
(t + u) \cdot v = t \cdot v + u \cdot v
(
t
+
u
)
⋅
v
=
t
⋅
v
+
u
⋅
v
\newline
(C)
0
=
0
⋅
t
0 = 0 \cdot t
0
=
0
⋅
t
\newline
(D)
v
+
w
=
t
⋅
u
v + w = t \cdot u
v
+
w
=
t
⋅
u
Get tutor help
Which property of multiplication is shown?
\newline
h
⋅
j
=
j
⋅
h
h \cdot j = j \cdot h
h
⋅
j
=
j
⋅
h
\newline
Choices:
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(A)zero
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(B)associative
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(C)identity
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(D)commutative
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Which equation shows the associative property of multiplication?
\newline
Choices:
\newline
(A)
(
h
⋅
j
)
⋅
k
=
h
⋅
(
j
⋅
k
)
(h \cdot j) \cdot k = h \cdot (j \cdot k)
(
h
⋅
j
)
⋅
k
=
h
⋅
(
j
⋅
k
)
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(B)
h
⋅
k
+
j
⋅
k
=
(
h
+
j
)
⋅
k
h \cdot k + j \cdot k = (h + j) \cdot k
h
⋅
k
+
j
⋅
k
=
(
h
+
j
)
⋅
k
\newline
(C)
h
=
h
⋅
1
h = h \cdot 1
h
=
h
⋅
1
\newline
(D)
0
⋅
h
=
0
0 \cdot h = 0
0
⋅
h
=
0
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