# Spectrum Math Grade 3 Chapter 10 Lesson 2 Answer Key Number Sentences

Students can use the Spectrum Math Grade 3 Answer Key Chapter 10 Lesson 10.2 Number Sentences as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 3 Chapter 10 Lesson 10.2 Number Sentences Answers Key

A number sentence is an equation with numbers.
Identity Property
for addition: 0 + 3 = 3
for multiplication: 1 × 3 = 3

Commutative Property
for addition: 3 + 2 = 2 + 3
for multiplication: 4 × 2 = 2 × 4
A number sentence can change its look but not change its value.
3 + 5 = 8 or 3 + 5 = 4 + 4
3 × 8 = 24 or 3 × 8 = 6 × 4

Complete each number sentence.

Question 1.
a. 0 + 4 = ___________
Try to implement the Addition identity as shown below
0 + 4 = 4 . When zero and 4 are added , the result is 4.

b. 0 + 6 = ___________
Try to implement the Addition identity as shown below
0 + 6 = 6 . When zero and 6 are added , the result is 6.

c. ___________ + 2 = 2
Try to implement the Addition identity as shown below
0 + 2 = 2 . When zero and 2 are added , the result is 2.

d. ___________ + 7 = 7
Try to implement the Addition identity as shown below
0 + 7 = 7 . When zero and 7 are added , the result is 7.

Question 2.
a. 1 × 2 = ____________
Given values are 1 and 2 .When 1 and 2 are multiplied , the result obtained is 1 x  2 = 2 .

b. 1 × 5 = ____________
Given values are 1 and 5 .When 1 and 5 are multiplied , the result obtained is 1 x  5 = 5 .

c. ___________ × 4 = 4
The answer is 1. Since 4  is obtained only when 1 and 4 are multiplied. i.e. 1 x 4 = 4

d. ___________ × 9 = 9
The answer is 1. Since 9  is obtained only when 1 and 9 are multiplied. i.e. 1 x 9 = 9

Question 3.
a. 7 + 2 = ___________ + 7
Try to implement the Commutative addition property. So, As per this property the answer is 2 i.e. 7  + 2 = 2 + 7.

b. 3 + 4 = ____________ + 3
Try to implement the Commutative addition property. So, As per this property the answer is 4 i.e.  3 + 4 = 4 + 3.

c. 1 + 2 = 2 + ____________
Try to implement the Commutative addition property. So, As per this property the answer is 1 i.e.   1+ 2 = 2 + 1.

d. ____________ + 5 = 5 + 4
Try to implement the Commutative addition property. So, As per this property the answer is 4 i.e.  4 + 5 = 5 + 4.

Question 4.
a. 5 × 7 = 7 × _____________
Try to implement the Commutative Multiplication property. So, As per this property the answer is 5 i.e. 5 x 7  =  7 x 5.

b. 4 × ____________ = 3 × 4
Try to implement the Commutative Multiplication property. So, As per this property the answer is 3 i.e. 4 x 3  =  3 x 4.

c. ___________ × 3 = 3 × 5
Try to implement the Commutative Multiplication property. So, As per this property the answer is 5 i.e. 5 x 3  =  3 x 5.

d. 9 × 4 = _____________ × 9
Try to implement the Commutative Multiplication property. So, As per this property the answer is 4 i.e. 9 x 4  =  4 x 9.

Complete the following.

Question 5.
a. 2 + 7 = 9 or
2 + 7 = 5 + ____________
Try to implement the Commutative Addition property. So, As per this property the answer is 4 i.e. 2 + 7  =  5 + 4 .

b. 5 + 7 = 12 or
5 + 7 = 6 + ___________
Try to implement the Commutative Addition property. So, As per this property the answer is 6 i.e. 5 + 7  =  6 + 6 .

c. 4 + 3 = 7 or
4 + 3 = 5 + ____________
Try to implement the Commutative Addition property. So, As per this property the answer is 2 i.e. 4 + 3  =  5 +2

d. 6 + 9 = 15 or
6 + 9 = 10 + ____________
Try to implement the Commutative Addition property. So, As per this property the answer is 5 i.e. 5 + 7  =  10 +5

Question 6.
a. 6 + 4 = 10 or
6 + 4 = 5 + _____________
Try to implement the Commutative Addition property. So, As per this property the answer is 5 i.e. 6 + 4  =  5 +5

b. 6 + 7 = 13 or
6 + 7 = 8 + _____________
Try to implement the Commutative Addition property. So, As per this property the answer is 5 i.e. 6 + 7  =  8 + 5.

c. 5 + 3 = 8 or
5 + 3 = 6 + _____________
Try to implement the Commutative Addition property. So, As per this property the answer is 2 i.e. 5 + 3  =  6 + 2.

d. 9 + 2 = 11 or
9 + 2 = 5 + ______________
Try to implement the Commutative Addition property. So, As per this property the answer is 6 i.e. 5 + 7  =  5 +6.

Question 7.
a. 5 × 6 = 30 or
5 × 6 = 10 × ______________
Try to implement the Commutative Multiplication property. So, As per this property the answer is 3 i.e. 5 x 6  = 10 x 3.

b. 4 × 3 = 12 or
4 × 3 = 2 × _____________
Try to implement the Commutative Multiplication property. So, As per this property the answer is 6 i.e. 4 x 3  = 2 x 6

c. 6 × 3 = 18 or
6 × 3 = 9 × _____________
Try to implement the Commutative Multiplication property. So, As per this property the answer is 2 i.e. 6 x 3  = 9 x 2

d. 6 × 2 = 12 or
6 × 2 = 4 × ______________
Try to implement the Commutative Multiplication property. So, As per this property the answer is 3 i.e. 6 x 2  = 4 x 3`

Associative Property
2 × 3 × 4 = c
2 × 3 = 6
6 × 4 = 24
c = 24

Distributive Property
11 × 8 = (6 × 8) + (5 × 8)
48 + 40 = 88
11 × 8 = 88

Solve using the associative property.

Question 1.
a. 2 × 3 × 5 = d
___________ × ___________ = _____________
___________ × ___________ = _____________
d = _____________
Given 2 x 3 x 5 = d
According to the Associative property
2 x 3 = 6
6 x 5 = 30
30 =d
Hence the Resultant value obtained after Simplification is d = 30

b. 1 × 2 × 9 = h
___________ × ___________ = _____________
___________ × ___________ = _____________
h = _____________
Given 1 x 2 x 9 = h
According to the Associative property
1 x 2 = 2
2 x 9 = 18
18 = h
Hence the Resultant value obtained after Simplification is h = 18

Question 2.
a. 2 × 4 × 6 = e
___________ × ___________ = _____________
___________ × ___________ = _____________
e = _____________
Given 2 x 4 x 6 = e
According to the Associative property
2 x 4 = 8
8 x 4 = 32
32 = e
Hence the Resultant value obtained after Simplification is e = 32

b. 2 × 4 × 7 = g
___________ × ___________ = _____________
___________ × ___________ = _____________
g = _____________
Given 2 x 4 x 7 = g
According to the Associative property
2 x 4 = 8
8 x 7 = 56
56 =g
Hence the Resultant value obtained after Simplification is g = 56

Solve using the distributive property.

Question 3.
12 × 4 = (10 × 4) + (___________ × 4)
__________ + ____________
12 × 4 = _____________
Given 12 × 4 = (10 × 4) + (___________ × 4)
According to the distributive property
12 x 4 = ( 10 x 4 ) + ( 2 x 4 )
40 + 8 = 48
12 x 4 = 48
Hence the Resultant value obtained after Simplification is 48.

14 × 3 = (10 × 3) + (___________ × 3)
__________ + ____________
14 × 3 = _____________
Given 14 × 3 = (10 × 3) + (___________× 3)
According to the distributive property
14 x 3 = ( 10 x 3 ) + ( 4 x 3 )
30 + 12  = 42
14 x 3 = 42
Hence the Resultant value obtained after Simplification is 42.

Question 4.
19 × 2 = (10 × 2) + (_________ × 2)
____________ + ____________
19 × 2 = ____________
Given 19 × 2 = (10 × 2) + (_________ × 2)
According to the distributive property
( 10 x 2 ) + (9 x 2 )
20 + 18 = 38
19 x 2  = 38
Hence the Resultant value obtained after Simplification is 38.

16 × 5 = (10 × 5) + (__________ × 5)
____________ + ____________
16 × 5 = ____________
Given 16 × 5 = (10 × 5) + (__________ × 5)
According to the distributive property
( 10 x 5 ) + (6 x 5 )
50 + 30 = 80
16 x 5  = 80
Hence the Resultant value obtained after Simplification is 80. Write each number sentence. Put a box ( ) in the sentence for the missing part. Solve each number sentence.

Question 1.
The sum of two and three is what number? 2 + 3 = 5
The sum of two and three is _____________.
When both the numbers are added i.e. 2 + 3 = 5
Hence the result obtained after the summation of two and three is i.e. 2 + 3 = 5.

Question 2.
Seven minus two is what number? ______________
Seven minus two is ____________.
Given seven and 2 are two numbers i.e. 7 – 2  = 5
Hence the result obtained after the subtraction two from seven is i.e. 7 – 2 = 5.

Question 3.
Four times three is what number? _____________
Four times three is ____________.
Given number is 3 and when it is 3 times Multiplied the value obtained is i.e. 3 x 3 x 3 x 3= 12
Therefore 4 times 3 is 12.

Question 4.
Fourteen divided by two is what number? ____________
Fourteen divided by two is ___________.
Fourteen divided by two is 14 / 2 = 7
Hence the value obtained when Fourteen divided by two is 14  /  2 = 7

Question 5.
Five added to what number is seven? _____________
Five added to ______________ is seven.
Let the unknown number be x , when five is added to it i.e. 5 + x = 7
x = 7 -5 = 2
Five added to two is seven.
Therefore , Five is added to 2 and generates the value is 7.

Question 6.
Thirteen minus what number is ten? _____________
Thirteen minus _____________ is ten.
Let the unknown number be x
When 13 – x = 10
x = 13 – 10 = 3
Therefore thirteen minus three is ten.

Write each number sentence. Put a box ( ) in the sentence for the missing part. Solve each number sentence.

Question 1.
Twenty-seven divided by a number equals three. _____________
Twenty-seven divided by ____________ equals three.
Let unknown number be S
As per the Given data , When 27 is Divided with unknown number S i.e. 27 ÷  S = 3
S = 27 ÷ 3
S = 9
Therefore, Twenty-seven divided by 9 equals three.

Question 2.
This number divided by eight equals eight. ____________
____________ divided by eight equals eight.
Let the Number be K.
As per the Given Data , When K is divided with eight is 8 as shown below.
K ÷ 8 = 8
K = 8 x 8
K= 64
Therefore , 64 divided by eight equals eight.

Question 3.
Twelve divided by three equals what number? ____________
Twelve divided by three equals _____________
Divide the number 12 by 3 is as shown below
12 ÷ 3 = 4
Therefore, Twelve divided by three equals is 4.

Question 4.
Four times nine is what number? ___________
Four times nine is ____________.
Write the given number 9 as 4 times  as shown below
9 x 4 = 36
Therefore, Four times nine is 36

Question 5.
The is number times eight is fifty -six. ___________
_____________ times eight is fifty-six.
Let unknown number be x
As per the Given data , When x is multiplied with eight i.e. X x 8 = 56
x = 56 ÷  8
x = 7 is the number
Then 7 x 8 =56
Therefore 7 times eight is fifty-six.

Question 6.
Nine times this number is eighty-one.
Nine times ____________ is eighty-one.
Let unknown number be p
As per the Given data , 9 x p = 81
p = 81 ÷ 9
p = 9
Therefore, Nine times Nine is eighty-one

Question 7.
Twenty divided by four is what number? ____________
Twenty divided by four is _____________.
When twenty is divided with 4 , The result is as shown below.
20 ÷ 4 = 5
Therefore , The result obtained Twenty divided by four is five.

Question 8.
Ten times this number is ninety. ___________
Ten times ___________ is ninety.
We have to know the number which is Ninety. So, Write the 9 number as ten times which is shown Below.
9 x 10 = 90
Therefore, Ten times nine is ninety.

Question 9.
The is number times five is twenty-five. ___________
___________ times five is twenty-five.
We have to know the number which is Twenty-five. So, Write the 5 number as five times which is shown Below.
5 x 5 = 25
Therefore, Five times five is Twenty -five.

Question 10.
This number divided by seven is nine. ___________
___________ divided by seven is nine.