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 Ã— 3 = 3

Commutative Property

for addition: 3 + 2 = 2 + 3

for multiplication: 4 Ã— 2 = 2 Ã— 4

A number sentence can change its look but not change its value.

3 + 5 = 8 or 3 + 5 = 4 + 4

3 Ã— 8 = 24 or 3 Ã— 8 = 6 Ã— 4

**Complete each number sentence.**

Question 1.

a. 0 + 4 = ___________

Answer:

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 = ___________

Answer:

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

Answer:

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

Answer:

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 Ã— 2 = ____________

Answer:

Given values are 1 and 2 .When 1 and 2 are multiplied , the result obtained is 1 xÂ 2 = 2 .

b. 1 Ã— 5 = ____________

Answer:

Given values are 1 and 5 .When 1 and 5 are multiplied , the result obtained is 1 xÂ 5 = 5 .

c. ___________ Ã— 4 = 4

Answer:

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

d. ___________ Ã— 9 = 9

Answer:

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

Question 3.

a. 7 + 2 = ___________ + 7

Answer:

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

b. 3 + 4 = ____________ + 3

Answer:

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

c. 1 + 2 = 2 + ____________

Answer:

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

d. ____________ + 5 = 5 + 4

Answer:

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

Question 4.

a. 5 Ã— 7 = 7 Ã— _____________

Answer:

Try to implement the Commutative Multiplication property. So, As per this property the answer is 5 i.e. 5 x 7Â =Â 7 x 5.

b. 4 Ã— ____________ = 3 Ã— 4

Answer:

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

c. ___________ Ã— 3 = 3 Ã— 5

Answer:

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

d. 9 Ã— 4 = _____________ Ã— 9

Answer:

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

**Complete the following.**

Question 5.

a. 2 + 7 = 9 or

2 + 7 = 5 + ____________

Answer:

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

b. 5 + 7 = 12 or

5 + 7 = 6 + ___________

Answer:

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

c. 4 + 3 = 7 or

4 + 3 = 5 + ____________

Answer:

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

d. 6 + 9 = 15 or

6 + 9 = 10 + ____________

Answer:

Try to implement the Commutative Addition property. So, As per this property the answer is 5 i.e. 5 + 7Â =Â 10 +5

Question 6.

a. 6 + 4 = 10 or

6 + 4 = 5 + _____________

Answer:

Try to implement the Commutative Addition property. So, As per this property the answer is 5 i.e. 6 + 4Â =Â 5 +5

b. 6 + 7 = 13 or

6 + 7 = 8 + _____________

Answer:

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

c. 5 + 3 = 8 or

5 + 3 = 6 + _____________

Answer:

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

d. 9 + 2 = 11 or

9 + 2 = 5 + ______________

Answer:

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

Question 7.

a. 5 Ã— 6 = 30 or

5 Ã— 6 = 10 Ã— ______________

Answer:

Try to implement the Commutative Multiplication property. So, As per this property the answer is 3 i.e. 5 x 6Â = 10 x 3.

b. 4 Ã— 3 = 12 or

4 Ã— 3 = 2 Ã— _____________

Answer:

Try to implement the Commutative Multiplication property. So, As per this property the answer is 6 i.e. 4 x 3Â = 2 x 6

c. 6 Ã— 3 = 18 or

6 Ã— 3 = 9 Ã— _____________

Answer:

Try to implement the Commutative Multiplication property. So, As per this property the answer is 2 i.e. 6 x 3Â = 9 x 2

d. 6 Ã— 2 = 12 or

6 Ã— 2 = 4 Ã— ______________

Answer:

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

Associative Property

2 Ã— 3 Ã— 4 = c

2 Ã— 3 = 6

6 Ã— 4 = 24

c = 24

Distributive Property

11 Ã— 8 = (6 Ã— 8) + (5 Ã— 8)

48 + 40 = 88

11 Ã— 8 = 88

**Solve using the associative property.**

Question 1.

a. 2 Ã— 3 Ã— 5 = d

___________ Ã— ___________ = _____________

___________ Ã— ___________ = _____________

d = _____________

Answer:

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 Ã— 2 Ã— 9 = h

___________ Ã— ___________ = _____________

___________ Ã— ___________ = _____________

h = _____________

Answer:

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 Ã— 4 Ã— 6 = e

___________ Ã— ___________ = _____________

___________ Ã— ___________ = _____________

e = _____________

Answer:

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 Ã— 4 Ã— 7 = g

___________ Ã— ___________ = _____________

___________ Ã— ___________ = _____________

g = _____________

Answer:

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 Ã— 4 = (10 Ã— 4) + (___________ Ã— 4)

__________ + ____________

12 Ã— 4 = _____________

Answer:

Given 12 Ã— 4 = (10 Ã— 4) + (___________ Ã— 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 Ã— 3 = (10 Ã— 3) + (___________ Ã— 3)

__________ + ____________

14 Ã— 3 = _____________

Answer:

Given 14 Ã— 3 = (10 Ã— 3)Â + (___________Ã— 3)

According to the distributive property

14 x 3 = ( 10 x 3 ) + ( 4 x 3 )

30 + 12Â = 42

14 x 3 = 42

Hence the Resultant value obtained after Simplification is 42.

Question 4.

19 Ã— 2 = (10 Ã— 2) + (_________ Ã— 2)

____________ + ____________

19 Ã— 2 = ____________

Given 19 Ã— 2 = (10 Ã— 2) + (_________ Ã— 2)

According to the distributive property

( 10 x 2 ) + (9 x 2 )

20 + 18 = 38

19 x 2Â = 38

Hence the Resultant value obtained after Simplification is 38.

16 Ã— 5 = (10 Ã— 5) + (__________ Ã— 5)

____________ + ____________

16 Ã— 5 = ____________

Answer:

Given 16 Ã— 5 = (10 Ã— 5) + (__________ Ã— 5)

According to the distributive property

( 10 x 5 ) + (6 x 5 )

50 + 30 = 80

16 x 5Â = 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 _____________.

Answer:

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 ____________.

Answer:

Given seven and 2 are two numbers i.e. 7 – 2Â = 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 ____________.

Answer:

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 ___________.

Answer:

Fourteen divided by two is 14 / 2 = 7

Hence the value obtained when Fourteen divided by two is 14Â /Â 2 = 7

Question 5.

Five added to what number is seven? _____________

Five added to ______________ is seven.

Answer:

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.

Answer:

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.

Answer:

Let unknown number be S

As per the Given data , When 27 is Divided with unknown number S i.e. 27 Ã·Â S = 3

S = 27 Ã· 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.

Answer:

Let the Number be K.

As per the Given Data , When K is divided with eight is 8 as shown below.

K Ã· 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 _____________

Answer:

Divide the number 12 by 3 is as shown below

12 Ã· 3 = 4

Therefore, Twelve divided by three equals is 4.

Question 4.

Four times nine is what number? ___________

Four times nine is ____________.

Answer:

Write the given number 9 as 4 timesÂ 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.

Answer:

Let unknown number be x

As per the Given data , When x is multiplied with eight i.e. X x 8 = 56

x = 56 Ã·Â 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.

Answer:

Let unknown number be p

As per the Given data , 9 x p = 81

p = 81 Ã· 9

p = 9

Therefore, Nine times Nine is eighty-one

Question 7.

Twenty divided by four is what number? ____________

Twenty divided by four is _____________.

Answer:

When twenty is divided with 4 , The result is as shown below.

20 Ã· 4 = 5

Therefore , The result obtained Twenty divided by four is five.

Question 8.

Ten times this number is ninety. ___________

Ten times ___________ is ninety.

Answer:

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.

Answer:

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.

Answer:

Let unknown number be x c

As per the Given data , When x is divided with seven i.e. X Ã· 7 = 9

x = 7 xÂ 9 = 63

x = 63 is the number when divided by 7 is nine.

ThereforeÂ 63 divided by seven is nine.