Answer :
Certainly! Let's work through each part step-by-step:
---
### 6. Write down the answers to:
a) [tex]\(2 \times -12\)[/tex]
To solve:
[tex]\[ 2 \times -12 = -24 \][/tex]
b) [tex]\(-12 \times 2\)[/tex]
To solve:
[tex]\[ -12 \times 2 = -24 \][/tex]
c) [tex]\(7 + (-15)\)[/tex]
To solve:
[tex]\[ 7 + (-15) = -8 \][/tex]
d) [tex]\(2 \times (-3 \times -4) - 24\)[/tex]
First, solve the innermost multiplication:
[tex]\[ -3 \times -4 = 12 \][/tex]
Then multiply:
[tex]\[ 2 \times 12 = 24 \][/tex]
And finally:
[tex]\[ 24 - 24 = 0 \][/tex]
e) [tex]\(-15 + 7\)[/tex]
To solve:
[tex]\[ -15 + 7 = -8 \][/tex]
f) [tex]\((2 \times -3) \times -4\)[/tex]
First, solve the inner parenthesis:
[tex]\[ 2 \times -3 = -6 \][/tex]
Then multiply:
[tex]\[ -6 \times -4 = 24 \][/tex]
g) [tex]\(-8 + (-12 + 2)\)[/tex]
First, solve the inner parenthesis:
[tex]\[ -12 + 2 = -10 \][/tex]
Then add:
[tex]\[ -8 + (-10) = -18 \][/tex]
h) [tex]\((-8 + -12) + 2\)[/tex]
First, solve the inner parenthesis:
[tex]\[ -8 + -12 = -20 \][/tex]
Then add:
[tex]\[ -20 + 2 = -18 \][/tex]
---
### What do these questions illustrate about multiplication and addition of integers?
These questions illustrate various properties of integer operations:
- Both (a) and (b) demonstrate the commutative property of multiplication, which states that [tex]\( a \times b = b \times a \)[/tex].
- (d) and (f) demonstrate the associative property of multiplication and addition, which states that [tex]\( a \times (b \times c) = (a \times b) \times c \)[/tex] and [tex]\( a + (b + c) = (a + b) + c \)[/tex].
- (g) and (h) illustrate the associative property of addition.
---
### 7. Write down the answers to:
a) [tex]\(-12 \div 6\)[/tex]
To solve:
[tex]\[ -12 \div 6 = -2 \][/tex]
b) [tex]\(6 \div -12\)[/tex]
To solve:
[tex]\[ 6 \div -12 = -0.5 \][/tex]
c) [tex]\(-10 - 4\)[/tex]
To solve:
[tex]\[ -10 - 4 = -14 \][/tex]
d) [tex]\(4 - (-10)\)[/tex]
To solve:
[tex]\[ 4 - (-10) = 4 + 10 = 14 \][/tex]
e) [tex]\(18 \div -3\)[/tex]
To solve:
[tex]\[ 18 \div -3 = -6 \][/tex]
f) [tex]\(540 - (-9)\)[/tex]
To solve:
[tex]\[ 540 - (-9) = 540 + 9 = 549 \][/tex]
---
### What do these questions illustrate about division and subtraction of integers?
These questions illustrate various properties of integer operations:
- (a), (b), and (e) demonstrate that division of integers can result in a negative quotient when one of the numbers is negative.
- (c) and (d) illustrate the properties of subtraction, including changing subtraction of a negative to addition.
- (f) involves converting subtraction of a negative to addition, a fundamental property of integers.
---
### 8. Copy and complete this table showing the properties of integers:
| Property | Examples |
|------------------------|------------------------------------------------|
| Commutative property | [tex]\(2 \times -12 = -12 \times 2\)[/tex] |
| Associative property | [tex]\((7 + (-15)) + 3 = 7 + ((-15) + 3)\)[/tex] |
| Distributive property | [tex]\(-4 \times (3 + 8) = -4 \times 3 + -4 \times 8\)[/tex] |
| Identity property | [tex]\(4 + 0 = 0 + 4 = 4\)[/tex] |
| Multiplicative identity | [tex]\(4 \times 1 = 4\)[/tex] |
---
Each property illustrated in the table shows how these fundamental rules apply to integers during addition, multiplication, division, and subtraction operations.
---
### 6. Write down the answers to:
a) [tex]\(2 \times -12\)[/tex]
To solve:
[tex]\[ 2 \times -12 = -24 \][/tex]
b) [tex]\(-12 \times 2\)[/tex]
To solve:
[tex]\[ -12 \times 2 = -24 \][/tex]
c) [tex]\(7 + (-15)\)[/tex]
To solve:
[tex]\[ 7 + (-15) = -8 \][/tex]
d) [tex]\(2 \times (-3 \times -4) - 24\)[/tex]
First, solve the innermost multiplication:
[tex]\[ -3 \times -4 = 12 \][/tex]
Then multiply:
[tex]\[ 2 \times 12 = 24 \][/tex]
And finally:
[tex]\[ 24 - 24 = 0 \][/tex]
e) [tex]\(-15 + 7\)[/tex]
To solve:
[tex]\[ -15 + 7 = -8 \][/tex]
f) [tex]\((2 \times -3) \times -4\)[/tex]
First, solve the inner parenthesis:
[tex]\[ 2 \times -3 = -6 \][/tex]
Then multiply:
[tex]\[ -6 \times -4 = 24 \][/tex]
g) [tex]\(-8 + (-12 + 2)\)[/tex]
First, solve the inner parenthesis:
[tex]\[ -12 + 2 = -10 \][/tex]
Then add:
[tex]\[ -8 + (-10) = -18 \][/tex]
h) [tex]\((-8 + -12) + 2\)[/tex]
First, solve the inner parenthesis:
[tex]\[ -8 + -12 = -20 \][/tex]
Then add:
[tex]\[ -20 + 2 = -18 \][/tex]
---
### What do these questions illustrate about multiplication and addition of integers?
These questions illustrate various properties of integer operations:
- Both (a) and (b) demonstrate the commutative property of multiplication, which states that [tex]\( a \times b = b \times a \)[/tex].
- (d) and (f) demonstrate the associative property of multiplication and addition, which states that [tex]\( a \times (b \times c) = (a \times b) \times c \)[/tex] and [tex]\( a + (b + c) = (a + b) + c \)[/tex].
- (g) and (h) illustrate the associative property of addition.
---
### 7. Write down the answers to:
a) [tex]\(-12 \div 6\)[/tex]
To solve:
[tex]\[ -12 \div 6 = -2 \][/tex]
b) [tex]\(6 \div -12\)[/tex]
To solve:
[tex]\[ 6 \div -12 = -0.5 \][/tex]
c) [tex]\(-10 - 4\)[/tex]
To solve:
[tex]\[ -10 - 4 = -14 \][/tex]
d) [tex]\(4 - (-10)\)[/tex]
To solve:
[tex]\[ 4 - (-10) = 4 + 10 = 14 \][/tex]
e) [tex]\(18 \div -3\)[/tex]
To solve:
[tex]\[ 18 \div -3 = -6 \][/tex]
f) [tex]\(540 - (-9)\)[/tex]
To solve:
[tex]\[ 540 - (-9) = 540 + 9 = 549 \][/tex]
---
### What do these questions illustrate about division and subtraction of integers?
These questions illustrate various properties of integer operations:
- (a), (b), and (e) demonstrate that division of integers can result in a negative quotient when one of the numbers is negative.
- (c) and (d) illustrate the properties of subtraction, including changing subtraction of a negative to addition.
- (f) involves converting subtraction of a negative to addition, a fundamental property of integers.
---
### 8. Copy and complete this table showing the properties of integers:
| Property | Examples |
|------------------------|------------------------------------------------|
| Commutative property | [tex]\(2 \times -12 = -12 \times 2\)[/tex] |
| Associative property | [tex]\((7 + (-15)) + 3 = 7 + ((-15) + 3)\)[/tex] |
| Distributive property | [tex]\(-4 \times (3 + 8) = -4 \times 3 + -4 \times 8\)[/tex] |
| Identity property | [tex]\(4 + 0 = 0 + 4 = 4\)[/tex] |
| Multiplicative identity | [tex]\(4 \times 1 = 4\)[/tex] |
---
Each property illustrated in the table shows how these fundamental rules apply to integers during addition, multiplication, division, and subtraction operations.
