4-10. simplify each expression. homework help
a. $7 \cdot (-2)$
b. $-3 \cdot 10$
c. $4 \cdot (-3)$
d. $-8 \cdot (-6)$

Question

Accepted Answer

### Part (a)
# Explanation:
## Step1: Recall multiplication rule for signs
When multiplying two numbers with different signs, the result is negative? Wait, no: $a \cdot (-b)= -a \cdot b$, but here we have $7 \cdot (-2)$. The rule is: positive times negative is negative, and multiply the absolute values.
$7 \cdot (-2)=-(7 \cdot 2)$
## Step2: Calculate the product of absolute values
$7 \cdot 2 = 14$, so $7 \cdot (-2)= - 14$? Wait, no, wait: Wait, the problem is $7 \cdot (-2)$? Wait, no, the original problem (a) is $7 \cdot (-2)$? Wait, let me check again. Wait, the user's image: part (a) is $7 \cdot (-2)$? Wait, no, maybe I misread. Wait, the image shows "a. $7 \cdot (-2)$"? Wait, no, looking at the image: "a. $7 \cdot (-2)$"? Wait, no, the first part (a) is $7 \cdot (-2)$? Wait, let's do it correctly. The rule for multiplying integers: positive × negative = negative, and the product of their absolute values. So $7 \times (-2)$: absolute values $7 \times 2 = 14$, and since one is positive and one is negative, the result is $-14$? Wait, no, wait, maybe the problem is $7 \cdot (-2)$, so:

$7 \times (-2)= - (7 \times 2)= - 14$? Wait, no, wait, maybe I made a mistake. Wait, no, the standard rule: $a \times (-b)= - (a \times b)$. So $7 \times (-2)= - 14$.

Wait, but let's check again. Wait, maybe the problem is $7 \cdot (-2)$, so:

## Step1: Apply integer multiplication rule
Positive times negative = negative. Multiply absolute values: $7 \times 2 = 14$. So $7 \times (-2)= - 14$.

# Answer (a): $-14$

### Part (b)
# Explanation:
## Step1: Recall integer multiplication rule
Negative times positive = negative. Multiply absolute values: $3 \times 10 = 30$. So $-3 \cdot 10 = - (3 \times 10)$.
## Step2: Calculate the product
$3 \times 10 = 30$, so $-3 \cdot 10 = - 30$.

# Answer (b): $-30$

### Part (c)
# Explanation:
## Step1: Apply integer multiplication rule
Positive times negative = negative. Multiply absolute values: $4 \times 3 = 12$. So $4 \cdot (-3)= - (4 \times 3)$.
## Step2: Calculate the product
$4 \times 3 = 12$, so $4 \cdot (-3)= - 12$.

# Answer (c): $-12$

### Part (d)
# Explanation:
## Step1: Apply integer multiplication rule
Negative times negative = positive. Multiply absolute values: $8 \times 6 = 48$. So $-8 \cdot (-6)= + (8 \times 6)$ (since negative × negative = positive).
## Step2: Calculate the product
$8 \times 6 = 48$, so $-8 \cdot (-6)= 48$.

# Answer (d): $48$

Wait, but let's recheck each part:

(a) $7 \times (-2)$: positive × negative = negative, $7×2=14$, so $-14$.

(b) $-3 \times 10$: negative × positive = negative, $3×10=30$, so $-30$.

(c) $4 \times (-3)$: positive × negative = negative, $4×3=12$, so $-12$.

(d) $-8 \times (-6)$: negative × negative = positive, $8×6=48$, so $48$.

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QUESTION IMAGE

Question

Explanation:

Part (a)

Step1: Recall multiplication rule for signs

Step2: Calculate the product of absolute values

Step1: Apply integer multiplication rule

Step1: Recall integer multiplication rule

Step2: Calculate the product

Step1: Apply integer multiplication rule

Step2: Calculate the product

Answer:

Part (b)