Question

Multiply or divide:

(a) $-115÷\left(-5\right)$

(b) $5·12$

(c) $9\left(-7\right)$

(d)$-63÷7$

Short answer

(a) 23

(b) 60

(c) $-63$

(d)$-9$

Step-by-step solution

Step 1. Concept Used:

Suppose $a$and $b$are two integers with same signs.

• The number obtained after multiplying$a$and$b$is a positive number.
• The quotient obtained by dividing $a$by $b$is a positive number.

Suppose $a$and $b$are two integers with different signs.

• The number obtained after multiplying$a$and$b$is a negative number.
• The quotient obtained by dividing $a$by $b$is a negative number.

Part (a). Step 1. Given Information: 

Consider the given problem $-115÷\left(-5\right)$.

Part (a). Step 2. Calculation:

Divide $-115$by $-5$. Since $-115$and $-5$are both negative numbers, the quotient will be a positive number.

Note that$23\left(-5\right)=-115$. So,

$-115÷\left(-5\right)=23$

Part (a). Step 3. Conclusion: 

The value obtained is $-115÷\left(-5\right)=23$.

Part (b). Step 1. Given Information:

Consider the given problem$5·12$.

Part (b). Step 2. Calculation:

Since 5 and 12 are both positive numbers, the number obtained after multiplying 5 and 12 will again be a positive number.

Multiply 5 by 12.

$5·12=60$

Part (b). Step 3. Conclusion:

The value obtained is$5·12=60$.

Part (c). Step 1. Given Information:

Consider the given problem $9\left(-7\right)$.

Part (c). Step 2. Calculation:

Since 9 is a positive number and $-7$is a negative number, the number obtained after multiplying 9 by $-7$will be a negative number.

Multiply 9 by $-7$.

$9\left(-7\right)=-63$

Part (c). Step 3. Conclusion:

The value obtained is$9\left(-7\right)=-63$.

Part (d). Step 1. Given Information:

Consider the given problem$-63÷7$.

Part (d). Step 2. Calculation:

Since 7 is a positive number and $-63$is a negative number, the number obtained after dividing $-63$by 7 is a negative number.

Note that, $\left(-9\right)7=-63$. So,

$-63÷7=-9$

Part (d). Step 3: Conclusion:

The value obtained is$-63÷7=-9$.