Question

Multiple Choices which expression has a positive value?

1. $\frac{-16(-5)}{4(-9)}$
   
2. $-7^2-2$
   
3. $5-4(-6)$
   
4. $19-6\left(7\right)$
   

Short answer

Correct Option: C

Step-by-step solution

Step-1 – Apply the concept of product and quotient 

When two or more numbers are multiplied together, it gives a number. The numbers that are multiplied are called the factors. And the result of the multiplication of numbers is called the product of those numbers.

In mathematics, the quotient is the number obtained by dividing one number by another number.

Step-2 – Rule of multiplication and division of integers 

Multiplication of Integers

RULE 1: The product of a positive integer and a negative integer is negative.

RULE 2: The product of two positive integers is positive.

RULE 3: The product of two negative integers is positive.

Rules and example of Division of integers

RULE 1: The quotient of a positive integer and a negative integer is negative.

RULE 2: The quotient of two positive integers is positive.

RULE 3: The quotient of two negative integers is positive.

Step-3 – which expression has a positive value? 

$\begin{array}{l}\text{a}:\frac{-16(-5)}{4(-9)}\\ \text{b}:-7^2-2\\ \text{c}:5-4(-6)\\ \text{d}:19-6\left(7\right)\end{array}$

Let us evaluate each options separately

$\text{a}:\frac{-16(-5)}{4(-9)}=\frac{80}{-36}=-2.22$

$\text{b}:-7^2-2=-49-2=-51$

$\text{c}:5-4(-6)=5+24=+29$

$\text{d}:19-6\left(7\right)=19-42=-23$

After the calculation , we can decide the correct option is C , which is only positive.