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Evaluate the expression using the distributive property and mental math.

-5(396)

Short Answer

Expert verified

-5(396)=-1980.

Step by step solution

01

Step-1 – What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

02

Step-2 – Distributive Property of Multiplication 

Suppose a, b, and c is three real numbers.

Distributive Property of Multiplication

Property: -a(b-c)=(-a)·b-(-a)·c

Example: -3(8-5)=(-3)·8-(-3)·5=-24+15=-9

03

Step-3:  Use the distributive property to evaluate the expression.

We can write 396 as (400 – 4), to evaluate the expression 7(109), we can use the distributive method of multiplication.

We know that double negative is always positive. -5·-4=+20

Distributive Property of Multiplication

Property: -a(b-c)=(-a)·b-(-a)·c

  5(  396  )  =    5  (4004)  =    5    ·  400  +  (  5)   ·  (  4)  =    2000  +  20  =    1980  5(  396  )  =    1980

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