Question

Evaluate the expression using the distributive property and mental math.

$( 211 ) (- 3)$

Short answer

$( 211 ) (- \text{3}) = - 633$.

Step-by-step solution

Step-1 – What are real numbers? 

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

Step-2 – Distributive Property of Multiplication 

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

Distributive Property of Multiplication

Property: $( \text{b} + \text{c} ) (- \text{a} ) = \text{b} · (- \text{a} ) + \text{c} · (- \text{a} ) \text{=} -\text{b} · \text{a} - \text{c} · \text{a}$

Example: $\text{(8} + \text{5} \text{)} (- 3)= 8 · (-3) + 5 · (-3) = -24-15=- 39$

Step-3:  Evaluate the expression using the distributive property and mental math.        

We can write 211 as (200 + 11), to evaluate the expression 211(-3), we can use the distributive method of multiplication.

Distributive Property of Multiplication

Property: $( \text{b} + \text{c} ) (- \text{a} ) = \text{b} · (- \text{a} ) + \text{c} · (- \text{a} ) \text{=} -\text{b} · \text{a} - \text{c} · \text{a}$

$( 211 ) (- \text{3}) = (200+11) (- \text{3}) = 200 · (- \text{3}) + 11 · (- \text{3}) = - 600 - 33 = - 633$

$( 211 ) (- \text{3}) = - 633$