Evaluate the expression using the distributive property and mental math.

$(4.02 ) (-9)$

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

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

We can write 4.02 as (4 + 0.02), to evaluate the expression (4.02)(– 9), we can use the distributive method of multiplication.

Distributive Property of Multiplication

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

localid="1649117560616" $\begin{array}{l}\text{\hspace{0.17em}(}4.02\text{\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}}(-\text{\hspace{0.17em}\hspace{0.17em}9})=(4+0.02)(-9)=4·(-9)+0.02(-9)=-36-0.18=-36.18\\ \text{\hspace{0.17em}(}4.02\text{\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}}(-\text{\hspace{0.17em}\hspace{0.17em}9})=-36.18\end{array}$