Question

practice & problem solving
guided practice in 8 - 11, apply the properties of operations to multiply.

1. $\frac{1}{8}xcdot\frac{-4}{5}x=\frac{1}{2}cdot\frac{square}{5}cdot xcdotsquare=\frac{square}{square}x^{square}$
2. $(y - 1.1)(-3y)=(y)(square)(square)(-3y)=-3y^{square}square3.3square$
3. $(1.1 - 2.7k)(-3.5k)=(-3.5k)(1.1 - 2.7k)

square+9.45k^{2}=-3.85k+squaresquare$

1. $\frac{1}{8}w(-1 + w)=square w+square w^{square}$

Explanation:

Step1: Simplify fraction - multiply coefficients

For $\frac{1}{8}x\cdot\frac{-4}{5}x$, first multiply the coefficients $\frac{1}{8}$ and $\frac{-4}{5}$. $\frac{1}{8}\times\frac{-4}{5}=\frac{1\times(-4)}{8\times5}=\frac{-4}{40}=-\frac{1}{10}$.

Step2: Multiply variables

Multiply the $x$ - terms: $x\cdot x = x^{2}$.

Step3: Combine results

The product is $-\frac{1}{10}x^{2}$.

For $(y - 1.1)(-3y)$:

Step1: Apply distributive property

$(y-1.1)(-3y)=y\times(-3y)-1.1\times(-3y)$.

Step2: Multiply terms

$y\times(-3y)=-3y^{2}$ and $-1.1\times(-3y) = 3.3y$. So the result is $-3y^{2}+3.3y$.

For $(1.1 - 2.7k)(-3.5k)$:

Step1: Apply distributive property

$(-3.5k)(1.1 - 2.7k)=(-3.5k)\times1.1-(-3.5k)\times2.7k=-3.85k + 9.45k^{2}$.

For $\frac{1}{8}w(-1 + w)$:

Step1: Apply distributive property

$\frac{1}{8}w(-1 + w)=\frac{1}{8}w\times(-1)+\frac{1}{8}w\times w=-\frac{1}{8}w+\frac{1}{8}w^{2}$.

Answer:

1. $\frac{1}{8}x\cdot\frac{-4}{5}x=-\frac{1}{10}x^{2}$
2. $(y - 1.1)(-3y)=-3y^{2}+3.3y$
3. $(1.1 - 2.7k)(-3.5k)=-3.85k + 9.45k^{2}$
4. $\frac{1}{8}w(-1 + w)=-\frac{1}{8}w+\frac{1}{8}w^{2}$