Question

1. what is the product of the following mixed fractions?

$4\frac{1}{8} \bullet 2\frac{2}{3}$
a. $8\frac{3}{11}$
b. $9\frac{6}{11}$
c. $10\frac{9}{11}$
d. 11

1. evaluate the expression when x = 4, y = -5 and z = -3.

$3x + 2y - z + 8$
a. 13
b. 16
c. 9
d. -2

Explanation:

Question 2:

Step1: Convert mixed fractions to improper fractions

The mixed fractions are \(4\frac{1}{8}\) and \(2\frac{2}{3}\). Converting them:
\(4\frac{1}{8}=\frac{4\times8 + 1}{8}=\frac{33}{8}\)
\(2\frac{2}{3}=\frac{2\times3+2}{3}=\frac{8}{3}\)

Step2: Multiply the improper fractions

Multiply \(\frac{33}{8}\) and \(\frac{8}{3}\):
\(\frac{33}{8}\times\frac{8}{3}=\frac{33\times8}{8\times3}\)
The 8 in the numerator and denominator cancels out:
\(\frac{33}{3}=11\)

Step1: Substitute the values of x, y, z into the expression

The expression is \(3x + 2y - z + 8\). Substitute \(x = 4\), \(y=-5\), \(z = -3\):
\(3(4)+2(-5)-(-3)+8\)

Step2: Simplify each term

Calculate each term:
\(3(4)=12\)
\(2(-5)=-10\)
\(-(-3)=3\)

Step3: Combine the terms

Now combine all the terms:
\(12-10 + 3+8\)
First, \(12-10 = 2\)
Then, \(2 + 3=5\)
Then, \(5+8 = 13\)

Answer:

d. 11

Question 3: