CPM Homework Help : CC3 Problem 9-132

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9-132.

Simplify each of the following expressions.

$3 \frac { 1 } { 5 } \cdot \frac { 7 } { 4 }$
Hint (a):
Convert the mixed number into a fraction greater than one.
More Help (a):
$\frac{16}{5}\left(\frac{7}{4}\right)$
Answer (a):
$\frac{28}{5} = 5\frac{3}{5}$

$5^3\cdot(-\frac{4}{5})$
Hint (b):
$\frac{4}{5}=(-1)(4)\left(\frac{1}{5}\right)$
More Help 1(b):
Notice that the $5$ in the denominator would have an exponent of $-1$ .
More Help 2(b):
$5^{(3-1)}(-4)$
Answer (b):
$5^2(-4)=-100$

$2 ^ { 4 } \cdot \frac { 5 } { 8 }$
Hint (c):
This can be rewritten as:
$2^{4}\left(\frac{5}{2^{3}}\right)$
More Help (c):
See part (b).
Answer (c):
$10$

$-\frac{1}{2}\cdot3^2$
Hint (d):
Use the Order of Operations.

$-\frac{5}{6}+(\frac{1}{2})^2$
Hint (e):
Use the Order of Operations.
Step 1 (e):
$-\frac{5}{6}+\frac{1}{4}$
Step 2 (e):
$-\frac{20}{24}+\frac{6}{24}=-\frac{14}{24}$

$(-\frac{4}{5})^2-\frac{3}{50}$
Hint (f):
Notice that squaring a negative number has the same result as multiplying two negative numbers: the product is always positive.

$(\frac{3}{10})^2-(-\frac{2}{5})^2$
Hint (g):
Follow the Order of Operations.

$8^2(-\frac{7}{8})-\frac{1}{2}$
Step 1 (h):
$8^{(2-1)}(-7)-\frac{1}{2}$
Step 2 (h):
$8(-7)-\frac{1}{2}$
Step 3 (h):
$(-56)-\frac{1}{2}$
Answer (h):
$-56\frac{1}{2}$

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