CPM Homework Help : CC2MN Problem 10-81

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10-81.

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 1 (b):
$- \frac{4}{5} = (-1)(4)\left(\frac{1}{5}\right)$
Hint 2 (b):
Notice that the $5$ in the denominator is like dividing by $5$ .
More Help (b):
$\frac{5^{\left(3\right)}}{5\left(-4\right)}$
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):
$10$

$- \frac { 1 } { 2 } \cdot 3 ^ { 2 }$
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.

$\left(\frac{3}{10}\right)^2-\left(-\frac{2}{5}\right)^2$
Hint (g):
Follow the order of operations.

$8^2\left(-\frac{7}{8}\right)-\frac{1}{2}$
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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