CPM Homework Help : MC2 Problem 10-111

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10-111.

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):
Refer to the Math Notes box of Lesson 10.1.6.
Hint 2(b):
Notice that the 5 in the denominator would have an exponent of 1.
More Help (b):
5^{(3 − 1)}(−4)
Answer (b):
5²(−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.

$( \frac { 3 } { 10 } ) ^ { 2 } - ( - \frac { 2 } { 5 } ) ^ { 2 }$
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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