How do you evaluate #\frac { 1} { 3} ( 2\frac { 1} { 4} \cdot 1\frac { 1} { 5}  \frac { 17} { 20} )#?
we should follow the order of operations PEMDAS i.e. first parentheses, then exponents, multiplication, division, addition and subtraction. Here we do not have exponents, but have parentheses and within the parentheses, we should first solve multiplication.
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To evaluate ( \frac {1} {3} \left( 2\frac {1} {4} \cdot 1\frac {1} {5}  \frac {17} {20} \right) ), we follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
First, we simplify the expression inside the parentheses:
( 2\frac {1} {4} \cdot 1\frac {1} {5} )
To multiply mixed numbers, we first convert them into improper fractions:
( 2\frac {1} {4} = \frac {9} {4} ) ( 1\frac {1} {5} = \frac {6} {5} )
Then, we multiply:
( \frac {9} {4} \cdot \frac {6} {5} = \frac {9 \times 6} {4 \times 5} = \frac {54} {20} )
Next, we subtract ( \frac {17} {20} ) from ( \frac {54} {20} ):
( \frac {54} {20}  \frac {17} {20} = \frac {54  17} {20} = \frac {37} {20} )
Now, we multiply the result by ( \frac {1} {3} ):
( \frac {1} {3} \cdot \frac {37} {20} = \frac {37} {60} )
Therefore, ( \frac {1} {3} \left( 2\frac {1} {4} \cdot 1\frac {1} {5}  \frac {17} {20} \right) ) evaluates to ( \frac {37} {60} ).
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To evaluate the expression (\frac{1}{3} \left(2\frac{1}{4} \cdot 1\frac{1}{5}  \frac{17}{20}\right)), follow these steps:

Convert the mixed numbers to improper fractions: [ 2\frac{1}{4} = \frac{9}{4} ] [ 1\frac{1}{5} = \frac{6}{5} ]

Multiply the mixed numbers: [ \frac{9}{4} \cdot \frac{6}{5} = \frac{54}{20} = \frac{27}{10} ]

Substitute the results back into the original expression: [ \frac{1}{3} \left(\frac{27}{10}  \frac{17}{20}\right) ]

Subtract the fractions inside the parentheses: [ \frac{1}{3} \left(\frac{27}{10}  \frac{17}{20}\right) = \frac{1}{3} \left(\frac{27}{10}  \frac{17}{20} \cdot \frac{2}{2}\right) ] [ = \frac{1}{3} \left(\frac{27}{10}  \frac{34}{20}\right) ] [ = \frac{1}{3} \left(\frac{27}{10}  \frac{17}{10}\right) ] [ = \frac{1}{3} \cdot \frac{10}{10} = \frac{10}{30} = \frac{1}{3} ]
So, (\frac{1}{3} \left(2\frac{1}{4} \cdot 1\frac{1}{5}  \frac{17}{20}\right) = \frac{1}{3}).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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