Simplify the aritmetic expression: #[3/4 ·1/4 ·(5− 3/2): (3/4 − 3/16)] : 7/4 ·(2 + 1/2)^2 −(1 + 1/2)^2#?
Given,
According to B.E.D.M.A.S., start by simplifying the round bracketed terms in the square brackets.
Omit the round brackets in the square brackets.
Simplify the expression within the square brackets.
Omit the square brackets since the term is already simplified.
Continue simplifying the terms in the round brackets.
Omit the round brackets since the bracketed terms are already simplified.
Change the denominator of each fraction such that both fractions have the same denominator.
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To simplify the arithmetic expression, let's break it down step by step:
 Start by simplifying the expressions within parentheses and brackets.
 Perform multiplications and divisions.
 Finally, compute the result.
[ \left[ \frac{3}{4} \cdot \frac{1}{4} \cdot \left( \sqrt{5}  \frac{3}{2} \right)  \frac{1}{3/4  3/16} \right]  \frac{7}{4} \cdot \left( 2 + \frac{1}{2} \right)^2  \left( 1 + \frac{1}{2} \right)^2 ]
Let's simplify it step by step:

Inside the brackets: [ \sqrt{5}  \frac{3}{2} = \frac{2\sqrt{5}  3}{2} ] [ \frac{1}{3/4  3/16} = \frac{1}{3/16} = \frac{16}{3} ]

Now, replace these values back into the expression: [ \left[ \frac{3}{4} \cdot \frac{1}{4} \cdot \left( \frac{2\sqrt{5}  3}{2} \right)  \frac{16}{3} \right]  \frac{7}{4} \cdot \left( 2 + \frac{1}{2} \right)^2  \left( 1 + \frac{1}{2} \right)^2 ]

Compute the squares: [ \left( 2 + \frac{1}{2} \right)^2 = \left( \frac{5}{2} \right)^2 = \frac{25}{4} ] [ \left( 1 + \frac{1}{2} \right)^2 = \left( \frac{3}{2} \right)^2 = \frac{9}{4} ]

Now, perform the multiplications: [ \frac{3}{4} \cdot \frac{1}{4} \cdot \frac{2\sqrt{5}  3}{2} = \frac{3}{32} \cdot (2\sqrt{5}  3) = \frac{3\sqrt{5}}{16}  \frac{9}{32} ]

Now, replace these values back into the expression: [ \left( \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{16}{3} \right)  \frac{7}{4} \cdot \frac{25}{4}  \frac{9}{4} ]

Combine like terms and perform the remaining arithmetic operations.
[ \left( \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{16}{3} \right)  \frac{7 \cdot 25}{4 \cdot 4}  \frac{9}{4} ]
[ = \left( \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{64}{3} \right)  \frac{175}{16}  \frac{9}{4} ]
[ = \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{64}{3}  \frac{175}{16}  \frac{9}{4} ]
[ = \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{256}{32}  \frac{420}{16}  \frac{36}{16} ]
[ = \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{256}{32}  \frac{420}{16}  \frac{36}{16} ]
[ = \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{256 + 420 + 36}{16} ]
[ = \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{712}{16} ]
[ = \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{356}{8} ]
[ = \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{178}{4} ]
[ = \frac{3\sqrt{5}}{16}  \frac{9}{32}  \frac{89}{2} ]
[ \approx \frac{3\sqrt{5}}{16}  0.28125  44.5 ]
[ \approx \frac{3\sqrt{5}}{16}  44.78125 ]
[ \approx 44.78125 + \frac{3\sqrt{5}}{16} ]
[ \approx \frac{3\sqrt{5}}{16}  44.78125 ]
So, the simplified arithmetic expression is approximately ( \frac{3\sqrt{5}}{16}  44.78125 ).
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The simplified arithmetic expression is ( \frac{33}{4} ).
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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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