Q:

# $$(1 + 0.12 \div 12) { 12 \times 1 \div 2} - 1 \div 0.12 \div 12 =$$

Accepted Solution

A:
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" $$\frac{4829}{900}$$ ";  or, "5$$\frac{329}{900}$$" ;
or, write as:  "5.366" .
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Explanation:
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Given:  " (1 + 0.12 ÷ 12)12 * 1 ÷ 2− 1 ÷ 0.12 ÷ 12 = ? " ;
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"(1 + 0.12 ÷ 12) = ??

Start with the division:  " 0.12 ÷ 12 = 0.01 " .

"(1 + 0.01)" = (1.01) .

We have:  "1.01 (12)
Given:  " (1.01)12 * 1 ÷ 2 − 1 ÷ 0.12 ÷ 12 = ? " ;

So, 1.01 * 12 = 12 .12 .
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" 12.12 * 1 ÷  2 − 1 ÷ 0.12 ÷ 12 = ? " ;

Note:  Using order of operations, treat this problem as:

" [ (12.12 * 1) ÷  2 ]  −  [ (1 ÷ 0.12) ÷ 12 ] = ? " ;

→    ( 12.12 ÷ 2 )  −  (25/3) ÷ 12 ] = ? " ;

→    ( 6.06)  −  { (25/3) * 1/12) }  = ?

→    ( 6.06)  −  { ( 25* 1) / (3*12)  = ?

→    ( 6.06)  −  { ( 25* 1) / (3*12)  = ?

→    ( 6.06)  −  (25/36) ;

→     6 $$\frac{6}{100}$$  −  $$\frac{25}{36}$$  ;

→  6 $$\frac{3}{50}$$   −  $$\frac{25}{36}$$  ;

Rewrite " 6 $$\frac{3}{50}$$ " ; as an improper fraction:

→   " 6 $$\frac{3}{50}$$ "  = "[ (50*6) + 3 ] / 50 = $$\frac{303}{50}$$ ;
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→  6 $$\frac{3}{50}$$   −  $$\frac{25}{36}$$  ;

=  $$\frac{303}{50}$$  −  $$\frac{25}{36}$$ ;

= $$\frac{(303*36)-(25*50)}{50*36} = \frac{10,908-1250}{1800}$$ ;

=  $$\frac{9658}{1800}$$ ;
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→ Divide EACH SIDE of the "fraction" by "2" ; to simplify:
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→   $$\frac{9658/2}{1800/2}$$ ;
=$$\frac{4829}{900}$$  = 5$$\frac{329}{900}$$ ; or, write as:

(5 + (329 ÷ 900)   =   →  5.3655555555555556 .
→ round to:  5.366 .
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