The answer is:
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" [tex]\frac{4829}{900} [/tex] "; or, "5[tex] \frac{329}{900} [/tex]" ;
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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First, start with the "parentheses" ;
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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 [tex] \frac{6}{100} [/tex] − [tex] \frac{25}{36} [/tex] ;
→ 6 [tex] \frac{3}{50} [/tex] − [tex] \frac{25}{36} [/tex] ;
Rewrite " 6 [tex] \frac{3}{50} [/tex] " ; as an improper fraction:
→ " 6 [tex] \frac{3}{50}[/tex] " = "[ (50*6) + 3 ] / 50 = [tex] \frac{303}{50} [/tex] ;
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→ 6 [tex] \frac{3}{50} [/tex] − [tex] \frac{25}{36} [/tex] ;
= [tex] \frac{303}{50} [/tex] − [tex] \frac{25}{36} [/tex] ;
= [tex] \frac{(303*36)-(25*50)}{50*36} = \frac{10,908-1250}{1800}[/tex] ;
= [tex] \frac{9658}{1800}[/tex] ;
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→ Divide EACH SIDE of the "fraction" by "2" ; to simplify:
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→ [tex] \frac{9658/2}{1800/2}[/tex] ;
=[tex]\frac{4829}{900} [/tex] = 5[tex]\frac{329}{900} [/tex] ; or, write as:
(5 + (329 ÷ 900) = → 5.3655555555555556 .
→ round to: 5.366 .
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