The answer is: 35/4; or; " 8 ¾ " ; or, write as: " 8.75 " .
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Step-by-step explanation:
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Given: 58 ⅓ ÷ 6 ⅔ = ? ;
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Note: 58 ⅓ = [ (3*58) + 1 ] / 3 = (174 + 1) / 3 = 175 / 3 ;
6 ⅔ = [ (3*6) + 2 ] / 3 = (18 + 2) / 3 = 20/3 ;
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So; Rewrite: "58 ⅓ ÷ 6 ⅔ " ; as:
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"(175/3) ÷ (20/3) = ??
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Note: "(175/3) ÷ (20/3) = (175/3) * (3/20) = ?
→ The "3's cancel out to "1" ; since "(3÷3 = 1)" ;
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and we have: "175 * (1/20) = 175/20 ;
= 35/4; or; " 8 ¾ " ; or, " 8.75 " .
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Alternate method:
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Given: 58 ⅓ ÷ 6 ⅔ = ? ;
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→ Using calculator:
"58 ⅓ = 58.3333333333333333.... = 175/3 " ;
"6 ⅔ =6.6666666666666667 = 20/3 ;
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58 ⅓ ÷ 6 ⅔ = (58.3333333333333333) (58.3333333333333333) ÷ (6.6666666666666667) (6.6666666666666667) = 8.75 ;
or; better (using a calculator): (175 ÷ 3) ÷ (20 ÷ 3) = 8.75 .
{or: " (175 / 3) / (20 / 3) = 8.75 " .
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