Answer: m = 9 .
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Explanation:
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Given: (3 ¾) m = (33 ¾) ; Solve for "m" ;
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Method 1):
Rewrite the fractions in "decimal form"; and rewrite the equation:
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(3.75) m = 33.75 ;
Divide each side of the equation by: "(3.75)" ;
to isolate "m" on one side of the equation; and to solve for "m" ;
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(3.75) m / 3.75 = 33.75 / 3.75 ;
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m = 33.75 / 3.75 ;
m = 9 .
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Method 2):
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Rewrite the fractions as improper fractions:
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3 ¾ = [ (4*3) + 3 ] / 4 = (12 + 3) / 4 = 15/4 ;
33 ¾ = [ (4*33) + 3 ] / 4 = (132 + 3) / 4 = 135/4 ;
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And rewrite the equation:
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(15/4)m = (135/4) ;
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→ Multiply the entire equation (both sides) by "4" to eliminate the fractions ;
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→ 4 * (15/4)m = 4 * (135/4) ;
→ All the "4's" on BOTH sides "cancel out" to "1" ;
and we are left with:
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→ 15 m = 135 ;
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Now, divide EACH side of the equation by "15" ; to isolate "m" on one side of the equation; and to solve for "m" ;
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→ 15 m / 15 = 135 / 15 ;
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→ to get: m = 9 .
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Method 3):
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Similar to "(Method 2)" directly above, except the step at which we get to:
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→ (15/4)m = (135/4) ;
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Instead of multiplying each side of the equation by "4" ;
We divide EACH side of the equation by "(15/4)" ; to isolate "m" on one side of the equation; and to solve for "m" ;
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→ (15/4)m / (15/4) = (135/4) / (15/4)
= (135/4) ÷ (15/4) = (135/4) * (4/15)
= (135*4) / (15*4) = (540) / (60) = 54/6 = 9 .
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