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Difference between revisions of "2021 JMPSC Sprint Problems/Problem 1"

(Created page with "== Problem == Compute <math>\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{9}\right)(3+6+9)</math>. == Solution == Solving the right side gives <math>3 + 6 + 9 = 18</math>. Distri...")
 
(→‎Solution)
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Solving the right side gives <math>3 + 6 + 9 = 18</math>. Distributing into the left side gives <math>\frac{18}{3}+\frac{18}{6}+\frac{18}{9}</math>, so the answer is <math>6 + 3 + 2 = \boxed{11}</math>.
 
Solving the right side gives <math>3 + 6 + 9 = 18</math>. Distributing into the left side gives <math>\frac{18}{3}+\frac{18}{6}+\frac{18}{9}</math>, so the answer is <math>6 + 3 + 2 = \boxed{11}</math>.
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== Solution 2 ==
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<math>\frac{1}{3}+\frac{1}{6}+\frac{1}{9}=\frac{6}{18}+\frac{3}{18}+\frac{2}{18}=\frac{11}{18}</math> and <math>3+6+9=18</math>, so the answer is <math>\frac{11}{18}\cdot18=\boxed{11}</math>.

Revision as of 07:23, 11 July 2021

Problem

Compute $\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{9}\right)(3+6+9)$.

Solution

Solving the right side gives $3 + 6 + 9 = 18$. Distributing into the left side gives $\frac{18}{3}+\frac{18}{6}+\frac{18}{9}$, so the answer is $6 + 3 + 2 = \boxed{11}$.


Solution 2

$\frac{1}{3}+\frac{1}{6}+\frac{1}{9}=\frac{6}{18}+\frac{3}{18}+\frac{2}{18}=\frac{11}{18}$ and $3+6+9=18$, so the answer is $\frac{11}{18}\cdot18=\boxed{11}$.

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