reduced fraction

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• July 10th 2007, 06:45 PM
ccdalamp
reduced fraction
Give the sum p+q where p/q is the reduced fraction represented by the repeating decimal 1.36

Choices

a. 13
b. 19
c. 26
d. 28

:confused:
• July 10th 2007, 07:08 PM
ThePerfectHacker
Hint: 1.363636... = 1+36/99
• July 10th 2007, 07:47 PM
Soroban
Hello, ccdalamp!

Quote:

Give the sum $p+q$ where $\frac{p}{q}$ is the reduced fraction

represented by the repeating decimal $1.\overline{36}$

Choices: . $a)\;13\qquad b)\;19 \qquad c)\;26\qquad d)\; 28$

Here's an algebraic solution . . .

Let $N \:=\:1.363636...$

Multiply 100: . $100N \;=\;136.363636...$
. Subtract $N\!:\quad\;\;\;N \;=\quad\; 1.363636...$

And we have:. $99N \;=\;135\quad\Rightarrow\quad N \:=\:\frac{135}{99} \:=\:\frac{15}{11}$

Therefore: . $p + q\:=\:15 + 11\:=\:26$