reduced fraction

**ccdalamp** · July 10th 2007, 06:45 PM

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

**ThePerfectHacker** · July 10th 2007, 07:08 PM

Hint: 1.363636... = 1+36/99

**Soroban** · July 10th 2007, 07:47 PM

Hello, ccdalamp!

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

Thread: reduced fraction

LinkBack

Thread Tools

Display

reduced fraction

Similar Math Help Forum Discussions

How is this reduced ech form?

How is this radical being reduced?

Reduced mass transformation

equations reduced

reduced augmented

Search Tags