anonymous
  • anonymous
a pice of wire 5 /3 m long is to be cut into 15 pieces of the same length. what is the length of each piece
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
5/3 divided by 15 to divide fractions...multiply by the reciprocal so 5/3*1/15=5/45=1/9=.1 repeating
anonymous
  • anonymous
wouldnt it be 5/3 *15/1=45/3=15
anonymous
  • anonymous
No, when you divide two fractions like\[\frac{(\frac{a}{b})}{(\frac{c}{d})}\]the algebra leads you to making this calculation:\[\frac{(\frac{a}{b})}{(\frac{c}{d})}=\frac{a}{b}\times \frac{d}{c}=\frac{ad}{bc}\]Notice the fraction on the bottom (denominator) has flipped before you multiply.

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anonymous
  • anonymous
In your question, a=5, b=3 c=15 and d=1.
anonymous
  • anonymous
\[\frac{5\times1}{3\times15}=\frac{5}{45}=\frac{1}{9}\]
anonymous
  • anonymous
-35/17=-49/136n
anonymous
  • anonymous
Are you solving for n?
anonymous
  • anonymous
yes
anonymous
  • anonymous
\[\frac{-35}{17}=\frac{-49}{16n}\]Multiply both sides by 16n to get\[\frac{-35 \times 16n}{17}=-49 \rightarrow \frac{-560n}{17}=-49\]Multiply both sides by 17 to then get,\[-560n=-49 \times 17 \rightarrow -560n=-833\]and finally divide by -560 to isolate n\[n=\frac{-833}{-560}=\frac{119}{80}\]after simplifying.
anonymous
  • anonymous
^ 7 is a common factor of 833 and 560, so 833 = 7 x 119 560 = 7 x 80 The 7s cancel.

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