multiply denom., num. by same to elim. decimal: −10−(−6.75) / 17.4−15.4

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multiply denom., num. by same to elim. decimal: −10−(−6.75) / 17.4−15.4

−10−(−6.75) / 17.4−15.4

= −3.25 / 2

= −4⋅3.25 / 4⋅2

= −13/8


In the last step, how was it decided to use a 4 to multiply in numerator and denominator?

Thanks.
 
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−10−(−6.75) / 17.4−15.4

= −3.25 / 2

= −4⋅3.25 / 4⋅2

= −13/8


In the last step, how was it decided to use a 4 to multiply in numerator and denominator?

Thanks.

3.25 = 314 =134\displaystyle 3\frac{1}{4} \ = \frac{13}{4}
 
−10−(−6.75) / 17.4−15.4

= −3.25 / 2

= −4⋅3.25 / 4⋅2

= −13/8


In the last step, how was it decided to use a 4 to multiply in numerator and denominator?

Thanks.
Hi,
Possibly a little more detail than Subhotosh Khan gave. It was something you should know/recognize or, at the very least be able to work out. However, if you have to work it out, it could cost significant time in a test. Other numbers you should recognize include
0.1 = 110\displaystyle \frac{1}{10}
0.111... = 19\displaystyle \frac{1}{9}
0.125 = 18\displaystyle \frac{1}{8}
0.1666... = 16\displaystyle \frac{1}{6}
0.2 = 15\displaystyle \frac{1}{5}
0.25 = 14\displaystyle \frac{1}{4}
0.333... = 13\displaystyle \frac{1}{3}
You should also know 0.14 is about 17\displaystyle \frac{1}{7} and possibly suspect something like 0.142857145827... means 17\displaystyle \frac{1}{7}. Please note, this is not a full list but many are based arount these, i.e. 0.666...= 20.333...=23\displaystyle 2*0.333...=\frac{2}{3}
 
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