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

[xbyxeqwhat]

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.

 

[Deleted member 4993]

−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 = \(\displaystyle 3\frac{1}{4} \ = \frac{13}{4}\)

 

[Ishuda]

−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 = \(\displaystyle \frac{1}{10}\)
0.111... = \(\displaystyle \frac{1}{9}\)
0.125 = \(\displaystyle \frac{1}{8}\)
0.1666... = \(\displaystyle \frac{1}{6}\)
0.2 = \(\displaystyle \frac{1}{5}\)
0.25 = \(\displaystyle \frac{1}{4}\)
0.333... = \(\displaystyle \frac{1}{3}\)
You should also know 0.14 is about \(\displaystyle \frac{1}{7}\) and possibly suspect something like 0.142857145827... means \(\displaystyle \frac{1}{7}\). Please note, this is not a full list but many are based arount these, i.e. 0.666...= \(\displaystyle 2*0.333...=\frac{2}{3}\)