College

Find the equivalent fractions for [tex]\frac{36}{48}[/tex] in each case:

[tex]\begin{array}{llll}
\frac{18}{96} & \frac{7}{5} & -\frac{9}{5} & \frac{30}{45} \\
\frac{15}{5} & \frac{49}{35} & -\frac{18}{20} & -\frac{1}{4}
\end{array}[/tex]

Answer :

To find equivalent fractions for [tex]\(\frac{36}{48}\)[/tex] from the given list, we should first simplify [tex]\(\frac{36}{48}\)[/tex] and then compare it with each provided fraction to see if they are equal when simplified.

Here are the steps:

1. Simplify the original fraction: [tex]\(\frac{36}{48}\)[/tex]:

- Find the greatest common divisor (GCD) of 36 and 48. The GCD of 36 and 48 is 12.
- Divide both the numerator and the denominator by their GCD.

[tex]\[
\frac{36 \div 12}{48 \div 12} = \frac{3}{4}
\][/tex]

So, the simplified form of [tex]\(\frac{36}{48}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex].

2. Compare with the given fractions:

We now need to check if any of the given fractions simplify to [tex]\(\frac{3}{4}\)[/tex]:

- [tex]\(\frac{18}{96}\)[/tex]: Simplifies to [tex]\(\frac{3}{16}\)[/tex].
- [tex]\(\frac{7}{5}\)[/tex]: Remains [tex]\(\frac{7}{5}\)[/tex].
- [tex]\(-\frac{9}{5}\)[/tex]: Remains [tex]\(-\frac{9}{5}\)[/tex].
- [tex]\(\frac{30}{45}\)[/tex]: Simplifies to [tex]\(\frac{2}{3}\)[/tex].
- [tex]\(\frac{15}{5}\)[/tex]: Simplifies to [tex]\(\frac{3}{1}\)[/tex].
- [tex]\(\frac{49}{35}\)[/tex]: Simplifies to [tex]\(\frac{7}{5}\)[/tex].
- [tex]\(-\frac{18}{20}\)[/tex]: Simplifies to [tex]\(-\frac{9}{10}\)[/tex].
- [tex]\(-\frac{1}{4}\)[/tex]: Remains [tex]\(-\frac{1}{4}\)[/tex].

None of these fractions, when simplified, are equal to [tex]\(\frac{3}{4}\)[/tex].

Therefore, none of the given fractions are equivalent to [tex]\(\frac{36}{48}\)[/tex].

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