College

Simplify the fractions.

1. [tex]\frac{6}{30}[/tex] = _________

2. [tex]\frac{5}{10}[/tex] = _________

3. [tex]\frac{4}{40}[/tex] = _________

4. [tex]\frac{24}{30}[/tex] = _________

5. [tex]\frac{6}{8}[/tex] = _________

6. [tex]\frac{8}{1}[/tex] = _________

7. [tex]\frac{12}{24}[/tex] = _________

Answer :

Let's simplify each of the given fractions step-by-step.

1. [tex]\(\frac{6}{30}\)[/tex]:
- Find the greatest common divisor (GCD) of 6 and 30, which is 6.
- Divide both the numerator and the denominator by 6:
[tex]\[
\frac{6 \div 6}{30 \div 6} = \frac{1}{5}
\][/tex]
So, [tex]\(\frac{6}{30}\)[/tex] simplifies to [tex]\(\frac{1}{5}\)[/tex].

2. [tex]\(\frac{5}{10}\)[/tex]:
- The GCD of 5 and 10 is 5.
- Divide both numbers by 5:
[tex]\[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]
So, [tex]\(\frac{5}{10}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].

3. [tex]\(\frac{4}{40}\)[/tex]:
- The GCD of 4 and 40 is 4.
- Divide both by 4:
[tex]\[
\frac{4 \div 4}{40 \div 4} = \frac{1}{10}
\][/tex]
So, [tex]\(\frac{4}{40}\)[/tex] simplifies to [tex]\(\frac{1}{10}\)[/tex].

4. [tex]\(\frac{24}{30}\)[/tex]:
- The GCD of 24 and 30 is 6.
- Divide them by 6:
[tex]\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
So, [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].

5. [tex]\(\frac{6}{8}\)[/tex]:
- The GCD of 6 and 8 is 2.
- Divide each by 2:
[tex]\[
\frac{6 \div 2}{8 \div 2} = \frac{3}{4}
\][/tex]
So, [tex]\(\frac{6}{8}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex].

6. [tex]\(\frac{8}{1}\)[/tex]:
- Since 8 is already over 1, it remains as:
[tex]\[
8
\][/tex]
So, [tex]\(\frac{8}{1}\)[/tex] simplifies to 8.

7. [tex]\(\frac{12}{24}\)[/tex]:
- The GCD of 12 and 24 is 12.
- Divide both by 12:
[tex]\[
\frac{12 \div 12}{24 \div 12} = \frac{1}{2}
\][/tex]
So, [tex]\(\frac{12}{24}\)[/tex] simplifies to [tex]\(\frac{1}{2}\)[/tex].

And there you have it, each fraction simplified!

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