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Simplify the following:

[tex]\[
\frac{2}{24} = \frac{4}{48} = \frac{5}{55} = \frac{11}{25} = \frac{6}{36}
\][/tex]

Sagot :

GinnyAnswer
Sure, let's simplify each fraction step-by-step.

1. Simplifying [tex]\(\frac{2}{24}\)[/tex]:

- Identify the greatest common divisor (GCD) of the numerator and the denominator: [tex]\( \text{GCD}(2, 24) = 2 \)[/tex].
- Divide both the numerator and the denominator by their GCD:

[tex]\[ \frac{2}{24} = \frac{2 \div 2}{24 \div 2} = \frac{1}{12} \][/tex]

- The decimal form of [tex]\(\frac{1}{12}\)[/tex] is [tex]\(0.08333333333333333 \)[/tex].

2. Simplifying [tex]\(\frac{4}{48}\)[/tex]:

- Identify the greatest common divisor (GCD) of the numerator and the denominator: [tex]\( \text{GCD}(4, 48) = 4 \)[/tex].
- Divide both the numerator and the denominator by their GCD:

[tex]\[ \frac{4}{48} = \frac{4 \div 4}{48 \div 4} = \frac{1}{12} \][/tex]

- The decimal form of [tex]\(\frac{1}{12}\)[/tex] is [tex]\(0.08333333333333333 \)[/tex].

3. Simplifying [tex]\(\frac{5}{55}\)[/tex]:

- Identify the greatest common divisor (GCD) of the numerator and the denominator: [tex]\( \text{GCD}(5, 55) = 5 \)[/tex].
- Divide both the numerator and the denominator by their GCD:

[tex]\[ \frac{5}{55} = \frac{5 \div 5}{55 \div 5} = \frac{1}{11} \][/tex]

- The decimal form of [tex]\(\frac{1}{11}\)[/tex] is [tex]\(0.09090909090909091 \)[/tex].

4. Simplifying [tex]\(\frac{11}{25}\)[/tex]:

- Identify the greatest common divisor (GCD) of the numerator and the denominator: [tex]\( \text{GCD}(11, 25) = 1 \)[/tex] (since 11 and 25 are co-prime).
- Therefore, the fraction remains the same:

[tex]\[ \frac{11}{25} \][/tex]

- The decimal form of [tex]\(\frac{11}{25}\)[/tex] is [tex]\( 0.44 \)[/tex].

5. Simplifying [tex]\(\frac{6}{36}\)[/tex]:

- Identify the greatest common divisor (GCD) of the numerator and the denominator: [tex]\( \text{GCD}(6, 36) = 6 \)[/tex].
- Divide both the numerator and the denominator by their GCD:

[tex]\[ \frac{6}{36} = \frac{6 \div 6}{36 \div 6} = \frac{1}{6} \][/tex]

- The decimal form of [tex]\(\frac{1}{6}\)[/tex] is [tex]\(0.16666666666666666 \)[/tex].

Summary of the simplified fractions in their decimal forms:

[tex]\[ \frac{2}{24} = 0.08333333333333333, \quad \frac{4}{48} = 0.08333333333333333, \quad \frac{5}{55} = 0.09090909090909091, \quad \frac{11}{25} = 0.44, \quad \frac{6}{36} = 0.16666666666666666 \][/tex]
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