High School

Match the fractions with their simplest form:

[tex]
\[
\begin{aligned}
\frac{5}{10} &= \\
\frac{3}{9} &= \\
\frac{5}{25} &= \\
\frac{24}{30} &= \\
\frac{15}{20} &= \\
\end{aligned}
\]
[/tex]

Answer :

Sure! Let's simplify each of the fractions to their simplest form step-by-step:

1. Simplifying [tex]\(\frac{5}{10}\)[/tex]:
- To simplify, find the greatest common divisor (GCD) of 5 and 10, which is 5.
- Divide both the numerator and the denominator by 5:
[tex]\[
\frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]

2. Simplifying [tex]\(\frac{3}{9}\)[/tex]:
- Find the GCD of 3 and 9, which is 3.
- Divide both the numerator and the denominator by 3:
[tex]\[
\frac{3 \div 3}{9 \div 3} = \frac{1}{3}
\][/tex]

3. Simplifying [tex]\(\frac{5}{25}\)[/tex]:
- Find the GCD of 5 and 25, which is 5.
- Divide both the numerator and the denominator by 5:
[tex]\[
\frac{5 \div 5}{25 \div 5} = \frac{1}{5}
\][/tex]

4. Simplifying [tex]\(\frac{24}{30}\)[/tex]:
- Find the GCD of 24 and 30, which is 6.
- Divide both the numerator and the denominator by 6:
[tex]\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]

5. Simplifying [tex]\(\frac{15}{20}\)[/tex]:
- Find the GCD of 15 and 20, which is 5.
- Divide both the numerator and the denominator by 5:
[tex]\[
\frac{15 \div 5}{20 \div 5} = \frac{3}{4}
\][/tex]

So, the simplest forms of the fractions are:
- [tex]\(\frac{5}{10} = \frac{1}{2}\)[/tex]
- [tex]\(\frac{3}{9} = \frac{1}{3}\)[/tex]
- [tex]\(\frac{5}{25} = \frac{1}{5}\)[/tex]
- [tex]\(\frac{24}{30} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{15}{20} = \frac{3}{4}\)[/tex]

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