College

Match each fraction on the left with an equivalent fraction on the right. Some options on the right will be used more than once.

[tex]
\[
\begin{array}{ll}
\frac{4}{7} & \\
\frac{9}{10} & \\
\frac{18}{20} & \\
\frac{30}{25} & \\
\frac{6}{5} & \\
\frac{12}{21} & \\
\end{array}
\]
[/tex]

Answer :

Sure! Let's find the equivalent fractions step by step for each fraction given in the matching problem.

### Fractions to Compare:
- On the left:
- [tex]\(\frac{4}{7}\)[/tex]
- [tex]\(\frac{18}{20}\)[/tex]
- [tex]\(\frac{6}{5}\)[/tex]

- On the right:
- [tex]\(\frac{9}{10}\)[/tex]
- [tex]\(\frac{30}{25}\)[/tex]
- [tex]\(\frac{12}{21}\)[/tex]

### Step-by-Step Matching:
1. Matching [tex]\(\frac{4}{7}\)[/tex]:

First, let's simplify [tex]\(\frac{12}{21}\)[/tex] to see if it matches [tex]\(\frac{4}{7}\)[/tex]:
[tex]\[
\frac{12}{21} = \frac{12 \div 3}{21 \div 3} = \frac{4}{7}
\][/tex]
- Therefore, [tex]\(\frac{4}{7}\)[/tex] is equivalent to [tex]\(\frac{12}{21}\)[/tex].

2. Matching [tex]\(\frac{18}{20}\)[/tex]:

Simplifying [tex]\(\frac{18}{20}\)[/tex]:
[tex]\[
\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]
- Therefore, [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].

3. Matching [tex]\(\frac{6}{5}\)[/tex]:

To simplify [tex]\(\frac{30}{25}\)[/tex]:
[tex]\[
\frac{30}{25} = \frac{30 \div 5}{25 \div 5} = \frac{6}{5}
\][/tex]
- Therefore, [tex]\(\frac{6}{5}\)[/tex] is equivalent to [tex]\(\frac{30}{25}\)[/tex].

### Conclusion:

- [tex]\(\frac{4}{7}\)[/tex] matches with [tex]\(\frac{12}{21}\)[/tex]
- [tex]\(\frac{18}{20}\)[/tex] matches with [tex]\(\frac{9}{10}\)[/tex]
- [tex]\(\frac{6}{5}\)[/tex] matches with [tex]\(\frac{30}{25}\)[/tex]

Each pair of fractions is equivalent, confirming the matches are correct.

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