To match each fraction from the left column to an equivalent fraction in the right column, we can follow these steps:
1. Convert each mixed number to an improper fraction in the left column:
- [tex]\( 2 \frac{1}{12} = \frac{2 \times 12 + 1}{12} = \frac{25}{12} \)[/tex]
- [tex]\( 1 \frac{5}{12} = \frac{1 \times 12 + 5}{12} = \frac{17}{12} \)[/tex]
2. List the fractions in the left column:
- [tex]\( \frac{5}{12} \)[/tex]
- [tex]\( \frac{18}{12} \)[/tex]
- [tex]\( \frac{25}{12} \)[/tex]
- [tex]\( \frac{17}{12} \)[/tex]
3. List the fractions in the right column, including the mixed numbers converted to improper fractions:
- [tex]\( \frac{1}{2} \)[/tex]
- [tex]\( \frac{17}{12} \)[/tex]
- [tex]\( \frac{10}{24} = \frac{5}{12} \)[/tex]
- [tex]\( 1 \frac{1}{2} = \frac{1 \times 12 + 6}{12} = \frac{18}{12} \)[/tex]
- [tex]\( 1 \frac{1}{12} = \frac{1 \times 12 + 1}{12} = \frac{13}{12} \)[/tex]
- [tex]\( \frac{25}{12} \)[/tex]
4. Pair the equivalent fractions between the left and right columns:
- [tex]\( \frac{5}{12} \)[/tex] from the left column matches with [tex]\( \frac{10}{24} \)[/tex] from the right column because [tex]\( \frac{10}{24} = \frac{5}{12} \)[/tex], which is listed at position 3 in the right column.
- [tex]\( \frac{18}{12} \)[/tex] from the left column matches with [tex]\( 1 \frac{1}{2} \)[/tex] from the right column because [tex]\( 1 \frac{1}{2} = \frac{18}{12} \)[/tex], which is listed at position 4 in the right column.
- [tex]\( \frac{25}{12} \)[/tex] from the left column matches with [tex]\( \frac{25}{12} \)[/tex] from the right column, which is listed at position 6 in the right column.
- [tex]\( \frac{17}{12} \)[/tex] from the left column matches with [tex]\( \frac{17}{12} \)[/tex] from the right column, which is listed at position 2 in the right column.
So, the following matches are made:
- [tex]\( \frac{5}{12} \)[/tex] matches with the right column at position 3.
- [tex]\( \frac{18}{12} \)[/tex] matches with the right column at position 4.
- [tex]\( 2 \frac{1}{12} \)[/tex] matches with the right column at position 6.
- [tex]\( 1 \frac{5}{12} \)[/tex] matches with the right column at position 2.
These matches correspond to:
[tex]\[ [4, 6, 2] \][/tex]
Therefore, the equivalent fractions are:
[tex]\[ \frac{5}{12} \][/tex] matches with [tex]\(\frac{10}{24}\)[/tex] (Position 3),
[tex]\[ \frac{18}{12} \][/tex] matches with [tex]\(1\frac{1}{2}\)[/tex] (Position 4),
[tex]\[ 2\frac{1}{12} \][/tex] matches with [tex]\(\frac{25}{12}\)[/tex] (Position 6),
[tex]\[ 1\frac{5}{12} \][/tex] matches with [tex]\(\frac{17}{12}\)[/tex] (Position 2).
