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Answer :
Sure! Let's match each fraction on the left with an equivalent fraction on the right. We have the following fractions:
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]
- [tex]\(\frac{81}{90}\)[/tex]
We'll find equivalent fractions by simplifying or cross-checking the fractions:
1. For [tex]\(\frac{4}{7}\)[/tex]:
Simplifying [tex]\(\frac{4}{7}\)[/tex] keeps it as [tex]\(\frac{4}{7}\)[/tex] because 4 and 7 have no common factors other than 1.
- Match: [tex]\(\frac{4}{7}\)[/tex] is equivalent to [tex]\(\frac{12}{21}\)[/tex] because when you simplify [tex]\(\frac{12}{21}\)[/tex] by dividing both the numerator and denominator by 3, you get [tex]\(\frac{4}{7}\)[/tex].
2. For [tex]\(\frac{18}{20}\)[/tex]:
Simplify [tex]\(\frac{18}{20}\)[/tex] by dividing both numbers by their greatest common divisor, which is 2. This gives us [tex]\(\frac{9}{10}\)[/tex].
- Match: [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
3. For [tex]\(\frac{6}{5}\)[/tex]:
[tex]\(\frac{6}{5}\)[/tex] is already in simplest form, as 6 and 5 have no common factors other than 1.
- Match: [tex]\(\frac{6}{5}\)[/tex] is equivalent to [tex]\(\frac{30}{25}\)[/tex] because [tex]\(\frac{30}{25}\)[/tex] simplifies to [tex]\(\frac{6}{5}\)[/tex] when you divide both the numerator and denominator by 5.
In conclusion, the matches are:
- [tex]\(\frac{4}{7}\)[/tex] with [tex]\(\frac{12}{21}\)[/tex]
- [tex]\(\frac{18}{20}\)[/tex] with [tex]\(\frac{9}{10}\)[/tex]
- [tex]\(\frac{6}{5}\)[/tex] with [tex]\(\frac{30}{25}\)[/tex]
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]
- [tex]\(\frac{81}{90}\)[/tex]
We'll find equivalent fractions by simplifying or cross-checking the fractions:
1. For [tex]\(\frac{4}{7}\)[/tex]:
Simplifying [tex]\(\frac{4}{7}\)[/tex] keeps it as [tex]\(\frac{4}{7}\)[/tex] because 4 and 7 have no common factors other than 1.
- Match: [tex]\(\frac{4}{7}\)[/tex] is equivalent to [tex]\(\frac{12}{21}\)[/tex] because when you simplify [tex]\(\frac{12}{21}\)[/tex] by dividing both the numerator and denominator by 3, you get [tex]\(\frac{4}{7}\)[/tex].
2. For [tex]\(\frac{18}{20}\)[/tex]:
Simplify [tex]\(\frac{18}{20}\)[/tex] by dividing both numbers by their greatest common divisor, which is 2. This gives us [tex]\(\frac{9}{10}\)[/tex].
- Match: [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
3. For [tex]\(\frac{6}{5}\)[/tex]:
[tex]\(\frac{6}{5}\)[/tex] is already in simplest form, as 6 and 5 have no common factors other than 1.
- Match: [tex]\(\frac{6}{5}\)[/tex] is equivalent to [tex]\(\frac{30}{25}\)[/tex] because [tex]\(\frac{30}{25}\)[/tex] simplifies to [tex]\(\frac{6}{5}\)[/tex] when you divide both the numerator and denominator by 5.
In conclusion, the matches are:
- [tex]\(\frac{4}{7}\)[/tex] with [tex]\(\frac{12}{21}\)[/tex]
- [tex]\(\frac{18}{20}\)[/tex] with [tex]\(\frac{9}{10}\)[/tex]
- [tex]\(\frac{6}{5}\)[/tex] with [tex]\(\frac{30}{25}\)[/tex]
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