Answer :
To determine which fraction is equivalent to [tex]\(\frac{9}{10}\)[/tex], we need to see which option has the same value when simplified or converted to a decimal.
Let's go through each given fraction:
Option A: [tex]\(\frac{27}{40}\)[/tex]
Convert this fraction to a decimal:
- Divide 27 by 40, which equals 0.675.
Compare 0.675 to 0.9 (the decimal form of [tex]\(\frac{9}{10}\)[/tex]). They are not equal, so [tex]\(\frac{27}{40}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
Option B: [tex]\(\frac{18}{20}\)[/tex]
Convert this fraction to a decimal:
- Divide 18 by 20, which equals 0.9.
Compare 0.9 to 0.9. They are equal, so [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
Option C: [tex]\(\frac{36}{40}\)[/tex]
Convert this fraction to a decimal:
- Divide 36 by 40, which equals 0.9.
Compare 0.9 to 0.9. They are equal, so [tex]\(\frac{36}{40}\)[/tex] is also equivalent to [tex]\(\frac{9}{10}\)[/tex].
Therefore, both [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{36}{40}\)[/tex] are equivalent to [tex]\(\frac{9}{10}\)[/tex].
Let's go through each given fraction:
Option A: [tex]\(\frac{27}{40}\)[/tex]
Convert this fraction to a decimal:
- Divide 27 by 40, which equals 0.675.
Compare 0.675 to 0.9 (the decimal form of [tex]\(\frac{9}{10}\)[/tex]). They are not equal, so [tex]\(\frac{27}{40}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
Option B: [tex]\(\frac{18}{20}\)[/tex]
Convert this fraction to a decimal:
- Divide 18 by 20, which equals 0.9.
Compare 0.9 to 0.9. They are equal, so [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
Option C: [tex]\(\frac{36}{40}\)[/tex]
Convert this fraction to a decimal:
- Divide 36 by 40, which equals 0.9.
Compare 0.9 to 0.9. They are equal, so [tex]\(\frac{36}{40}\)[/tex] is also equivalent to [tex]\(\frac{9}{10}\)[/tex].
Therefore, both [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{36}{40}\)[/tex] are equivalent to [tex]\(\frac{9}{10}\)[/tex].
