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Answer :
To determine which fraction is equivalent to [tex]\(\frac{9}{10}\)[/tex], we need to compare each given fraction with [tex]\(\frac{9}{10}\)[/tex].
Let's analyze each option:
Option A: [tex]\(\frac{27}{40}\)[/tex]
To check if [tex]\(\frac{27}{40}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex], we need to see if they simplify to the same value. We can cross-multiply to check:
[tex]\[9 \times 40 \neq 10 \times 27\][/tex]
Since the cross-products are not equal, [tex]\(\frac{27}{40}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
Option B: [tex]\(\frac{18}{20}\)[/tex]
Next, let's consider [tex]\(\frac{18}{20}\)[/tex]. Simplify [tex]\(\frac{18}{20}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[ \frac{18 \div 2}{20 \div 2} = \frac{9}{10} \][/tex]
Since it simplifies to [tex]\(\frac{9}{10}\)[/tex], [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
Option C: [tex]\(\frac{36}{40}\)[/tex]
Finally, let's check [tex]\(\frac{36}{40}\)[/tex]. Simplify [tex]\(\frac{36}{40}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[ \frac{36 \div 4}{40 \div 4} = \frac{9}{10} \][/tex]
Since it simplifies to [tex]\(\frac{9}{10}\)[/tex], [tex]\(\frac{36}{40}\)[/tex] is also equivalent to [tex]\(\frac{9}{10}\)[/tex].
Conclusion:
Both [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{36}{40}\)[/tex] are equivalent to [tex]\(\frac{9}{10}\)[/tex]. Therefore, the correct answers are options B and C.
Let's analyze each option:
Option A: [tex]\(\frac{27}{40}\)[/tex]
To check if [tex]\(\frac{27}{40}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex], we need to see if they simplify to the same value. We can cross-multiply to check:
[tex]\[9 \times 40 \neq 10 \times 27\][/tex]
Since the cross-products are not equal, [tex]\(\frac{27}{40}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
Option B: [tex]\(\frac{18}{20}\)[/tex]
Next, let's consider [tex]\(\frac{18}{20}\)[/tex]. Simplify [tex]\(\frac{18}{20}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[ \frac{18 \div 2}{20 \div 2} = \frac{9}{10} \][/tex]
Since it simplifies to [tex]\(\frac{9}{10}\)[/tex], [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
Option C: [tex]\(\frac{36}{40}\)[/tex]
Finally, let's check [tex]\(\frac{36}{40}\)[/tex]. Simplify [tex]\(\frac{36}{40}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[ \frac{36 \div 4}{40 \div 4} = \frac{9}{10} \][/tex]
Since it simplifies to [tex]\(\frac{9}{10}\)[/tex], [tex]\(\frac{36}{40}\)[/tex] is also equivalent to [tex]\(\frac{9}{10}\)[/tex].
Conclusion:
Both [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{36}{40}\)[/tex] are equivalent to [tex]\(\frac{9}{10}\)[/tex]. Therefore, the correct answers are options B and C.
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