Answer :
To find a fraction that is equivalent to [tex]\(\frac{9}{10}\)[/tex], you need to look for a fraction that represents the same value.
Fractions are equivalent if they have the same proportion between the numerator (top number) and the denominator (bottom number). One way to determine if two fractions are equivalent is by cross-multiplying and checking if the products are equal.
Let's check each option to see if it's equivalent to [tex]\(\frac{9}{10}\)[/tex]:
1. [tex]\(\frac{6}{8}\)[/tex]:
[tex]\[
9 \times 8 \neq 10 \times 6
\][/tex]
This is not equivalent.
2. [tex]\(\frac{18}{20}\)[/tex]:
[tex]\[
9 \times 20 = 180 \quad \text{and} \quad 10 \times 18 = 180
\][/tex]
These products are equal, so [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
3. [tex]\(\frac{16}{19}\)[/tex]:
[tex]\[
9 \times 19 \neq 10 \times 16
\][/tex]
This is not equivalent.
4. [tex]\(\frac{13}{16}\)[/tex]:
[tex]\[
9 \times 16 \neq 10 \times 13
\][/tex]
This is not equivalent.
So, the fraction that is equivalent to [tex]\(\frac{9}{10}\)[/tex] is [tex]\(\frac{18}{20}\)[/tex].
Fractions are equivalent if they have the same proportion between the numerator (top number) and the denominator (bottom number). One way to determine if two fractions are equivalent is by cross-multiplying and checking if the products are equal.
Let's check each option to see if it's equivalent to [tex]\(\frac{9}{10}\)[/tex]:
1. [tex]\(\frac{6}{8}\)[/tex]:
[tex]\[
9 \times 8 \neq 10 \times 6
\][/tex]
This is not equivalent.
2. [tex]\(\frac{18}{20}\)[/tex]:
[tex]\[
9 \times 20 = 180 \quad \text{and} \quad 10 \times 18 = 180
\][/tex]
These products are equal, so [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
3. [tex]\(\frac{16}{19}\)[/tex]:
[tex]\[
9 \times 19 \neq 10 \times 16
\][/tex]
This is not equivalent.
4. [tex]\(\frac{13}{16}\)[/tex]:
[tex]\[
9 \times 16 \neq 10 \times 13
\][/tex]
This is not equivalent.
So, the fraction that is equivalent to [tex]\(\frac{9}{10}\)[/tex] is [tex]\(\frac{18}{20}\)[/tex].
