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Answer :
To find a fraction that is equivalent to [tex]\( \frac{18}{20} \)[/tex] but with a denominator of 10, follow these steps:
1. Understand the original fraction:
The original fraction given is [tex]\( \frac{18}{20} \)[/tex].
2. Determine the target denominator:
We need an equivalent fraction with a denominator of 10.
3. Find the scale factor:
We need to determine how the original denominator (20) can be converted into the target denominator (10). This involves finding the factor by which we scale down the denominator from 20 to 10.
[tex]\[
\text{Scale factor} = \frac{20}{10} = 2
\][/tex]
4. Scale the numerator accordingly:
To maintain equivalence, we must also scale down the numerator by the same factor. This is calculated as follows:
[tex]\[
\text{Scaled numerator} = \frac{18}{2} = 9
\][/tex]
5. Write the new fraction:
Now that we have the scaled numerator and target denominator, we can write the equivalent fraction:
[tex]\[
\frac{18}{20} \equiv \frac{9}{10}
\][/tex]
6. Match with the provided choices:
From the given choices:
[tex]\[
\frac{11}{10}, \quad \frac{9}{10}, \quad \frac{8}{10}, \quad \frac{18}{10}
\][/tex]
We see that the fraction [tex]\( \frac{9}{10} \)[/tex] matches our calculated equivalent fraction.
So, the fraction equivalent to [tex]\( \frac{18}{20} \)[/tex] with a denominator of 10 is [tex]\( \frac{9}{10} \)[/tex].
1. Understand the original fraction:
The original fraction given is [tex]\( \frac{18}{20} \)[/tex].
2. Determine the target denominator:
We need an equivalent fraction with a denominator of 10.
3. Find the scale factor:
We need to determine how the original denominator (20) can be converted into the target denominator (10). This involves finding the factor by which we scale down the denominator from 20 to 10.
[tex]\[
\text{Scale factor} = \frac{20}{10} = 2
\][/tex]
4. Scale the numerator accordingly:
To maintain equivalence, we must also scale down the numerator by the same factor. This is calculated as follows:
[tex]\[
\text{Scaled numerator} = \frac{18}{2} = 9
\][/tex]
5. Write the new fraction:
Now that we have the scaled numerator and target denominator, we can write the equivalent fraction:
[tex]\[
\frac{18}{20} \equiv \frac{9}{10}
\][/tex]
6. Match with the provided choices:
From the given choices:
[tex]\[
\frac{11}{10}, \quad \frac{9}{10}, \quad \frac{8}{10}, \quad \frac{18}{10}
\][/tex]
We see that the fraction [tex]\( \frac{9}{10} \)[/tex] matches our calculated equivalent fraction.
So, the fraction equivalent to [tex]\( \frac{18}{20} \)[/tex] with a denominator of 10 is [tex]\( \frac{9}{10} \)[/tex].
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