Answer :
To determine which fractions are equivalent to [tex]\(\frac{9}{10}\)[/tex], we'll check each option by finding a common relationship. Two fractions are equivalent if they have the same value when simplified or if their cross-products are equal. Here's how we can check each option:
1. Option A: [tex]\(\frac{15}{20}\)[/tex]
- To check equivalence, we can cross multiply:
[tex]\[
9 \times 20 = 180 \quad \text{and} \quad 15 \times 10 = 150
\][/tex]
- Since [tex]\(180 \neq 150\)[/tex], [tex]\(\frac{15}{20}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
2. Option B: [tex]\(\frac{18}{20}\)[/tex]
- Again, cross multiply to check:
[tex]\[
9 \times 20 = 180 \quad \text{and} \quad 18 \times 10 = 180
\][/tex]
- Since [tex]\(180 = 180\)[/tex], [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
3. Option C: [tex]\(\frac{5}{14}\)[/tex]
- Cross multiply:
[tex]\[
9 \times 14 = 126 \quad \text{and} \quad 5 \times 10 = 50
\][/tex]
- Since [tex]\(126 \neq 50\)[/tex], [tex]\(\frac{5}{14}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
4. Option D: [tex]\(\frac{27}{30}\)[/tex]
- Cross multiply:
[tex]\[
9 \times 30 = 270 \quad \text{and} \quad 27 \times 10 = 270
\][/tex]
- Since [tex]\(270 = 270\)[/tex], [tex]\(\frac{27}{30}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
In conclusion, the fractions equivalent to [tex]\(\frac{9}{10}\)[/tex] are [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{27}{30}\)[/tex].
1. Option A: [tex]\(\frac{15}{20}\)[/tex]
- To check equivalence, we can cross multiply:
[tex]\[
9 \times 20 = 180 \quad \text{and} \quad 15 \times 10 = 150
\][/tex]
- Since [tex]\(180 \neq 150\)[/tex], [tex]\(\frac{15}{20}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
2. Option B: [tex]\(\frac{18}{20}\)[/tex]
- Again, cross multiply to check:
[tex]\[
9 \times 20 = 180 \quad \text{and} \quad 18 \times 10 = 180
\][/tex]
- Since [tex]\(180 = 180\)[/tex], [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
3. Option C: [tex]\(\frac{5}{14}\)[/tex]
- Cross multiply:
[tex]\[
9 \times 14 = 126 \quad \text{and} \quad 5 \times 10 = 50
\][/tex]
- Since [tex]\(126 \neq 50\)[/tex], [tex]\(\frac{5}{14}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
4. Option D: [tex]\(\frac{27}{30}\)[/tex]
- Cross multiply:
[tex]\[
9 \times 30 = 270 \quad \text{and} \quad 27 \times 10 = 270
\][/tex]
- Since [tex]\(270 = 270\)[/tex], [tex]\(\frac{27}{30}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
In conclusion, the fractions equivalent to [tex]\(\frac{9}{10}\)[/tex] are [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{27}{30}\)[/tex].
