Answer :
To determine which fractions are equivalent to [tex]\(\frac{9}{10}\)[/tex], we can follow these steps:
1. Understanding Equivalent Fractions: Two fractions are equivalent if they represent the same part of a whole. This can be determined by cross-multiplying the numerators and denominators of the two fractions. If the cross-products are equal, the fractions are equivalent.
2. Check Each Fraction:
- Option A: [tex]\(\frac{15}{20}\)[/tex]
- Cross-multiply: [tex]\(9 \times 20\)[/tex] and [tex]\(10 \times 15\)[/tex]
- Calculate: [tex]\(9 \times 20 = 180\)[/tex] and [tex]\(10 \times 15 = 150\)[/tex]
- Since [tex]\(180 \neq 150\)[/tex], [tex]\(\frac{15}{20}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
- Option B: [tex]\(\frac{5}{14}\)[/tex]
- Cross-multiply: [tex]\(9 \times 14\)[/tex] and [tex]\(10 \times 5\)[/tex]
- Calculate: [tex]\(9 \times 14 = 126\)[/tex] and [tex]\(10 \times 5 = 50\)[/tex]
- Since [tex]\(126 \neq 50\)[/tex], [tex]\(\frac{5}{14}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
- Option C: [tex]\(\frac{27}{30}\)[/tex]
- Cross-multiply: [tex]\(9 \times 30\)[/tex] and [tex]\(10 \times 27\)[/tex]
- Calculate: [tex]\(9 \times 30 = 270\)[/tex] and [tex]\(10 \times 27 = 270\)[/tex]
- Since [tex]\(270 = 270\)[/tex], [tex]\(\frac{27}{30}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
- Option D: [tex]\(\frac{18}{20}\)[/tex]
- Cross-multiply: [tex]\(9 \times 20\)[/tex] and [tex]\(10 \times 18\)[/tex]
- Calculate: [tex]\(9 \times 20 = 180\)[/tex] and [tex]\(10 \times 18 = 180\)[/tex]
- Since [tex]\(180 = 180\)[/tex], [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
3. Conclusion: The fractions [tex]\(\frac{27}{30}\)[/tex] and [tex]\(\frac{18}{20}\)[/tex] are equivalent to [tex]\(\frac{9}{10}\)[/tex]. Therefore, the correct options are C and D.
1. Understanding Equivalent Fractions: Two fractions are equivalent if they represent the same part of a whole. This can be determined by cross-multiplying the numerators and denominators of the two fractions. If the cross-products are equal, the fractions are equivalent.
2. Check Each Fraction:
- Option A: [tex]\(\frac{15}{20}\)[/tex]
- Cross-multiply: [tex]\(9 \times 20\)[/tex] and [tex]\(10 \times 15\)[/tex]
- Calculate: [tex]\(9 \times 20 = 180\)[/tex] and [tex]\(10 \times 15 = 150\)[/tex]
- Since [tex]\(180 \neq 150\)[/tex], [tex]\(\frac{15}{20}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
- Option B: [tex]\(\frac{5}{14}\)[/tex]
- Cross-multiply: [tex]\(9 \times 14\)[/tex] and [tex]\(10 \times 5\)[/tex]
- Calculate: [tex]\(9 \times 14 = 126\)[/tex] and [tex]\(10 \times 5 = 50\)[/tex]
- Since [tex]\(126 \neq 50\)[/tex], [tex]\(\frac{5}{14}\)[/tex] is not equivalent to [tex]\(\frac{9}{10}\)[/tex].
- Option C: [tex]\(\frac{27}{30}\)[/tex]
- Cross-multiply: [tex]\(9 \times 30\)[/tex] and [tex]\(10 \times 27\)[/tex]
- Calculate: [tex]\(9 \times 30 = 270\)[/tex] and [tex]\(10 \times 27 = 270\)[/tex]
- Since [tex]\(270 = 270\)[/tex], [tex]\(\frac{27}{30}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
- Option D: [tex]\(\frac{18}{20}\)[/tex]
- Cross-multiply: [tex]\(9 \times 20\)[/tex] and [tex]\(10 \times 18\)[/tex]
- Calculate: [tex]\(9 \times 20 = 180\)[/tex] and [tex]\(10 \times 18 = 180\)[/tex]
- Since [tex]\(180 = 180\)[/tex], [tex]\(\frac{18}{20}\)[/tex] is equivalent to [tex]\(\frac{9}{10}\)[/tex].
3. Conclusion: The fractions [tex]\(\frac{27}{30}\)[/tex] and [tex]\(\frac{18}{20}\)[/tex] are equivalent to [tex]\(\frac{9}{10}\)[/tex]. Therefore, the correct options are C and D.
