Answer :
To find out which fractions are equivalent to [tex]\(\frac{9}{10}\)[/tex], we need to determine which of the given options can be simplified or transformed to the same fraction.
A fraction [tex]\(\frac{a}{b}\)[/tex] is equivalent to [tex]\(\frac{c}{d}\)[/tex] if the cross products are equal, meaning [tex]\(a \times d = b \times c\)[/tex].
Let's check each option:
A. [tex]\(\frac{15}{20}\)[/tex]
- Cross multiply: [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].
B. [tex]\(\frac{18}{20}\)[/tex]
- Cross multiply: [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].
C. [tex]\(\frac{27}{30}\)[/tex]
- Cross multiply: [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].
D. [tex]\(\frac{5}{14}\)[/tex]
- Cross multiply: [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].
Therefore, the fractions that are equivalent to [tex]\(\frac{9}{10}\)[/tex] are:
- [tex]\(\frac{18}{20}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
A fraction [tex]\(\frac{a}{b}\)[/tex] is equivalent to [tex]\(\frac{c}{d}\)[/tex] if the cross products are equal, meaning [tex]\(a \times d = b \times c\)[/tex].
Let's check each option:
A. [tex]\(\frac{15}{20}\)[/tex]
- Cross multiply: [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].
B. [tex]\(\frac{18}{20}\)[/tex]
- Cross multiply: [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].
C. [tex]\(\frac{27}{30}\)[/tex]
- Cross multiply: [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].
D. [tex]\(\frac{5}{14}\)[/tex]
- Cross multiply: [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].
Therefore, the fractions that are equivalent to [tex]\(\frac{9}{10}\)[/tex] are:
- [tex]\(\frac{18}{20}\)[/tex]
- [tex]\(\frac{27}{30}\)[/tex]
