Answer :
To determine which fractions are equivalent to [tex]\(\frac{12}{15}\)[/tex], we need to check each option by seeing if it simplifies to the same fraction or if they are equal through cross-multiplication.
1. Option A: [tex]\(\frac{4}{20}\)[/tex]
Cross-multiply:
[tex]\(12 \times 20 = 240\)[/tex]
[tex]\(15 \times 4 = 60\)[/tex]
Since [tex]\(240 \neq 60\)[/tex], [tex]\(\frac{4}{20}\)[/tex] is not equivalent to [tex]\(\frac{12}{15}\)[/tex].
2. Option B: [tex]\(\frac{24}{30}\)[/tex]
Cross-multiply:
[tex]\(12 \times 30 = 360\)[/tex]
[tex]\(15 \times 24 = 360\)[/tex]
Since both products are [tex]\(360\)[/tex], [tex]\(\frac{24}{30}\)[/tex] is equivalent to [tex]\(\frac{12}{15}\)[/tex].
3. Option C: [tex]\(\frac{4}{5}\)[/tex]
Cross-multiply:
[tex]\(12 \times 5 = 60\)[/tex]
[tex]\(15 \times 4 = 60\)[/tex]
Since both products are [tex]\(60\)[/tex], [tex]\(\frac{4}{5}\)[/tex] is equivalent to [tex]\(\frac{12}{15}\)[/tex].
4. Option D: [tex]\(\frac{4}{16}\)[/tex]
Cross-multiply:
[tex]\(12 \times 16 = 192\)[/tex]
[tex]\(15 \times 4 = 60\)[/tex]
Since [tex]\(192 \neq 60\)[/tex], [tex]\(\frac{4}{16}\)[/tex] is not equivalent to [tex]\(\frac{12}{15}\)[/tex].
In conclusion, the equivalent fractions to [tex]\(\frac{12}{15}\)[/tex] are [tex]\(\frac{24}{30}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex].
1. Option A: [tex]\(\frac{4}{20}\)[/tex]
Cross-multiply:
[tex]\(12 \times 20 = 240\)[/tex]
[tex]\(15 \times 4 = 60\)[/tex]
Since [tex]\(240 \neq 60\)[/tex], [tex]\(\frac{4}{20}\)[/tex] is not equivalent to [tex]\(\frac{12}{15}\)[/tex].
2. Option B: [tex]\(\frac{24}{30}\)[/tex]
Cross-multiply:
[tex]\(12 \times 30 = 360\)[/tex]
[tex]\(15 \times 24 = 360\)[/tex]
Since both products are [tex]\(360\)[/tex], [tex]\(\frac{24}{30}\)[/tex] is equivalent to [tex]\(\frac{12}{15}\)[/tex].
3. Option C: [tex]\(\frac{4}{5}\)[/tex]
Cross-multiply:
[tex]\(12 \times 5 = 60\)[/tex]
[tex]\(15 \times 4 = 60\)[/tex]
Since both products are [tex]\(60\)[/tex], [tex]\(\frac{4}{5}\)[/tex] is equivalent to [tex]\(\frac{12}{15}\)[/tex].
4. Option D: [tex]\(\frac{4}{16}\)[/tex]
Cross-multiply:
[tex]\(12 \times 16 = 192\)[/tex]
[tex]\(15 \times 4 = 60\)[/tex]
Since [tex]\(192 \neq 60\)[/tex], [tex]\(\frac{4}{16}\)[/tex] is not equivalent to [tex]\(\frac{12}{15}\)[/tex].
In conclusion, the equivalent fractions to [tex]\(\frac{12}{15}\)[/tex] are [tex]\(\frac{24}{30}\)[/tex] and [tex]\(\frac{4}{5}\)[/tex].
