Answer :
To determine which ratio forms a proportion with [tex]\(\frac{12}{16}\)[/tex], we need to figure out which of the given options is equivalent to [tex]\(\frac{12}{16}\)[/tex]. Normally, this can be done by cross-multiplying and seeing if the cross-products are equal.
Let's check each option:
1. Option a: [tex]\(\frac{8}{12}\)[/tex]
- Cross multiply: [tex]\(12 \times 12\)[/tex] and [tex]\(16 \times 8\)[/tex].
- Calculate: [tex]\(144\)[/tex] vs. [tex]\(128\)[/tex].
- Since [tex]\(144 \neq 128\)[/tex], [tex]\(\frac{8}{12}\)[/tex] does not form a proportion with [tex]\(\frac{12}{16}\)[/tex].
2. Option b: [tex]\(\frac{16}{20}\)[/tex]
- Cross multiply: [tex]\(12 \times 20\)[/tex] and [tex]\(16 \times 16\)[/tex].
- Calculate: [tex]\(240\)[/tex] vs. [tex]\(256\)[/tex].
- Since [tex]\(240 \neq 256\)[/tex], [tex]\(\frac{16}{20}\)[/tex] does not form a proportion with [tex]\(\frac{12}{16}\)[/tex].
3. Option c: [tex]\(\frac{18}{20}\)[/tex]
- Cross multiply: [tex]\(12 \times 20\)[/tex] and [tex]\(16 \times 18\)[/tex].
- Calculate: [tex]\(240\)[/tex] vs. [tex]\(288\)[/tex].
- Since [tex]\(240 \neq 288\)[/tex], [tex]\(\frac{18}{20}\)[/tex] does not form a proportion with [tex]\(\frac{12}{16}\)[/tex].
4. Option d: [tex]\(\frac{24}{30}\)[/tex]
- Cross multiply: [tex]\(12 \times 30\)[/tex] and [tex]\(16 \times 24\)[/tex].
- Calculate: [tex]\(360\)[/tex] vs. [tex]\(384\)[/tex].
- Since [tex]\(360 \neq 384\)[/tex], [tex]\(\frac{24}{30}\)[/tex] does not form a proportion with [tex]\(\frac{12}{16}\)[/tex].
After checking all the options, we find that none of them forms a proportion with [tex]\(\frac{12}{16}\)[/tex].
Let's check each option:
1. Option a: [tex]\(\frac{8}{12}\)[/tex]
- Cross multiply: [tex]\(12 \times 12\)[/tex] and [tex]\(16 \times 8\)[/tex].
- Calculate: [tex]\(144\)[/tex] vs. [tex]\(128\)[/tex].
- Since [tex]\(144 \neq 128\)[/tex], [tex]\(\frac{8}{12}\)[/tex] does not form a proportion with [tex]\(\frac{12}{16}\)[/tex].
2. Option b: [tex]\(\frac{16}{20}\)[/tex]
- Cross multiply: [tex]\(12 \times 20\)[/tex] and [tex]\(16 \times 16\)[/tex].
- Calculate: [tex]\(240\)[/tex] vs. [tex]\(256\)[/tex].
- Since [tex]\(240 \neq 256\)[/tex], [tex]\(\frac{16}{20}\)[/tex] does not form a proportion with [tex]\(\frac{12}{16}\)[/tex].
3. Option c: [tex]\(\frac{18}{20}\)[/tex]
- Cross multiply: [tex]\(12 \times 20\)[/tex] and [tex]\(16 \times 18\)[/tex].
- Calculate: [tex]\(240\)[/tex] vs. [tex]\(288\)[/tex].
- Since [tex]\(240 \neq 288\)[/tex], [tex]\(\frac{18}{20}\)[/tex] does not form a proportion with [tex]\(\frac{12}{16}\)[/tex].
4. Option d: [tex]\(\frac{24}{30}\)[/tex]
- Cross multiply: [tex]\(12 \times 30\)[/tex] and [tex]\(16 \times 24\)[/tex].
- Calculate: [tex]\(360\)[/tex] vs. [tex]\(384\)[/tex].
- Since [tex]\(360 \neq 384\)[/tex], [tex]\(\frac{24}{30}\)[/tex] does not form a proportion with [tex]\(\frac{12}{16}\)[/tex].
After checking all the options, we find that none of them forms a proportion with [tex]\(\frac{12}{16}\)[/tex].
