Answer :
To determine which of the given proportional statements is true, we'll compare each fraction to [tex]\(\frac{19}{23}\)[/tex] and see if they are equivalent.
1. Check the first statement:
[tex]\[
\frac{19}{23} \quad \text{and} \quad \frac{38}{45}
\][/tex]
To check if these are proportions, we cross-multiply to see if we get the same product:
[tex]\[
19 \times 45 = 855
\][/tex]
[tex]\[
23 \times 38 = 874
\][/tex]
Since the products are not equal, [tex]\(\frac{19}{23} \neq \frac{38}{45}\)[/tex].
2. Check the second statement:
[tex]\[
\frac{19}{23} \quad \text{and} \quad \frac{76}{92}
\][/tex]
Cross-multiply to see if the products are equal:
[tex]\[
19 \times 92 = 1748
\][/tex]
[tex]\[
23 \times 76 = 1748
\][/tex]
Since the products are equal, [tex]\(\frac{19}{23} = \frac{76}{92}\)[/tex]. Hence, this statement is true.
3. Check the third statement:
[tex]\[
\frac{19}{23} \quad \text{and} \quad \frac{75}{92}
\][/tex]
Cross-multiply to check:
[tex]\[
19 \times 92 = 1748
\][/tex]
[tex]\[
23 \times 75 = 1725
\][/tex]
The products are not equal, so [tex]\(\frac{19}{23} \neq \frac{75}{92}\)[/tex].
4. Check the fourth statement:
[tex]\[
\frac{19}{23} \quad \text{and} \quad \frac{37}{46}
\][/tex]
Cross-multiply for verification:
[tex]\[
19 \times 46 = 874
\][/tex]
[tex]\[
23 \times 37 = 851
\][/tex]
The products are not equal, indicating [tex]\(\frac{19}{23} \neq \frac{37}{46}\)[/tex].
So, the true proportional statement is [tex]\(\frac{19}{23} = \frac{76}{92}\)[/tex].
1. Check the first statement:
[tex]\[
\frac{19}{23} \quad \text{and} \quad \frac{38}{45}
\][/tex]
To check if these are proportions, we cross-multiply to see if we get the same product:
[tex]\[
19 \times 45 = 855
\][/tex]
[tex]\[
23 \times 38 = 874
\][/tex]
Since the products are not equal, [tex]\(\frac{19}{23} \neq \frac{38}{45}\)[/tex].
2. Check the second statement:
[tex]\[
\frac{19}{23} \quad \text{and} \quad \frac{76}{92}
\][/tex]
Cross-multiply to see if the products are equal:
[tex]\[
19 \times 92 = 1748
\][/tex]
[tex]\[
23 \times 76 = 1748
\][/tex]
Since the products are equal, [tex]\(\frac{19}{23} = \frac{76}{92}\)[/tex]. Hence, this statement is true.
3. Check the third statement:
[tex]\[
\frac{19}{23} \quad \text{and} \quad \frac{75}{92}
\][/tex]
Cross-multiply to check:
[tex]\[
19 \times 92 = 1748
\][/tex]
[tex]\[
23 \times 75 = 1725
\][/tex]
The products are not equal, so [tex]\(\frac{19}{23} \neq \frac{75}{92}\)[/tex].
4. Check the fourth statement:
[tex]\[
\frac{19}{23} \quad \text{and} \quad \frac{37}{46}
\][/tex]
Cross-multiply for verification:
[tex]\[
19 \times 46 = 874
\][/tex]
[tex]\[
23 \times 37 = 851
\][/tex]
The products are not equal, indicating [tex]\(\frac{19}{23} \neq \frac{37}{46}\)[/tex].
So, the true proportional statement is [tex]\(\frac{19}{23} = \frac{76}{92}\)[/tex].
