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Answer :
Sure, I'd be happy to help! Let's determine which of the provided proportional statements is true.
We need to check each statement to see if both fractions are equivalent. Two fractions are equal if their cross-products are equal.
1. [tex]\(\frac{19}{23} = \frac{76}{92}\)[/tex]
2. [tex]\(\frac{19}{23} = \frac{37}{46}\)[/tex]
3. [tex]\(\frac{19}{23} = \frac{75}{92}\)[/tex]
4. [tex]\(\frac{19}{23} = \frac{38}{45}\)[/tex]
Let's go through each option step-by-step:
### Check 1: [tex]\(\frac{19}{23} = \frac{76}{92}\)[/tex]
Cross-multiply to check:
[tex]\[ 19 \times 92 = 23 \times 76 \][/tex]
[tex]\[ 1748 = 1748 \][/tex]
This statement is true.
### Check 2: [tex]\(\frac{19}{23} = \frac{37}{46}\)[/tex]
Cross-multiply to check:
[tex]\[ 19 \times 46 = 23 \times 37 \][/tex]
[tex]\[ 874 = 851 \][/tex]
This statement is false.
### Check 3: [tex]\(\frac{19}{23} = \frac{75}{92}\)[/tex]
Cross-multiply to check:
[tex]\[ 19 \times 92 = 23 \times 75 \][/tex]
[tex]\[ 1748 \neq 1725 \][/tex]
This statement is false.
### Check 4: [tex]\(\frac{19}{23} = \frac{38}{45}\)[/tex]
Cross-multiply to check:
[tex]\[ 19 \times 45 = 23 \times 38 \][/tex]
[tex]\[ 855 \neq 874 \][/tex]
This statement is false.
So, the only true statement is:
[tex]\[ \frac{19}{23} = \frac{76}{92} \][/tex]
Thus, the correct answer is the first option:
[tex]\[ \frac{19}{23} = \frac{76}{92} \][/tex]
We need to check each statement to see if both fractions are equivalent. Two fractions are equal if their cross-products are equal.
1. [tex]\(\frac{19}{23} = \frac{76}{92}\)[/tex]
2. [tex]\(\frac{19}{23} = \frac{37}{46}\)[/tex]
3. [tex]\(\frac{19}{23} = \frac{75}{92}\)[/tex]
4. [tex]\(\frac{19}{23} = \frac{38}{45}\)[/tex]
Let's go through each option step-by-step:
### Check 1: [tex]\(\frac{19}{23} = \frac{76}{92}\)[/tex]
Cross-multiply to check:
[tex]\[ 19 \times 92 = 23 \times 76 \][/tex]
[tex]\[ 1748 = 1748 \][/tex]
This statement is true.
### Check 2: [tex]\(\frac{19}{23} = \frac{37}{46}\)[/tex]
Cross-multiply to check:
[tex]\[ 19 \times 46 = 23 \times 37 \][/tex]
[tex]\[ 874 = 851 \][/tex]
This statement is false.
### Check 3: [tex]\(\frac{19}{23} = \frac{75}{92}\)[/tex]
Cross-multiply to check:
[tex]\[ 19 \times 92 = 23 \times 75 \][/tex]
[tex]\[ 1748 \neq 1725 \][/tex]
This statement is false.
### Check 4: [tex]\(\frac{19}{23} = \frac{38}{45}\)[/tex]
Cross-multiply to check:
[tex]\[ 19 \times 45 = 23 \times 38 \][/tex]
[tex]\[ 855 \neq 874 \][/tex]
This statement is false.
So, the only true statement is:
[tex]\[ \frac{19}{23} = \frac{76}{92} \][/tex]
Thus, the correct answer is the first option:
[tex]\[ \frac{19}{23} = \frac{76}{92} \][/tex]
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