To determine which statement is correct, we can simplify each expression.
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Statement 1: \[ \frac{1 \text{ inch}}{2.54 \text{ cm}} = \frac{7 \text{ inches}}{17.68 \text{ cm}} \] Let's check the left side:
- Convert 1 inch to cm: 1 inch = 2.54 cm.
- Therefore, \(\frac{1}{2.54}\) is indeed equal to 1 (since \(1 \text{ inch} = 2.54 \text{ cm}\)).
Now, check the right side:
- \(7 \text{ inches} = 7 \times 2.54 = 17.68 \text{ cm}\).
- Therefore, the right side also simplifies to 1.
The statement is true.
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Statement 2: \[ \frac{1 \text{ foot}}{12 \text{ inches}} = \frac{7 \text{ feet}}{74 \text{ inches}} \] Left side: \(\frac{1 \text{ foot}}{12 \text{ inches}} = \frac{1}{12}\).
Right side: \(7 \text{ feet} = 7 \times 12 = 84 \text{ inches}\), thus: \[ \frac{7 \text{ feet}}{74 \text{ inches}} = \frac{84}{74} \approx 1.135\ (not\ equal\ to\ \frac{1}{12}). \] This statement is false.
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Statement 3: \[ \frac{1 \text{ yard}}{36 \text{ inches}} = \frac{7 \text{ yards}}{252 \text{ inches}} \] Left side: \(\frac{1 \text{ yard}}{36 \text{ inches}} = \frac{1}{36}\).
Right side: \(7 \text{ yards} = 7 \times 36 = 252 \text{ inches}\), thus: \[ \frac{7 \text{ yards}}{252 \text{ inches}} = \frac{252}{252} = 1\ (not\ equal\ to\ \frac{1}{36}). \] This statement is false.
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Statement 4: \[ \frac{1 \text{ meter}}{3.28 \text{ feet}} = \frac{7 \text{ meters}}{22.86 \text{ feet}} \] Left side: \(\frac{1 \text{ m}}{3.28 \text{ ft}}\). Right side: \(7 \text{ meters} = 7 \times 3.28 = 22.96 \text{ feet}\), thus: \(\frac{7 \text{ m}}{22.86 \text{ ft}} \approx 0.305\ (not\ equal\ to\ \frac{1}{3.28})\).
This statement is also false.
After checking all statements, only the first statement is true:
The correct statement is: \[ \frac{1 \text{ inch}}{2.54 \text{ cm}} = \frac{7 \text{ inches}}{17.68 \text{ cm}} \]