Question

Which statement is correct?
StartFraction 1 inch Over 2.54 centimeters EndFraction = StartFraction 7 inches Over 17.68 centimeters EndFraction
StartFraction 1 foot Over 12 inches EndFraction = StartFraction 7 feet Over 74 inches EndFraction
StartFraction 1 yard Over 36 inches EndFraction = StartFraction 7 yards Over 252 inches EndFraction
StartFraction 1 meter Over 3.28 feet EndFraction = StartFraction 7 meters Over 22.86 feet EndFraction

Answer 1

To determine which statement is correct, we can simplify each expression.

1. **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.

2. **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.

3. **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.

4. **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:**
\[
\frac{1 \text{ inch}}{2.54 \text{ cm}} = \frac{7 \text{ inches}}{17.68 \text{ cm}}
\]