To determine whether 2.25 is the same as [tex]\( 2 \frac{1}{4} \)[/tex], we can follow these steps:
1. Convert 2.25 to a Fraction:
- The decimal 2.25 can be expressed as a fraction.
- To convert 2.25 into a fraction, recognize that 2.25 is the same as [tex]\( 2 + \frac{25}{100} \)[/tex].
- Simplifying [tex]\( \frac{25}{100} \)[/tex] gives [tex]\( \frac{1}{4} \)[/tex].
- Therefore, [tex]\( 2.25 = 2 + \frac{1}{4} \)[/tex].
2. Express [tex]\( 2 \frac{1}{4} \)[/tex] as an Improper Fraction:
- The mixed number [tex]\( 2 \frac{1}{4} \)[/tex] can be converted to an improper fraction.
- Multiply the whole number part 2 by the denominator of the fraction, which is 4, so [tex]\( 2 \times 4 = 8 \)[/tex].
- Add the numerator of the fraction, which is 1, so [tex]\( 8 + 1 = 9 \)[/tex].
- Therefore, [tex]\( 2 \frac{1}{4} \)[/tex] is the same as [tex]\( \frac{9}{4} \)[/tex].
3. Compare the Two Fractions:
- We have found that 2.25 converts to [tex]\( \frac{9}{4} \)[/tex] and [tex]\( 2 \frac{1}{4} \)[/tex] also converts to [tex]\( \frac{9}{4} \)[/tex].
- Since both fractions represent the same value, we can conclude that 2.25 is indeed the same as [tex]\( 2 \frac{1}{4} \)[/tex].
Given these steps, the correct answer is:
- True
