Rewrite 7.25 as a mixed number in lowest terms
The Correct Answer and Explanation is:
To convert 7.25 into a mixed number in its lowest terms, follow these steps:
Step 1: Understand the decimal representation
The number 7.25 consists of two parts:
- The whole number part: 7
- The decimal part: 0.25
Step 2: Convert the decimal part to a fraction
The decimal 0.25 represents 25 hundredths (since 25 is in the hundredths place). To express this as a fraction, write it as:
[
\frac{25}{100}
]
Step 3: Simplify the fraction
To simplify the fraction, divide both the numerator (25) and the denominator (100) by their greatest common divisor (GCD), which is 25:
[
\frac{25 \div 25}{100 \div 25} = \frac{1}{4}
]
Thus, 0.25 simplifies to (\frac{1}{4}).
Step 4: Combine the whole number and the fraction
Now, combine the whole number 7 with the fraction (\frac{1}{4}) to form the mixed number:
[
7 + \frac{1}{4} = 7\frac{1}{4}
]
Step 5: Verify the result
To verify that this is correct, convert the mixed number (7\frac{1}{4}) back into a decimal:
- The whole number part is 7.
- The fraction (\frac{1}{4}) is equal to 0.25.
Adding these together:
[
7 + 0.25 = 7.25
]
This matches the original number, confirming that the mixed number representation is correct.
Final Answer:
The decimal 7.25 as a mixed number in its lowest terms is:
[
7\frac{1}{4}
]
Explanation:
Converting a decimal to a mixed number involves separating the whole number and the decimal part. The decimal part is then converted into a fraction, and the fraction is simplified to its lowest terms. Finally, the whole number and the simplified fraction are combined to form the mixed number. By understanding these steps, we ensure that 7.25 is correctly represented as (7\frac{1}{4}), providing an exact, simplified mixed number.