Write 2.75 as a mixed number and as an improper fraction. Write your answers in simplest form.
The Correct Answer and Explanation is :
Answer:
- Mixed number: 2.75 can be written as ( 2 \frac{3}{4} ).
- Improper fraction: 2.75 can be written as ( \frac{11}{4} ).
Explanation:
- Understanding Decimal to Mixed Number Conversion:
A decimal like 2.75 consists of two parts:
- The whole number (2) and
- The decimal part (0.75). To convert this to a mixed number:
- The whole number remains unchanged: 2.
- Now, we focus on converting the decimal 0.75 into a fraction.
- Converting the Decimal (0.75) into a Fraction:
To convert 0.75 to a fraction, recognize that:
- 0.75 is the same as 75/100.
- Simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 25. [
\frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}
] Therefore, 0.75 equals ( \frac{3}{4} ).
- Writing the Mixed Number:
Now, combine the whole number 2 with the fractional part ( \frac{3}{4} ), and you get the mixed number: [
2 \frac{3}{4}
] - Converting to an Improper Fraction:
An improper fraction has a numerator larger than the denominator, representing the same value as the mixed number but without separating the whole number part. To convert ( 2 \frac{3}{4} ) to an improper fraction:
- Multiply the whole number (2) by the denominator (4): ( 2 \times 4 = 8 ).
- Add the result to the numerator (3): ( 8 + 3 = 11 ). This gives the improper fraction: [
\frac{11}{4}
]
Thus, 2.75 can be expressed as ( 2 \frac{3}{4} ) (mixed number) and ( \frac{11}{4} ) (improper fraction). Both represent the same value, but in different formats.