Write 3.5 as a mixed number and as an improper fraction. Write your answers in simplest form. mixed number: improper fraction:
The Correct Answer and Explanation is:
mixed number: 3 1/2
improper fraction: 7/2
Explanation
Understanding how to represent a number in different forms—such as a decimal, a mixed number, or an improper fraction—is a fundamental concept in mathematics. Each form has its use, and converting between them is a key skill. The number 3.5 is a decimal representation. Let’s explore how to convert it into its fractional equivalents.
Converting a Decimal to a Mixed Number
A mixed number consists of a whole number and a proper fraction combined. To convert the decimal 3.5 into a mixed number, one must first identify its whole and decimal parts.
- Identify the Parts: The number 3.5 is composed of the whole number 3 (the digit to the left of the decimal point) and the decimal part 0.5 (the digit to the right).
- Convert the Decimal to a Fraction: The decimal part, 0.5, is read as “five-tenths.” This name directly translates into the fraction 5/10. The digit 5 is the numerator, and its place value (tenths) determines the denominator, which is 10.
- Combine and Simplify: Combining the whole number and the new fraction gives the mixed number 3 and 5/10. However, answers should always be in their simplest form. The fraction 5/10 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5.
- 5 ÷ 5 = 1
- 10 ÷ 5 = 2
This simplifies the fraction to 1/2. Therefore, the simplified mixed number is 3 1/2.
Converting a Mixed Number to an Improper Fraction
An improper fraction is one where the numerator is greater than or equal to the denominator. To convert the mixed number 3 1/2 into an improper fraction, follow this procedure:
- Multiply and Add: Multiply the whole number (3) by the denominator of the fraction (2). Then, add the numerator (1) to this product.
- (3 × 2) + 1 = 6 + 1 = 7
- Form the Fraction: This result, 7, becomes the new numerator. The denominator remains the same, which is 2. The resulting improper fraction is 7/2. This fraction is already in its simplest form, as 7 and 2 are prime numbers and share no common factors other than 1. Both 3 1/2 and 7/2 are equivalent to the decimal 3.5.
