Write 4.5 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: 4 1/2
improper fraction: 9/2
Explanation
The goal is to express the decimal number 4.5 in two different fractional forms: as a mixed number and as an improper fraction, ensuring both are in their simplest form.
1. Converting to a Mixed Number
A mixed number consists of a whole number and a proper fraction. To convert 4.5, we first identify these two parts.
- The whole number is the digit to the left of the decimal point, which is 4.
- The fractional part is the number to the right of the decimal point, which is 0.5.
To write 0.5 as a fraction, we look at its place value. The digit “5” is in the tenths place, so we can write it as 5/10.
Now, we combine the whole number and the fraction to get the mixed number: 4 and 5/10.
The final step is to simplify the fractional part, 5/10. We find the greatest common divisor (GCD) of the numerator (5) and the denominator (10). The largest number that divides both 5 and 10 is 5. We divide both parts of the fraction by 5:
- 5 ÷ 5 = 1
- 10 ÷ 5 = 2
So, the simplified fraction is 1/2. Replacing the original fraction with the simplified one gives us the final mixed number: 4 1/2.
2. Converting to an Improper Fraction
An improper fraction is a fraction where the numerator is greater than or equal to the denominator. We can find this by converting our simplified mixed number, 4 1/2.
To do this, we multiply the whole number (4) by the denominator (2) and then add the numerator (1). This result becomes the new numerator. The denominator stays the same.
- Calculation: (4 × 2) + 1 = 8 + 1 = 9
The new numerator is 9, and the denominator remains 2. Therefore, the improper fraction is 9/2. This fraction is already in its simplest form because the only number that divides both 9 and 2 is 1.
