The Correct Answer and Explanation is:
83.5
To write the mixed number 83 1/2 as a decimal number, we need to convert the fractional part into its decimal form and then combine it with the whole number part.
A mixed number is composed of a whole number and a proper fraction. In this case, our whole number is 83, and our fraction is 1/2. The simplest way to perform this conversion is to focus on the fraction first. To convert any fraction to a decimal, you divide the numerator (the top number) by the denominator (the bottom number). For the fraction 1/2, we need to calculate 1 divided by 2.
The calculation 1 ÷ 2 equals 0.5.
Now that we have the decimal value for the fractional part, we add it to the whole number part. The whole number is 83. So, the final step is to add these two components together:
83 (the whole number) + 0.5 (the decimal fraction) = 83.5
Therefore, the mixed number 83 1/2 is equivalent to the decimal number 83.5.
An alternative method is to first convert the mixed number into an improper fraction. To do this, you multiply the whole number (83) by the fraction’s denominator (2) and then add the numerator (1). This gives you the new numerator for the improper fraction, while the denominator stays the same. The calculation is (83 × 2) + 1 = 166 + 1 = 167. This makes the improper fraction 167/2. Next, you perform the division represented by this fraction: 167 ÷ 2, which also equals 83.5. Both methods confirm that the correct decimal representation is 83.5. This conversion is a fundamental mathematical skill, useful for calculations and for representing values in a consistent format.
