Calculating 35 3/4 divided by 2 involves a mixed number, which represents a value greater than one but not yet a whole integer. To solve this, we first convert the mixed number into an improper fraction to simplify the division process. The fractional part, three-quarters, is expressed as 3/4, and the whole number 35 is combined with this to form 143/4. This transformation is the critical first step that allows for straightforward arithmetic manipulation.
Converting to an Improper Fraction
The expression 35 3/4 is a mixed number, which combines a whole number with a proper fraction. To divide this value effectively, it is standard practice to convert it into an improper fraction. This format is easier to manage mathematically because it represents the entire quantity as a single numerator over a consistent denominator. The calculation involves multiplying the whole number, 35, by the denominator, 4, which results in 140. Adding the original numerator, 3, to this product gives a total of 143. Consequently, the mixed number 35 3/4 is rewritten as the improper fraction 143/4.
Division by a Whole Number
With the mixed number converted to 143/4, we proceed to divide it by 2. In mathematical terms, dividing by a whole number is equivalent to multiplying by the reciprocal of that integer. The reciprocal of 2 is 1/2. This operation transforms the problem into a multiplication of two fractions: 143/4 multiplied by 1/2. When multiplying fractions, the numerators are multiplied together to form the new numerator, and the denominators are multiplied together to form the new denominator. This results in the fraction 143 over 8.
Result as an Improper Fraction and Decimal
The exact result of 35 3/4 divided by 2 is 143/8. This improper fraction represents the precise mathematical answer without any rounding. To express this value in a format that is more intuitive for everyday use, we can convert it to a decimal. By performing the division of 143 by 8, the result is 17.875. This decimal representation confirms that the value lies between 17 and 18, specifically at 17.875.
Breaking Down the Calculation
Understanding the mechanics behind the calculation ensures accuracy and builds numerical intuition. The process relies on the fundamental rule that dividing by a number scales the original quantity down by that factor. Since 35 3/4 is equal to 35.75 in decimal form, dividing this by 2 essentially halves the quantity. Halving 35 results in 17.5, and halving 0.75 results in 0.375. Summing these two results, 17.5 and 0.375, provides the same answer of 17.875, validating the fraction-based approach.
Verification and Logic
Logic dictates that if the result of 17.875 is multiplied by the divisor, 2, the original number 35.75 should be recovered. Performing this verification, 17.875 times 2 equals 35.75, confirming the solution is correct. This step is crucial for checking work and ensuring that the reciprocal multiplication was executed properly. The consistency between the fraction and decimal methods reinforces the reliability of the result.
