The Correct Answer and Explanation is:
The correct answer is B) 19/4.
The problem asks to convert the mixed number 4 3/4 into an equivalent improper fraction. A mixed number is a value that consists of a whole number and a proper fraction. An improper fraction is a fraction in which the numerator, the top number, is greater than or equal to the denominator, the bottom number. The conversion from a mixed number to an improper fraction can be completed in a few straightforward steps.
First, you need to multiply the whole number part of the mixed number by the denominator of the fractional part. In this problem, the whole number is 4 and the denominator is also 4. Multiplying these two numbers gives you 16. This step is essentially figuring out how many fractional pieces, in this case ‘fourths’, are contained within the four whole units. Since one whole unit is equal to 4/4, four whole units are equivalent to 16/4.
The second step is to take the result from the previous multiplication, which is 16, and add it to the numerator of the original fraction. The numerator in 4 3/4 is 3. Adding 16 and 3 results in 19. This new number, 19, represents the total number of ‘fourths’ when combining the whole number and the fraction. This value will become the numerator of your new improper fraction.
The final step is to place this new numerator over the original denominator. The denominator does not change because the size of the fractional unit, a fourth, remains constant throughout the conversion. Therefore, the improper fraction is 19/4.
If we check the given options, we can confirm our result. Option A, 14/4, is equal to 3 2/4. Option C, 11/4, is equal to 2 3/4. Option D, 6/4, is equal to 1 2/4. Only option B, 19/4, correctly represents the mixed number 4 3/4.
