Final answer:
The mixed number 7 3/4 is converted to an improper fraction by multiplying the whole number by the denominator (7*4=28) and adding the numerator of the fraction (28+3=31), resulting in 31/4.
Step-by-step explanation:
The rational number 7 3/4 can be expressed as a fraction where 'a' is the numerator and 'b' is the denominator. To convert the mixed number to an improper fraction, we multiply the whole number by the denominator of the fractional part and add the numerator of the fractional part. This mixed number consists of the whole number 7 and the fraction 3/4.
First, we convert the whole number 7 to a fraction with the same denominator as 3/4, which is 4:
7 = 7 * 4/4 = 28/4
Now we add the fractional part 3/4 to this:
28/4 + 3/4 = (28 + 3)/4 = 31/4
So the answer is 31/4, which corresponds to option a) 31/4.
An improper fraction is a fraction that has a numerator that is greater or equal to the denominator. The numerator is the number on the top, the denominator is the number on the bottom. You can have improper fractions when you have a whole or more than a whole.
7⁄5 18⁄18 100⁄13
The numerator shows us how many pieces of something we have, whereas the denominator shows us the number of parts we’re dividing by. When it comes to an improper fraction, such as the first one above, we have 7 parts and each part is a fifth of a whole.