Final answer:
The statement incorrectly demonstrates how an improper fraction is divided by a whole number. The correct representation of 13 ÷ 15 should be 3 and 161/225 after simplifying the improper fraction and performing division.
Step-by-step explanation:
The long answer to the question involves understanding that the statement 13 ÷ 15 = 53 1/3 ÷ 15 = 5 3/15 illustrates how improper fractions can be simplified.
This is because an improper fraction, such as 53 1/3 (which is 53 plus one-third), can be expressed as 53 plus 1/3, and when that sum is divided by 15, the division applies to both the whole number and the fraction separately. The whole number division (53 ÷ 15) equals to 3 with a remainder of 8 because 15 times 3 is 45 and 53 minus 45 leaves 8.
The fractional part (1/3 ÷ 15) converts to a division of 1 by 45, because dividing by 15 is the same as multiplying by the reciprocal of 15, which is 1/15. 1/3 multiplied by 1/15 equals 1/45.
Combining the separate divisions, we get 3 and 8/15 plus 1/45, which simplifies to 3 and 161/225, as both fractions are converted to have a common denominator of 225. Therefore, the correct representation would be 13 ÷ 15 = 3 and 161/225.