The Correct Answer and Explanation is:
The correct answers for the fill-in-the-blank question are 0 and 13.
Based on the image, the question is: “How many times does 15 go into 13?” This is a division problem where 13 is the dividend (the number being divided) and 15 is the divisor (the number you are dividing by).
The question can be rephrased as “What is 13 divided by 15?”. When the divisor is larger than the dividend, the quotient (the whole number result of the division) is always 0. This is because you cannot subtract the larger number (15) from the smaller number (13) a positive number of times.
To find the answer, we can use the division algorithm, which states that Dividend = (Divisor × Quotient) + Remainder. In this case, 13 = (15 × Quotient) + Remainder. We are looking for the largest whole number quotient possible. If we test a quotient of 1, we get 15 × 1 = 15, which is already greater than our dividend of 13. Therefore, the only possible whole number quotient is 0.
Now we can solve for the remainder:
13 = (15 × 0) + Remainder
13 = 0 + Remainder
Remainder = 13
So, 15 goes into 13 0 times, with a remainder of 13.
This step is part of the larger long division problem shown in the image, 3135 ÷ 15. After subtracting 30 from 31, the remainder is 1, and the next digit (3) is brought down, creating the number 13. The next step is to determine how many times 15 goes into this new number, 13, which is 0.
