Add. Write the answer in lowest terms.
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Question

Quizplus · Accepted Answer

The given number is in hexadecimal (base 16) format. To convert it into decimal (base 10) format, we can use the following method:
11ebb7d6_16 = (1 × 16^8) + (1 × 16^7) + (e × 16^6) + (b × 16^5) + (b × 16^4) + (7 × 16^3) + (d × 16^2) + (6 × 16^1)
+ (d × 16^0)

= (1 × 16^8) + (1 × 16^7) + (14 × 16^6) + (11 × 16^5) + (11 × 16^4) + (7 × 16^3) + (13 × 16^2) + (6 × 16^1) + (13 × 16^0)

= 3,044,054,740

Similarly, 62f7ad4c_16 = 1,664,509,452

Now, we need to find the GCD (greatest common divisor) of these two numbers. We can use the Euclidean algorithm for this:

3,044,054,740 ÷ 1,664,509,452 = 1 remainder 1,379,545,288
1,664,509,452 ÷ 1,379,545,288 = 1 remainder 284,964,164
1,379,545,288 ÷ 284,964,164 = 4 remainder 84,589,676
284,964,164 ÷ 84,589,676 = 3 remainder 31,194,836
84,589,676 ÷ 31,194,836 = 2 remainder 22,199,004
31,194,836 ÷ 22,199,004 = 1 remainder 8,995,832
22,199,004 ÷ 8,995,832 = 2 remainder 4,207,340
8,995,832 ÷ 4,207,340 = 2 remainder 1,580,152
4,207,340 ÷ 1,580,152 = 2 remainder 1,046,036
1,580,152 ÷ 1,046,036 = 1 remainder 534,116
1,046,036 ÷ 534,116 = 1 remainder 511,920
534,116 ÷ 511,920 = 1 remainder 22,196

So, the GCD of the two numbers is 22,196. We can simplify the given fraction by dividing both numerator and denominator by this GCD:

(1,664,509,452 ÷ 22,196) / (3,044,054,740 ÷ 22,196) = 75 / 137

This is already in lowest terms. Now, we need to find the hexadecimal representation of the numerator and denominator of this fraction. We can use the reverse method:

75 = 4b_16
137 = 89_16

So, the answer is 11ebb7d6_6dff_8a09_ad4c_43be607fae7a_TB8285_11, which is option B.

Add. Write the Answer in Lowest Terms