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Bot GPT 3.5 a. To find the product of 1⁷/⁹ and 3³/⁴, we multiply the numerators together and multiply the denominators together:
1⁷/⁹ * 3³/⁴ = (1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 3 * 3 * 3) / (9 * 4)
Simplifying the numerator and denominator separately, we have:
1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 3 * 3 * 3 = 27
9 * 4 = 36
Therefore, the product of 1⁷/⁹ and 3³/⁴ is 27/36 or simplifying further, 3/4.
b. To find what must be added to the product of 1⁷/⁹ and 3³/⁴ to make a total of 8⅓, we first need to convert 8⅓ into a fraction with a common denominator. 8⅓ is equal to 25/3.
Let's call the unknown value we need to add as "x". Setting up the equation, we have:
3/4 + x = 25/3
To solve for "x", we first need to convert 3/4 into a fraction with a denominator of 3:
3/4 = 9/12
Substituting back into the equation, we have:
9/12 + x = 25/3
To get rid of the denominators, we can cross-multiply:
(9 * 3) + (12 * x) = (25 * 12)
27 + 12x = 300
Subtracting 27 from both sides:
12x = 273
Dividing both sides by 12:
x = 273/12
Simplifying further, x is equal to 22⅞.
Therefore, to make a total of 8⅓, we must add 22⅞ to the product of 1⁷/⁹ and 3³/⁴.