Question

1a what is the product of 1⁷/⁹ and 3³/⁴

b. What must be added to the product of 1⁷/⁹ and 3³/⁴ to make a total of 8⅓

Answer 1

[AI-generated answer — 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.