Question

In a proportion where a ≠ 0 and b ≠ 0, which of the following are equivalent to the equation a/2 = 3/b?

a) a/3 = 2/b
b) (a - 2)/2 = (3 - y)/y
c) a * b = 3 * 2
d) They are all equivalent.

Answer 1

Option c) a * b = 3 * 2 is the equivalent expression to the original proportion a/2 = 3/b, as it represents the cross-multiplication of the proportion's terms.

Step-by-step explanation:

When analyzing the proportion a/2 = 3/b where a ≠ 0 and b ≠ 0, we look at the equivalent expressions given:

• a) a/3 = 2/b - This is not equivalent to the original proportion because the coefficients of a and b are not the same as in the original equation.
• b) (a - 2)/2 = (3 - y)/y - To determine if this is equivalent, we would need to solve for y. However, it does not appear equivalent as the original proportion does not have a subtraction operation in it.
• c) a * b = 3 * 2 - This is equivalent to the original proportion since multiplying both sides of the original equation by the denominators 2 and b would give us a * b = 6, which is the same as a * b = 3 * 2.

Therefore, option c is the correct equivalent expression to the original proportion a/2 = 3/b.