Question

Which pairs of ratios form a proportion?

a) 2/3, 10/5
b) 3/4, 30/40
c) 36/30, 18/15
d) 4/5, 28/35

Answer 1

Pairs of ratios that form proportions are found by simplifying them to see if they are equivalent. Options b, c, and d from the given ratios form proportions, as their simplified forms are equivalent.

Step-by-step explanation:

To determine which pairs of ratios form a proportion, we need to check if the ratios are equivalent by simplifying them or by performing cross multiplication.

• Option a: The ratios 2/3 and 10/5 do not form a proportion because 2/3 simplifies to 2/3, but 10/5 simplifies to 2, and these two ratios are not equivalent.
• Option b: The ratios 3/4 and 30/40 do form a proportion because they both simplify to the same ratio. Simplifying 30/40 gives us 3/4, which shows the two ratios are equivalent.
• Option c: The ratios 36/30 and 18/15 also form a proportion because they both simplify to the same ratio of 6/5, showing that these two ratios are equivalent.
• Option d: The ratios 4/5 and 28/35 form a proportion because 28/35 simplifies to 4/5, meaning the two are equivalent ratios.

Based on these evaluations, the pairs of ratios that form proportions are options b) 3/4, 30/40 and c) 36/30, 18/15, and d) 4/5, 28/35.