Question

Which set of ratios below is NOT equivalent to 3:42?

a) 6 to 9
b) 9 to 12
c) 25:32
d) 18 to 24

Answer 1

The ratio 3:42 simplifies to 1:14. Options b) 9 to 12 and d) 18 to 24 do not simplify to the ratio 1:14 and are therefore not equivalent to 3:42.

Step-by-step explanation:

To determine which set of ratios is NOT equivalent to 3:42, we need to simplify the given ratio and compare it to the simplified form of each option provided.

The ratio 3:42 can be simplified by dividing both numbers by their greatest common divisor, which is 3:

3/3 : 42/3 = 1 : 14

Now, let's analyze the given options:

• a) 6 to 84 can be simplified by dividing both numbers by 6:
• 6/6: 84/6 = 1: 14. This ratio is equivalent to 3:42.
• b) 9 to 12 cannot be simplified to a ratio of 1 to 14, as 9/12 simplifies to 3/4. Hence, this is NOT equivalent to 3:42.
• c) 25:350 can be simplified by dividing both numbers by 25:
• 25/25: 350/25 = 1: 14. This ratio is equivalent to 3:42.
• d) 18 to 24 can be simplified by dividing both numbers by 6:
• 18/6: 24/6 = 3: 4. This ratio is also NOT equivalent to 3:42.

Therefore, the sets of ratios that are NOT equivalent to 3:42 are options b) 9 to 12 and d) 18 to 24.