Question

quick check
the table depicts the following ratios: 36 : 16 (row 1) and 27 : 12 (row 2). use the equation method to find out whether the ratios in each row form a proportion.
yes, they form a proportion because they simplify to the same fraction.
yes, they form a proportion because they dont simplify to the same fraction.
no, they dont form a proportion because they simplify to the same fraction.
no, they dont form a proportion because they dont simplify to the same fraction.

Explanation:

Step1: Simplify 36:16

First, we convert the ratio \(36:16\) to a fraction \(\frac{36}{16}\). Then we simplify it by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So \(\frac{36\div4}{16\div4}=\frac{9}{4}\).

Step2: Simplify 27:12

Next, we convert the ratio \(27:12\) to a fraction \(\frac{27}{12}\). We simplify it by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So \(\frac{27\div3}{12\div3}=\frac{9}{4}\).

Step3: Determine if they form a proportion

Since both ratios simplify to the same fraction \(\frac{9}{4}\), they form a proportion.

Answer:

Yes, they form a proportion because they simplify to the same fraction.