Question

find 3 ratios that are equivalent to the given ratio.
12:14
find three ratios that are equivalent to the given ratio.
a. 6:28 b. 24:7
c. 36:7 d. 24:28
e. 36:42 f. 6:42
g. 6:7 h. 24:42

Explanation:

Step1: Simplify the given ratio

First, simplify the ratio \(12:14\) by dividing both terms by their greatest common divisor, which is 2. So, \(\frac{12\div2}{14\div2}=\frac{6}{7}\), so \(6:7\) (Option G) is equivalent.

Step2: Multiply numerator and denominator by 3

Multiply both terms of \(6:7\) by 3. \(6\times3 = 18\)? Wait, no, wait. Wait, original ratio is \(12:14\), or simplified \(6:7\). Let's take \(6:7\) and multiply numerator and denominator by 6? Wait, no, let's check the options. Let's take \(12:14\) and multiply both terms by 2: \(12\times2 = 24\), \(14\times2 = 28\), so \(24:28\) (Option D) is equivalent.

Step3: Multiply numerator and denominator by 3

Multiply both terms of \(6:7\) by 6? Wait, no, \(6:7\) multiplied by 6? Wait, \(6\times6 = 36\), \(7\times6 = 42\), so \(36:42\) (Option E) is equivalent. Also, \(6:7\) is Option G. So let's verify each option:

• Option A: \(6:28\) – Simplify \(6:28=\frac{3}{14}\), not equal to \(\frac{6}{7}\).
• Option B: \(24:7\) – Not equivalent.
• Option C: \(36:7\) – Not equivalent.
• Option D: \(24:28\) – Simplify \(\frac{24}{28}=\frac{6}{7}\), equivalent.
• Option E: \(36:42\) – Simplify \(\frac{36}{42}=\frac{6}{7}\), equivalent.
• Option F: \(6:42\) – Simplify \(\frac{6}{42}=\frac{1}{7}\), not equivalent.
• Option G: \(6:7\) – Simplify \(\frac{6}{7}\), equivalent.
• Option H: \(24:42\) – Simplify \(\frac{24}{42}=\frac{4}{7}\), not equivalent.

So the three equivalent ratios are \(6:7\) (G), \(24:28\) (D), and \(36:42\) (E). Wait, but the problem says "Find 3 ratios that are equivalent to the given ratio \(12:14\)". Let's confirm:

• \(12:14\) simplifies to \(6:7\) (G).
• Multiply \(12:14\) by 2: \(24:28\) (D).
• Multiply \(12:14\) by 3: \(36:42\) (E). Also, \(6:7\) (G) is simplified, \(24:28\) (D) is multiplied by 2, \(36:42\) (E) is multiplied by 3.

Answer:

D. 24:28, E. 36:42, G. 6:7