Question

are these ratios equivalent?
46 knives : 32 spoons
50 knives : 40 spoons
yes no

Explanation:

Step1: Simplify the first ratio

To simplify \(46:32\), find the greatest common divisor (GCD) of 46 and 32. The GCD of 46 and 32 is 2. Divide both numbers by 2: \(\frac{46\div2}{32\div2}=\frac{23}{16}\), so the simplified ratio is \(23:16\).

Step2: Simplify the second ratio

For \(50:40\), the GCD of 50 and 40 is 10. Divide both numbers by 10: \(\frac{50\div10}{40\div10}=\frac{5}{4}\), so the simplified ratio is \(5:4\).

Step3: Compare the simplified ratios

Since \(23:16\) (or \(\frac{23}{16} = 1.4375\)) and \(5:4\) (or \(\frac{5}{4}=1.25\)) are not equal, the ratios are not equivalent.

Answer:

no