Determine if each proportion on the left is True or False Answer options on the right side may be used more than once. (5)/(42)=(10)/(84) True (5)/(4)=(25)/(20) False (2)/(3)=(4)/(9) (3)/(4)=(87)/(116)

Let's evaluate each proportion one by one:<br /><br />1. $\frac{5}{42} = \frac{10}{84}$<br /><br />To determine if this proportion is true, we can cross-multiply and see if the products are equal.<br /><br />$5 \times 84 = 420$<br />$42 \times 10 = 420$<br /><br />Since the products are equal, the proportion is true.<br /><br />2. $\frac{5}{4} = \frac{25}{20}$<br /><br />Again, we can cross-multiply to check if the products are equal.<br /><br />$5 \times 20 = 100$<br />$4 \times 25 = 100$<br /><br />Since the products are equal, the proportion is true.<br /><br />3. $\frac{2}{3} = \frac{4}{9}$<br /><br />Cross-multiplying, we get:<br /><br />$2 \times 9 = 18$<br />$3 \times 4 = 12$<br /><br />Since the products are not equal, the proportion is false.<br /><br />4. $\frac{3}{4} = \frac{87}{116}$<br /><br />Cross-multiplying, we get:<br /><br />$3 \times 116 = 348$<br />$4 \times 87 = 348$<br /><br />Since the products are equal, the proportion is true.<br /><br />Therefore, the answers are:<br />$\frac{5}{42} = \frac{10}{84}$ is True<br />$\frac{5}{4} = \frac{25}{20}$ is True<br />$\frac{2}{3} = \frac{4}{9}$ is False<br />$\frac{3}{4} = \frac{87}{116}$ is True