Compare the ratios using the models. One model has 16 sections and is labeled 7 to 16. The second model has 8 sections and is labeled 6 to 8.

Question

Which statements are true? Check all that apply.

The model for the ratio 7 to 16 should show 7 cells shaded.
The model for the ratio 6:8 should show 8 cells shaded.
The ratio 7 to 16 is greater than 6:8.
The ratio 6:8 is greater than the ratio 7 to 16.

Answer 1

To compare the ratios 7:16 and 6:8, let's first analyze each ratio.

1. The model for the ratio 7 to 16 should show 7 cells shaded.

   • True. The ratio 7:16 means that out of 16 sections, 7 sections should be shaded.

2. The model for the ratio 6:8 should show 8 cells shaded.

   • False. The ratio 6:8 means that out of 8 sections, 6 sections should be shaded (not 8).

3. The ratio 7 to 16 is greater than 6:8.

   • To compare, we can simplify 6:8, which reduces to 3:4. Converting both ratios to a decimal form:
     • \( \frac{7}{16} \approx 0.4375 \)
     • \( \frac{6}{8} = 0.75 \)
   • Thus, \( \frac{7}{16} < \frac{6}{8} \). Therefore, this statement is false.

4. The ratio 6:8 is greater than the ratio 7 to 16.

   • As just calculated, \( \frac{6}{8} = 0.75 \) is greater than \( \frac{7}{16} \approx 0.4375 \). Therefore, this statement is true.

The true statements are:

• The model for the ratio 7 to 16 should show 7 cells shaded.
• The ratio 6:8 is greater than the ratio 7 to 16.