Use the given tables to compare the ratios 3:5

Question

and 2:3
.

3 5
6 10
9 15
12 20
15 25
2 3
4 6
6 9
8 12
10 15


(1 point)
Responses

3:5 = 2:3
ratio of 3 to 5 is equal to ratio of 2 to 3

3:5 < 2:3
ratio of 3 to 5 is less than ratio of 2 to 3

3:5 > 2:3
3:5 > 2:3

More rows need to be added to the tables to be able to compare the ratio

Answer 1

To compare the ratios 3:5 and 2:3, we can calculate their decimal representations or find a common term.

1. Calculate the decimal values:

   • The ratio \(3:5\) can be represented as \(3 ÷ 5 = 0.6\).
   • The ratio \(2:3\) can be represented as \(2 ÷ 3 \approx 0.6667\).

2. Compare:

   • \(0.6 < 0.6667\)

Thus, we can conclude that \(3:5 < 2:3\).

The correct response is: 3:5 < 2:3 ratio of 3 to 5 is less than ratio of 2 to 3.

Answer 2

The following tables show the amount of fat for a given number of crackers for two types of crackers. Which type of cracker has less fat per cracker?

Cracker A

Grams of Fat Number of Crackers
8 10
16 20
24 30
32 40
40 50
48 60


Cracker B

Grams of Fat Number of Crackers
6 12
12 24
18 36
24 48
30 60
36 72


(1 point)
Responses

More rows need to be added to the tables to be able to compare the crackers.
More rows need to be added to the tables to be able to compare the crackers.

Cracker B
Cracker B

Cracker A
Cracker A

The two types of crackers have the same amount of fat per cracker.

Answer 3

To determine which type of cracker has less fat per cracker, we can calculate the amount of fat per cracker for each type.

Cracker A

• 8 grams of fat for 10 crackers:
  \(\frac{8 \text{ grams}}{10 \text{ crackers}} = 0.8 \text{ grams per cracker}\)

• 16 grams of fat for 20 crackers:
  \(\frac{16 \text{ grams}}{20 \text{ crackers}} = 0.8 \text{ grams per cracker}\)

• 24 grams of fat for 30 crackers:
  \(\frac{24 \text{ grams}}{30 \text{ crackers}} = 0.8 \text{ grams per cracker}\)

• 32 grams of fat for 40 crackers:
  \(\frac{32 \text{ grams}}{40 \text{ crackers}} = 0.8 \text{ grams per cracker}\)

• 40 grams of fat for 50 crackers:
  \(\frac{40 \text{ grams}}{50 \text{ crackers}} = 0.8 \text{ grams per cracker}\)

• 48 grams of fat for 60 crackers:
  \(\frac{48 \text{ grams}}{60 \text{ crackers}} = 0.8 \text{ grams per cracker}\)

Average for Cracker A: 0.8 grams per cracker

Cracker B

• 6 grams of fat for 12 crackers:
  \(\frac{6 \text{ grams}}{12 \text{ crackers}} = 0.5 \text{ grams per cracker}\)

• 12 grams of fat for 24 crackers:
  \(\frac{12 \text{ grams}}{24 \text{ crackers}} = 0.5 \text{ grams per cracker}\)

• 18 grams of fat for 36 crackers:
  \(\frac{18 \text{ grams}}{36 \text{ crackers}} = 0.5 \text{ grams per cracker}\)

• 24 grams of fat for 48 crackers:
  \(\frac{24 \text{ grams}}{48 \text{ crackers}} = 0.5 \text{ grams per cracker}\)

• 30 grams of fat for 60 crackers:
  \(\frac{30 \text{ grams}}{60 \text{ crackers}} = 0.5 \text{ grams per cracker}\)

• 36 grams of fat for 72 crackers:
  \(\frac{36 \text{ grams}}{72 \text{ crackers}} = 0.5 \text{ grams per cracker}\)

Average for Cracker B: 0.5 grams per cracker

Conclusion

• Cracker A: 0.8 grams of fat per cracker
• Cracker B: 0.5 grams of fat per cracker

Thus, Cracker B has less fat per cracker.

The correct response is:
Cracker B.

Answer 4

Which of the following tables could you use to compare the ratios 2:5 and 3:4 ?(1 point)
Responses

2 5
4 10
3 4
6 82 5 4 10 3 4 6 8

2 5
3 10
4 15
5 20
6 25
3 4
4 8
5 12
6 16
7 202 5 3 10 4 15 5 20 6 25 3 4 4 8 5 12 6 16 7 20

2 5
6 15
10 25
3 4
9 12
16 202 5 6 15 10 25 3 4 9 12 16 20

2 5
4 10
6 15
8 20
10 25
3 4
6 8
9 12
12 16
15 202 5 4 10 6 15 8 20 10 25 3 4 6 8 9 12 12 16 15 20
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Answer 5

To compare the ratios \(2:5\) and \(3:4\), we need to look for tables that maintain the ratio integrity, allowing for easy comparison of their values.

Let's analyze each option:

1. Table 1:

   2    5
   4   10
   3    4
   6   8
   

   This table has the proper pairs for \(2:5\) (2, 5) and \(4:10\). However, it also includes \(3:4\) and \(6:8\), which do not help in comparing \(2:5\) and \(3:4\) effectively.

2. Table 2:

   2    5
   3   10
   4   15
   5   20
   6   25
   3    4
   4    8
   5   12
   6   16
   7   20
   

   Here, we have the ratio \(2:5\) represented and also pairs that aren't maintaining the specific ratios needed for comparison. For example, \(3:10\) does not directly relate to \(3:4\).

3. Table 3:

   2    5
   6   15
   10   25
   3    4
   9   12
   16   20
   

   While \(2:5\) is represented correctly, \(6:15\) and \(10:25\) are multiples of \(2:5\) but do not facilitate a direct comparison with \(3:4\).

4. Table 4:

   2    5
   4   10
   6   15
   8   20
   10   25
   3    4
   6    8
   9   12
   12   16
   15   20
   

   This table shows \(2:5\) correctly, and \(4:10\), \(6:15\), \(8:20\), and \(10:25\) all maintain a relationship to \(2:5\). The entries for \(3:4\) (3,4), \(6:8\), \(9:12\), etc., also hold true with \(3:4\).

Conclusion

Among these options, Table 4 offers the best setup for comparing both ratios effectively, as it maintains multiple valid proportional entries for each ratio.

The correct response is: Table 4.

Answer 6

Compare the ratios 7:4 and 12:5 using the following tables. Finish the tables by filling in the missing values A and B.

7 4
14 8
21 12
28 16
A B
12 5
24 10
36 15
48 20
60 25


(1 point)
Responses

A = 32 and B = 20.
upper A equals 32 and upper B equals 20 .

A = 35 and B = 18.
upper A equals 35 and upper B equals 18 .

A = 32 and B = 18.
upper A equals 32 and upper B equals 18 .

A = 35 and B = 20.

Answer 7

To find the values of \( A \) and \( B \) in the first table that correspond with the ratios \( 7:4 \) and \( 12:5 \), we can calculate the missing values based on the established proportion.

Given Ratios

1. \( 7:4 \)
2. \( 12:5 \)

Completing the First Table

In the first table, we can see a pattern based on multiplying:

• For every increase of \( 7 \) in the first column (the number of "parts" from the ratio), there is a corresponding increase of \( 4 \) in the second column.

Using this to fill in the missing values:

• The last entry visible in the first table is \( 28 : 16 \).
• The next entry, \( A \), would be \( 28 + 7 = 35 \), and \( B \) would be \( 16 + 4 = 20 \).

So, we can fill in:

• \( A = 35 \)
• \( B = 20 \)

Completing the Second Table

In the second table, we are also given the \( 12:5 \) ratio. Continuing the same increment pattern:

• To find how values are increasing in the second table:
• Starting at \( 12:5 \), the next increment would theoretically follow the proportions, just like before:
• If \( 12 \) increases by \( 12 \): \( 12, 24, 36, 48, 60 \).
• The corresponding values by multiplying by the scaling factor related to \( 5 \) (i.e., \( \frac{5}{12} \)) would yield:
  • \( 5, 10, 15, 20, 25 \)

Both tables have shown consistent patterns for maintaining ratios.

Conclusion

The final values complete as follows:

• For the first table: \( A = 35 \) and \( B = 20 \).

The correct response is: A = 35 and B = 20.

Answer 8

Use the given tables to compare the ratios 16:18 and 5:6 . Which ratio is greater?

8 9
16 18
24 27
32 36
5 6
10 12
15 18
20 24(1 point)
Responses

16:18 is greater.
ratio of 16 to 18 is greater.

5:6 is greater.
ratio of 5 to 6 is greater.

More rows need to be added to the tables to be able to compare the ratios.
More rows need to be added to the tables to be able to compare the ratios.

The two ratios are equal.

Answer 9

To compare the ratios \(16:18\) and \(5:6\), we can first convert them to their decimal (or fractional) equivalents, and then compare those values.

Converting the Ratios

1. For the ratio \(16:18\): \[ \frac{16}{18} = \frac{8}{9} \approx 0.8889 \]

2. For the ratio \(5:6\): \[ \frac{5}{6} \approx 0.8333 \]

Comparison of the Two Ratios

• Decimal Value:
  • \(16:18 \approx 0.8889\)
  • \(5:6 \approx 0.8333\)

Comparing these values:

• \(0.8889 > 0.8333\)

Conclusion

Thus, the ratio \(16:18\) is greater than the ratio \(5:6\).

The correct response is: 16:18 is greater. ratio of 16 to 18 is greater.

Answer 10

Thaankks!! :D

Answer 11

You're welcome! :D If you have any more questions or need further assistance, feel free to ask. I'm here to help!