Use the given tables to compare the ratios 7: 9 and 4:6
79
14 18
21 27
28 36
35 45
4 6
8 12
12 18
16 24
20 30
To compare the ratios 7:9 and 4:6, we need to create equivalent ratios using the given tables.
For the ratio 7:9:
- Starting with 7, we can see that 7 → 14 → 21 → 28 → 35. So the first column of the equivalent ratio would be 14, 21, 28, 35.
- Starting with 9, we can see that 9 → 18 → 27 → 36 → 45. So the second column of the equivalent ratio would be 18, 27, 36, 45.
For the ratio 4:6:
- Starting with 4, we can see that 4 → 8 → 12 → 16 → 20. So the first column of the equivalent ratio would be 8, 12, 16, 20.
- Starting with 6, we can see that 6 → 12 → 18 → 24 → 30. So the second column of the equivalent ratio would be 12, 18, 24, 30.
Now let's compare the columns of the equivalent ratios for 7:9 and 4:6:
- For the first column, we have 14, 21, 28, 35 for 7:9 and 8, 12, 16, 20 for 4:6.
- For the second column, we have 18, 27, 36, 45 for 7:9 and 12, 18, 24, 30 for 4:6.
We can see that the ratios 7:9 and 4:6 are equal.
To compare the ratios 7:9 and 4:6, we can simplify both ratios by dividing both terms of each ratio by their greatest common divisor.
Let's start with the ratio 7:9:
To find the greatest common divisor (GCD) of 7 and 9, we can use the method of prime factorization.
The prime factorization of 7 is 7.
The prime factorization of 9 is 3 * 3.
As there are no common prime factors, the GCD of 7 and 9 is 1.
Now let's simplify 7:9:
Dividing both terms (7 and 9) by their GCD (1), we get:
7 ÷ 1 = 7
9 ÷ 1 = 9
So the simplified ratio 7:9 remains the same.
Now let's move on to the ratio 4:6:
To find the GCD of 4 and 6:
The prime factorization of 4 is 2 * 2.
The prime factorization of 6 is 2 * 3.
The common prime factor is 2.
So the GCD of 4 and 6 is 2.
Now let's simplify 4:6:
Dividing both terms (4 and 6) by their GCD (2), we get:
4 ÷ 2 = 2
6 ÷ 2 = 3
So the simplified ratio 4:6 becomes 2:3.
Comparing the simplified ratios:
7:9 and 2:3
The simplified ratio 7:9 is not equal to the simplified ratio 2:3.
Therefore, 7:9 is not equivalent to 4:6.
To compare the ratios 7:9 and 4:6, we need to find equivalent ratios for both ratios.
For the ratio 7:9,
- Multiply both the numerator and the denominator by the same number to get an equivalent ratio.
- Let's multiply by 4 (because 4 is a common multiple of 7 and 4):
7 * 4 : 9 * 4
= 28 : 36
For the ratio 4:6,
- Multiply both the numerator and the denominator by the same number to get an equivalent ratio.
- Let's multiply by 7 (because 7 is a common multiple of 4 and 7):
4 * 7 : 6 * 7
= 28 : 42
Now we have the ratios 28:36 and 28:42.
To compare these ratios, we can divide the numerator of one ratio by the numerator of the other ratio and divide the denominator of one ratio by the denominator of the other ratio.
28/36 ≈ 0.778
28/42 ≈ 0.667
Comparing these values, we can see that 28:36 is larger than 28:42.
Therefore, in terms of ratios, 7:9 is larger than 4:6.