Ratios and Percents Unit Test 5 of 155 of 15 Items Question Use the given tables to compare the ratios 7:9 and 4:6 . 7 9 14 18 21 27 28 36 35 45 4 6 8 12 12 18 16 24 20 30(1 point) $$
The correct answer is not provided. To compare the ratios 7:9 and 4:6, we can simplify both ratios to their simplest form.
To simplify the ratio 7:9, we divide both numbers by their greatest common divisor, which is 1:
7 ÷ 1 = 7
9 ÷ 1 = 9
The simplified ratio is 7:9.
To simplify the ratio 4:6, we divide both numbers by their greatest common divisor, which is 2:
4 ÷ 2 = 2
6 ÷ 2 = 3
The simplified ratio is 2:3.
Therefore, the ratios 7:9 and 4:6 are not equivalent.
To compare the ratios 7:9 and 4:6, we can first simplify both ratios.
To simplify a ratio, we divide both parts of the ratio by their greatest common factor (GCF).
For the ratio 7:9, the GCF is 1, so the simplified ratio is also 7:9.
For the ratio 4:6, the GCF is 2, so we divide both parts of the ratio by 2 to get the simplified ratio of 2:3.
Now, we have the simplified ratios 7:9 and 2:3.
To compare two ratios, we can cross-multiply.
For the ratio 7:9, we multiply 7 by 3, which gives us 21.
For the ratio 2:3, we multiply 2 by 9, which gives us 18.
Since 21 is greater than 18, we can say that the ratio 7:9 is greater than the ratio 4:6.
So, the answer is that the ratios 7:9 is greater than 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 denominator by the same number to find equivalent ratios:
7 x 2 = 14
9 x 2 = 18
So, the equivalent ratio for 7:9 is 14:18.
For the ratio 4:6:
Multiply both the numerator and denominator by the same number to find equivalent ratios:
4 x 2 = 8
6 x 2 = 12
So, the equivalent ratio for 4:6 is 8:12.
Now we can compare the ratios:
7:9 is equivalent to 14:18.
4:6 is equivalent to 8:12.
In order to compare the ratios, we need to have the same denominator. Let's find the least common multiple (LCM) of 18 and 12, which is 36.
Multiplying both the numerator and denominator by the same number to convert the ratios into fractions:
14/18 = 28/36
8/12 = 24/36
Now we can see that the ratios 7:9 and 4:6 are equivalent to the fractions 28/36 and 24/36, respectively.
To compare these fractions, we can compare their numerators:
28 is greater than 24.
So, the ratio 7:9 is greater than the ratio 4:6.