compare the ratios 7:9 and 4:6 .
To compare the ratios 7:9 and 4:6, we need to find the equivalent ratios.
For 7:9:
To find the equivalent ratio to 4, we multiply both parts of the ratio by 4:
7 * 4 = 28
9 * 4 = 36
Therefore, the equivalent ratio to 7:9 is 28:36.
For 4:6:
To find the equivalent ratio to 6, we multiply both parts of the ratio by 6:
4 * 6 = 24
6 * 6 = 36
Therefore, the equivalent ratio to 4:6 is 24:36.
Now, we can directly compare the ratios:
28:36 and 24:36.
Since both ratios have the same second part of the ratio (36), we only need to compare the first parts.
28 is greater than 24, so the ratio 7:9 is greater than the ratio 4:6.
To compare the ratios 7:9 and 4:6, we can simplify them by dividing both sides of each ratio by their greatest common divisor (GCD).
Let's calculate the GCD of 7 and 9. The dividers of 7 are 1 and 7, and the dividers of 9 are 1, 3, and 9. The only common divider is 1, so the GCD of 7 and 9 is 1.
Next, let's calculate the GCD of 4 and 6. The dividers of 4 are 1, 2, and 4, and the dividers of 6 are 1, 2, 3, and 6. The greatest common divider is 2.
Now, we can simplify the ratios:
7:9 = (7 ÷ 1):(9 ÷ 1) = 7:9
4:6 = (4 ÷ 2):(6 ÷ 2) = 2:3
Therefore, the simplified ratios are 7:9 and 2:3.
To accurately compare these ratios, we can convert them into fractions. Let's do that next.
The ratio 7:9 can be written as 7/9,
and the ratio 2:3 can be written as 2/3.
To compare fractions, we need to find a common denominator. In this case, the smallest common multiple of 9 and 3 is 9.
Multiplying the numerator and denominator of 7/9 by 1 (which is equal to 3/3), we get:
(7 × 3) / (9 × 3) = 21/27.
Thus, the ratios 7:9 and 4:6 are equivalent to 21:27 and 2:3, respectively.
To compare the ratios 7:9 and 4:6, we need to find the equivalent fractions for each ratio in order to compare them.
First, let's find the equivalent fraction for the ratio 7:9:
The ratio 7:9 can be written as the fraction 7/9.
Next, let's find the equivalent fraction for the ratio 4:6:
The ratio 4:6 can be simplified by dividing both numbers by their greatest common divisor, which is 2. When we divide 4 by 2, we get 2, and when we divide 6 by 2, we get 3. Therefore, the equivalent fraction for the ratio 4:6 is 2/3.
Now, we can compare the equivalent fractions:
7/9 and 2/3
To compare fractions, we can cross-multiply. Multiply the numerator of the first fraction (7) by the denominator of the second fraction (3), and multiply the denominator of the first fraction (9) by the numerator of the second fraction (2).
7 * 3 = 21
9 * 2 = 18
Since 21 is greater than 18, we can conclude that 7/9 is greater than 2/3.
Therefore, the comparison of the ratios 7:9 and 4:6 is that 7:9 is greater than 4:6.