Compare the ratio 7:9 to 4:6
To compare the ratios 7:9 and 4:6, we can simplify them to their simplest form.
For the ratio 7:9, we can divide both terms by their greatest common divisor, which is 1. So, the simplified ratio is 7:9.
For the ratio 4:6, we can also divide both terms by their greatest common divisor, which is 2. So, the simplified ratio is 2:3.
Now, we can compare the simplified ratios: 7:9 and 2:3.
To do this, we can cross-multiply the values. Cross-multiplying means multiplying the first term of the first ratio with the second term of the second ratio, and multiplying the second term of the first ratio with the first term of the second ratio.
7 * 3 = 21
9 * 2 = 18
Since 21 is greater than 18, we can conclude that the ratio 7:9 is greater than the ratio 4:6.
To compare the ratios 7:9 and 4:6, we need to make sure that both ratios are in their simplest form. To simplify a ratio, we divide both parts of the ratio by their greatest common divisor (GCD).
For the ratio 7:9:
- The GCD of 7 and 9 is 1 (since 7 and 9 are prime numbers)
- Dividing both parts by 1, we get the simplified ratio: 7:9
For the ratio 4:6:
- The GCD of 4 and 6 is 2
- Dividing both parts by 2, we get the simplified ratio: 2:3
Now, we have the simplified ratios 7:9 and 2:3. To compare them, we can check if the corresponding parts of the ratios are equal.
Comparing the first parts:
7 and 2 are not equal.
Comparing the second parts:
9 and 3 are not equal.
Based on this comparison, we can conclude that the ratio 7:9 is not equal to the ratio 4:6.
To compare the ratios 7:9 and 4:6, we can follow these steps:
Step 1: Simplify the ratios
To compare ratios, it is often helpful to simplify them by dividing both sides by their greatest common divisor (GCD). The GCD of 7 and 9 is 1, so we don't need to simplify the first ratio. However, the GCD of 4 and 6 is 2, so we can simplify the second ratio by dividing both sides by 2, resulting in 2:3.
Now, the ratios are simplified to 7:9 and 2:3.
Step 2: Make the ratios equivalent
To compare two ratios, it's useful to make them equivalent by multiplying or dividing both sides of each ratio until they have a common denominator.
To make the denominators of 7:9 and 2:3 the same, we can find their least common multiple (LCM) which is 9.
Since the first ratio already has a denominator of 9, we don't need to make any changes to it. However, to make the second ratio have a denominator of 9, we can multiply both sides by 3, resulting in 6:9.
Now, the ratios are equivalent to 7:9 and 6:9.
Step 3: Compare the numerators
Now that the denominators are the same, we can directly compare the numerators to see which ratio is greater.
In this case, the numerator of the first ratio (7) is greater than the numerator of the second ratio (6). Therefore, we can conclude that the ratio 7:9 is greater than 4:6.
So, in comparison, the ratio 7:9 is greater than the ratio 4:6.