compare the ratios 7:9 and 4:6 .
To compare the ratios 7:9 and 4:6, we can simplify both ratios to their equivalent forms:
For 7:9:
Divide both numbers by their greatest common factor (GCF), which is 1:
7 ÷ 1 = 7
9 ÷ 1 = 9
Therefore, the simplified form of 7:9 is 7:9.
For 4:6:
Divide both numbers by their greatest common factor (GCF), which is 2:
4 ÷ 2 = 2
6 ÷ 2 = 3
Therefore, the simplified form of 4:6 is 2:3.
Comparing the ratios, we see that 7:9 and 2:3 are not the same.
To compare the ratios 7:9 and 4:6, we can simplify both ratios by finding the greatest common divisor (GCD) of each pair of numbers.
For the ratio 7:9:
- The GCD of 7 and 9 is 1.
- Dividing both numbers by 1, we get the simplified ratio of 7:9.
For the ratio 4:6:
- The GCD of 4 and 6 is 2.
- Dividing both numbers by 2, we get the simplified ratio of 2:3.
Now, we can compare the simplified ratios:
- The simplified ratio of 7:9 is greater than the simplified ratio of 2:3.
Therefore, the original ratio of 7:9 is greater than the original ratio of 4:6.
To compare the ratios 7:9 and 4:6, we need to find a common denominator for both ratios.
First, let's simplify the ratios by dividing both sides of each ratio by their greatest common divisor (GCD).
For the ratio 7:9, the GCD of 7 and 9 is 1, so the simplified ratio is 7:9.
For the ratio 4:6, the GCD of 4 and 6 is 2, so we divide both sides by 2 and get 2:3.
Now that both ratios are simplified, we can compare them.
The ratio 7:9 can be converted to a fraction by dividing 7 by 9: 7/9.
The ratio 4:6 can be converted to a fraction by dividing 4 by 6: 4/6, which can be further simplified to 2/3 by dividing both sides by 2.
To compare the two fractions 7/9 and 2/3, we can use a common denominator. The least common multiple (LCM) of 9 and 3 is 9.
Multiplying the numerator and denominator of 7/9 by 1, we get 7/9 * (3/3) = 21/27.
Multiplying the numerator and denominator of 2/3 by 3, we get 2/3 * (3/3) = 6/9.
Now we can see that 21/27 is greater than 6/9.
Therefore, the ratio 7:9 is greater than the ratio 4:6.