Question

Use the given tables to compare the ratios 7 : 9 and 4 : 6

Answer 1

[AI-generated answer — Bot GPT 3.5]

To compare the ratios 7:9 and 4:6, we need to find their equivalent forms with the same denominator.

Let's start with the ratio 7:9. To find an equivalent ratio with the same denominator as 4:6, we can multiply both the numerator and the denominator by 2:
7 * 2 = 14
9 * 2 = 18

So, the equivalent ratio of 7:9 with the same denominator as 4:6 is 14:18.

Now let's compare 14:18 with 4:6. To make the comparison easier, we can simplify both ratios by dividing both the numerator and the denominator by their greatest common divisor.

The greatest common divisor of 14 and 18 is 2. Dividing both by 2 yields:
14 ÷ 2 = 7
18 ÷ 2 = 9

Hence, the simplified ratio 14:18 becomes 7:9.

Therefore, the ratios 7:9 and 4:6 are equivalent.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To compare the ratios 7 : 9 and 4 : 6, we can first find the equivalent fractions for each ratio by dividing both sides by their greatest common divisor.

For the ratio 7 : 9:
- Divide both sides by their greatest common divisor which is 1: 7 ÷ 1 : 9 ÷ 1
- The equivalent ratio is 7 : 9.

For the ratio 4 : 6:
- Divide both sides by their greatest common divisor which is 2: 4 ÷ 2 : 6 ÷ 2
- Simplifying, we get the equivalent ratio 2 : 3.

Therefore, the ratios 7 : 9 and 4 : 6 are not equal.

Answer 3

[AI-generated answer — Explain Bot]

To compare the ratios 7 : 9 and 4 : 6, we can use equivalent ratios.

Step 1: Write the given ratios in fraction form.
The ratio 7 : 9 can be written as 7/9.
The ratio 4 : 6 can be written as 4/6.

Step 2: Simplify the fractions.
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, and then divide both the numerator and denominator by this common divisor.

For 7/9:
The GCD of 7 and 9 is 1 (since they have no common factors), so the fraction is already simplified.

For 4/6:
The GCD of 4 and 6 is 2, so divide both the numerator and denominator by 2 to get 2/3.

Step 3: Compare the simplified fractions.
Now that both fractions are simplified, we can compare them.
7/9 is greater than 2/3.

Therefore, the ratio 7:9 is greater than the ratio 4:6.