Use cross products to see if each pair of ratios forms a proportion. Replace each box with = or ≠.
To determine if each pair of ratios forms a proportion using cross products, we follow these steps:
1. Multiply the numerator of the first ratio by the denominator of the second ratio.
2. Multiply the denominator of the first ratio by the numerator of the second ratio.
3. Compare the two results obtained in steps 1 and 2.
If the results are equal (=), then the ratios form a proportion. If the results are not equal (≠), then the ratios do not form a proportion.
Let's take an example to illustrate this process:
Example:
Consider the ratios 2/3 and 4/6.
Step 1: Multiply the numerator of the first ratio by the denominator of the second ratio:
2 * 6 = 12
Step 2: Multiply the denominator of the first ratio by the numerator of the second ratio:
3 * 4 = 12
Step 3: Compare the results of step 1 and step 2:
12 = 12
Since the results are equal, the ratios 2/3 and 4/6 form a proportion.
Now you can follow the same steps to determine if each pair of ratios forms a proportion by replacing each box with = or ≠.
To determine if each pair of ratios forms a proportion, we can use the method of cross products. Here's how you can do it:
1. Write down the two ratios in the form of A/B = C/D, where A, B, C, and D are numbers.
2. Multiply the numerator of the first ratio by the denominator of the second ratio. This is called the cross product for the first ratio.
3. Multiply the denominator of the first ratio by the numerator of the second ratio. This is called the cross product for the second ratio.
4. Compare the two cross products.
- If the cross products are equal, then the two ratios form a proportion, and you can replace the boxes with "=".
- If the cross products are not equal, then the two ratios do not form a proportion, and you can replace the boxes with "≠".
Remember, a proportion is when the ratio of two quantities is equal to the ratio of two other quantities. The cross product method helps us determine if this equality holds true.
I hope this explanation helps you understand how to use cross products to determine if ratios form a proportion!