Understanding Equivalent Ratios: Simplifying and Multiplying for Equivalence in Math

Equivalent Ratios

Equivalent ratios are ratios that represent the same relationship between two or more numbers

Equivalent ratios are ratios that represent the same relationship between two or more numbers. They have the same value but may be expressed in different forms. To determine if two ratios are equivalent, we need to check if they simplify to the same value.

Let’s take an example to understand equivalent ratios:

Consider the following ratio: 3:6

To determine if this ratio is equivalent to another ratio, we can simplify both sides of the ratio. In this case, we can divide both numbers by their greatest common factor, which is 3. Dividing 3 by 3 gives 1, and dividing 6 by 3 gives 2. Therefore, the simplified form of the ratio is 1:2.

Now, let’s test if 1:2 is equivalent to 3:6. To check this, we can cross-multiply:

1 * 6 = 2 * 3
6 = 6

Since the cross product of both ratios is the same, we can conclude that 3:6 and 1:2 are equivalent ratios. Both ratios represent the same relationship between the numbers.

To find equivalent ratios, you can either simplify or multiply the original ratio by the same value. For example:

Original Ratio: 2:5

To find an equivalent ratio, we can multiply both sides of the ratio by the same number. Let’s multiply both sides by 2:

2 * 2: 5 * 2
4: 10

Therefore, an equivalent ratio to 2:5 is 4:10.

You can also simplify ratios to find equivalent forms. Let’s take another example:

Original Ratio: 6:15

To simplify this ratio, we can divide both numbers by their greatest common factor, which is 3:

6 ÷ 3: 15 ÷ 3
2: 5

Therefore, the simplified form of the ratio 6:15 is 2:5. Both ratios represent the same relationship and are considered equivalent.

In summary, equivalent ratios represent the same relationship between numbers, but may be expressed in different forms. Simplifying or multiplying the original ratio by the same value can help determine if two ratios are equivalent.

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