An example of equivalent numbers are fractions such as 1/2 and 2/4, which both simplify to 0.5.
Understanding Equivalent Numbers
Equivalent numbers, while appearing different, represent the same value. This concept is often encountered in fractions, ratios, and other mathematical contexts. These numbers might have different numerators and denominators but simplify to the same numerical value.
Examples of Equivalent Values
| Original Value | Equivalent Value | Decimal Representation |
|---|---|---|
| 1/2 | 2/4 | 0.5 |
| 3/6 | 1/2 | 0.5 |
| 1:5 | 2:10 | 0.2 |
| 4:20 | 1:5 | 0.2 |
Equivalent Fractions
Fractions are considered equivalent when they simplify to the same value.
For example:
- 1/2 and 2/4 are equivalent because 2/4 can be simplified by dividing both the numerator and denominator by 2 which results in 1/2.
- 3/6 and 1/2 are equivalent because both simplify to 0.5
Equivalent Ratios
Ratios represent a comparison between two or more quantities. Equivalent ratios show the same proportional relationship.
- 1:5 and 2:10 are equivalent. If we divide both parts of the ratio 2:10 by 2 we get 1:5.
- 4:20 and 1:5 are equivalent. Both ratios can be reduced to 1:5.
In summary, equivalent numbers maintain the same numerical value even if expressed in different forms. The reference provided states that examples of equivalent values include fractions such as 1/2 and 2/4 and ratios such as 1:5 and 2:10. These are simplified to the same decimal number 0.5 and 0.2 respectively.
