Summary of Mathematics on Proportional and Non-Proportional Comparisons

Summary of Equivalent and Unequivalent Comparisons

1. Equivalent Comparison

Definition:

An equivalent comparison occurs when two quantities have a direct proportional relationship. If one quantity increases, then the other quantity also increases proportionally.

Characteristics:

The comparative value between the two quantities is always constant.

Using the formula: x1/y1 = x2/y2

Example Question:

If 2 kg of rice costs Rp20,000, how much does 5 kg of rice cost?

Solution:

Because the equivalent comparison:

2 / 20,000 = 5 / x

2x = 20,000 . 5

x = 50,000

Answer: The price of 5 kg of rice is Rp50,000.

2. Unequivalent Comparison

Definition:

An unequal comparison occurs when two quantities have an opposite relationship. If one quantity increases, then the other quantity decreases, or vice versa.

Characteristics:

The product (multiplication) between the two quantities is always constant.

Using the formula: x1y1=x2y2

Example Question:

Four workers can complete the work in 6 days. If the number of workers is increased to 8 people, how many days will the work be completed?

Solution:

Because the ratio is not equivalent:

4×6=x8

x = 24/8 = 3

Answer: The work is completed in 3 days.

Conclusion

Equivalent ratio: x1/y1 = x2/y2

Non-equivalent ratio: x1.y1 = x2.y2

By understanding the difference between equivalent and unequal comparisons, we can solve comparison problems in everyday life.