حل التناسب وكيفية إيجاد قيمة المجهول | درس | تحدي الرياضيات #1

The episode opens with host Riham introducing a math challenge series where each episode tackles a different real-world problem. The first challenge involves calculating how long it would take Ali to travel from Sanaa to Aden — a distance of approximately 400 km — at a speed of 80 km/h, setting the stage for learning about proportionality.

Riham begins by explaining what a proportion is, using a relatable cooking example: if 2 cups of rice serve 4 people, then 6 cups are needed for 12 people. These two ratios (2/4 and 6/12) are equal, and when two ratios are equal, it is called a proportion. She then introduces the fundamental property of proportions — that the product of the extremes (outer terms) equals the product of the means (inner terms) — framed as a/b = c/d, where a and d are the extremes and b and c are the means.

The host then distinguishes between the two types of proportion. Direct (or direct) proportion describes a relationship where two quantities change in the same direction — if one increases, the other increases, and if one decreases, the other decreases, as in the rice cooking example. Inverse proportion, on the other hand, describes a relationship where one quantity increases as the other decreases. A mosque construction example illustrates this: 20 workers can build a mosque in 15 days, but how many workers are needed to finish it in just 10 days? Because the relationship is inverse, the second ratio is written in reverse, and the calculation yields 30 workers.

Finally, the episode returns to the original challenge: at 80 km/h over 400 km, the travel time is found by setting up a proportion, multiplying 400 by 1, and dividing by 80, giving an answer of 5 hours. The episode ends with a practice exercise asking viewers to calculate how many cups of rice are needed for 40 guests if 1 cup serves 4 people.