PART#01: BAHASAN SOAL TRYOUT-3 TKA NUMERASI (MATEMATIKA) SMP 2026

Summary

This educational video from Mat Official Channel focuses on solving math problems for SMP level TKA Numerasi. The session covers various topics such as ratios, discounts, and problem-solving using concepts like the least common multiple (LCM) and greatest common divisor (GCD). The instructor provides clear step-by-step explanations, guiding students through word problems involving money, percentages, and packaging, while emphasizing the importance of combining knowledge with faith. The goal is to help students sharpen their mathematical skills while applying logical reasoning to practical situations.

Takeaways

• 😀 The importance of sharing knowledge and helping others is emphasized at the beginning, reflecting the mission of the channel to spread goodness.
• 😀 The first problem in the script deals with the concept of ratios and proportions, specifically how to calculate the amount of money each person receives based on a given ratio.
• 😀 The second problem is about calculating discounts from two different online stores and comparing them. Key concepts include sequential discounts and calculating total price after discounts.
• 😀 In the second problem, the correct answers highlight understanding how to calculate the total percentage of discounts, considering multiple stages of discounting.
• 😀 The third problem involves the concept of recurring events, asking when three events with different frequencies will coincide again, using the concept of the least common multiple (LCM).
• 😀 A significant portion of the third problem focuses on how to calculate the LCM of different periods (4, 6, and 9 days) to determine when the events will overlap.
• 😀 The fourth problem illustrates how to distribute items (e.g., instant noodles, syrup, and cookies) evenly among several gift packages, based on the greatest common divisor (GCD) of the quantities.
• 😀 In the fourth problem, the GCD is used to find the maximum number of gift packages that can be made while ensuring each package has the same number of items.
• 😀 The script also emphasizes the importance of understanding the impact of leftover items when making packages and how to adjust the distribution to ensure all items are used up efficiently.
• 😀 Overall, the script provides a comprehensive walkthrough of mathematical problems related to ratios, percentages, LCM, and GCD, demonstrating practical applications for students and learners.

Q & A

What is the ratio of money between Ani and Citra, and how do you calculate Ani's share?

The ratio of money between Ani and Citra is 3:5. To calculate Ani's share, first find the total number of parts by adding the ratio: 3 + 5 = 8 parts. Then, calculate Ani's share by multiplying her ratio (3 parts) by the total money (Rp 400,000), and divide by the total parts: (3/8) × 400,000 = Rp 150,000.

How do you calculate the discount on the laptop at Toko Sinar Digital?

To calculate the discount at Toko Sinar Digital, multiply the discount percentage (43%) by the original price of the laptop (Rp 8,000,000). This results in a discount of (43/100) × 8,000,000 = Rp 3,440,000.

What is the total discount percentage at Toko Cahaya Jadget, and how is it calculated?

The total discount at Toko Cahaya Jadget is calculated in two stages: a 30% discount from the original price, followed by an additional 15% discount from the reduced price. After calculating the discounts step by step, the total discount is 40.5%, not 45% as suggested in the statement.

What is the formula used to calculate the price to pay after the double discount at Toko Cahaya Jadget?

After a 30% discount on the original price of Rp 8,000,000, the price is reduced to 70% of the original value. Then, a 15% discount is applied to the reduced price. The final price to pay is 59.5% of Rp 8,000,000, which equals Rp 4,760,000.

How do you find when the three activities (A, B, and C) will next occur on the same day?

To find when the three activities will coincide, you calculate the Least Common Multiple (LCM) of their individual periods: 4, 6, and 9 days. The LCM is 36, so the activities will next occur together 36 days after January 13, 2026, which is February 18, 2026.

What is the significance of calculating the LCM in this problem about periodic activities?

The LCM is significant because it helps to determine the smallest number of days after which all three activities will be held together again. It represents the point where the cycles of the activities align.

What is the GCD, and how is it used to solve the problem of distributing gift packages?

The Greatest Common Divisor (GCD) is used to find the maximum number of equal gift packages that can be made from the available quantities of items. In this case, the GCD of 150 (instant noodles), 125 (bottles of syrup), and 100 (boxes of cookies) is 25, meaning the maximum number of gift packages is 25.

How do you determine the number of items per package when distributing the gift packages?

To determine the number of items per package, divide the total quantity of each item by the number of gift packages. For example, 150 instant noodles ÷ 25 packages = 6 noodles per package, 125 bottles of syrup ÷ 25 = 5 bottles per package, and 100 boxes of cookies ÷ 25 = 4 boxes per package.

How do you calculate the number of packages if there are leftovers (e.g., 10 noodles and 5 syrup bottles left)?

If there are leftovers, such as 10 noodles and 5 syrup bottles, you calculate the GCD of the remaining quantities (140 noodles and 120 syrup bottles). The GCD of 140 and 120 is 20, meaning 20 packages can be made with the remaining items. There are no leftovers of cookies in this case.

What is the error in the last statement about the number of remaining cookies in the gift packages?

The error in the statement is in assuming that there would be leftover cookies. After calculating the number of packages (20) based on the remaining noodles and syrup, the total number of cookies (100) is perfectly divisible by 20, meaning no cookies are left over. The correct answer is that there is no leftover cookie.