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Brilio.net - Comparison is a very important basic concept in Mathematics , used to compare two or more objects based on quantity or size. In this article, you will discuss several examples of comparison problems in Mathematics that can help students understand and apply this concept better.
By understanding comparison, students can solve various problems involving ratios, proportions, and comparisons of numbers. Through examples of comparison problems in Mathematics, you can explore various situations that may be faced in everyday life.
For example, comparing the price of an item, the number of participants in two groups, or the results of two experiments. A full discussion of each problem will provide deeper insight into how comparisons are used in real-world contexts and the importance of a deep understanding of the material.
Not only that, this article will also present a systematic discussion for each example question given. Here is a complete review of examples of comparison questions in Mathematics, adapted by brilio.net from various sources, Thursday (26/9).
Examples of comparison questions in Mathematics
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1. The ratio of Ani and Budi's ages is 3:5. If Ani is 18 years old, how old is Budi?
Discussion:
- Age ratio Ani : Budi = 3 : 5
- Ani's age = 18 years
- Suppose 1 part = x years
- So: 3x = 18
- x = 18 3 = 6
- Budi's age = 5x = 5 6 = 30 years
2. If 2 : 3 = 8 : x, what is the value of x?
Discussion:
- Use the equivalent comparison formula: a/b = c/d
- 2/3 = 8/x
- 2x = 3 8
- 2x = 24
- x = 24 2 = 12
3. The ratio of length and width of a rectangle is 4:3. If the circumference is 70 cm, what is the length and width?
Discussion:
- Suppose length = 4x and width = 3x
- Circumference = 2(p + l) = 70 cm
- 2(4x + 3x) = 70
- 2(7x) = 70
- 14x = 70
- x = 5
- Length = 4x = 4 5 = 20 cm
- Width = 3x = 3 5 = 15 cm
4. In a class, the ratio of male to female students is 2:3. If the total number of students is 40, how many female students are there?
Discussion:
- Male : female ratio = 2 : 3
- Total parts = 2 + 3 = 5
- 1 part = 40 5 = 8
- Number of female students = 3 8 = 24 people
5. The distance between cities A and B is 300 km. On a map with a scale of 1:1,000,000, what is the distance between the two cities?
Discussion:
- A scale of 1:1,000,000 means that 1 cm on the map represents 1,000,000 cm in reality.
- Actual distance = 300 km = 30,000,000 cm
- Distance on the map = 30,000,000 1,000,000 = 30 cm
6. A cake recipe calls for 2 cups of flour to make 24 cookies. How many cups of flour are needed to make 36 cookies?
Discussion:
- Use equivalent comparisons
- 24 cakes : 2 cups = 36 cakes : x cups
- 24x = 2 36
- 24x = 72
- x = 72 24 = 3 cups
7. If 5 workers can complete a project in 12 days, how many days will it take if there are 8 workers?
Discussion:
- This is a reverse comparison of values
- 5 12 = 8 x
- 60 = 8x
- x = 60 8 = 7.5 days
8. A car travels at a speed of 60 km/h for 2 hours. If the speed is increased to 80 km/h, how long will it take to cover the same distance?
Discussion:
- Distance = speed time
- Distance = 60 2 = 120 km
- For a speed of 80 km/h:
- 120 = 80 x
- x = 120 80 = 1.5 hours
9. The ratio of the sides of a triangle is 3:4:5. If the perimeter of the triangle is 60 cm, what is the length of the longest side?
Discussion:
- Total comparison = 3 + 4 + 5 = 12
- 1 part = 60 12 = 5 cm
- Longest side = 5 5 = 25 cm
10. A map has a scale of 1:250,000. If the distance between two cities on the map is 8 cm, what is the actual distance in kilometers?
Discussion:
- 1 cm on the map = 250,000 cm in reality
- 8 cm on the map = 8 250,000 = 2,000,000 cm
- 2,000,000 cm = 20 km
11. Two gears are in contact with each other. Gear A has 15 teeth and gear B has 45 teeth. If gear A rotates 20 times, how many times will gear B rotate?
Discussion:
- The rotation ratio is inversely proportional to the number of teeth
- A : B = 45 : 15 = 3 : 1
- If A rotates 20 times, then B will rotate:
- 20 3 = 6.67 times
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