√ Definition of Comparison: Kinds, Formulas, Example Questions (Complete)
Definition of Comparison
Comparisons in mathematics can also be referred to as ratios.
Then, what is a comparison or ratio?
Comparison (ratio) is a technique or way of comparing two quantities.
Writing ratios or comparisons can be written as a: b or a/b with a and b being two quantities that have the same units.
Next will be explained examples of applying comparisons in everyday life.
Comparisons in Everyday Life
There are many applications of comparison in everyday life. Writing scale on a map is one application of comparison.
Then, when we are going to make bread there is usually a dough mixture of wheat flour and tapioca flour.
For example, the ratio is 2: 1, meaning that to make the bread you need 2 parts of wheat flour and 1 part of tapioca flour.
Next we will learn about value comparisons.
Comparison Worth
Comparison of worth is also known as a proportion. Equal comparisons involve two ratios that are the same.
So, it can be explained simply that a comparison of worth is a statement that states two ratios are the same.
An example of an equivalent comparison is the ratio of the amount of flour to the amount of bread made.
The more flour used, the more bread will be made, and vice versa.
Next will be explained about the comparison of reverse values.
Reverse Value Comparison
Comparison of turning values is between the two variables.
For example the comparison between the size of a motorized engine gear with speed. The small motorized gear size will produce a large speed, and vice versa.
In the following, a multilevel comparison will be explained.
Stratified Comparison
Stratified comparison is a comparison that involves more than one comparison.
Examples of problems related to multilevel comparisons, for example, the comparison of Abdul and Beni's marbles is 3: 5, while the comparison of Beni's and Ciko's marbles is 4: 3.
To solve this problem, it is necessary to determine the ratio or comparison of Abdul, Beni, and Ciko's marbles.
The following will explain how to calculate the comparison.
How to Calculate Comparisons
The way that can be done to calculate the comparison is as follows.
- Make a model of the problem to be solved.
- Specify the type of comparison to be completed. The types of comparisons can be comparisons of equal value, comparisons of inverse values, comparisons of levels, or other types.
- Set up the equations and calculate the comparisons to determine the information you want to get using the comparison formula.
In the following section, several comparison formulas will be explained.
Comparison Formula
From a problem regarding comparison, make a model in tabular form to make it easier to understand the problem.
The comparison table can be in the form of a table like the following.
| Variable 1 | Variable 2 |
| a1 | b1 |
| a2 | b2 |
From this model, equations or formulas can be developed to complete the comparison.
1. Worth Comparison Formula
a1/a2 = b1/b2
2. Reverse Value Comparison Formula
a1/a2 = b2/b1
In addition to these two comparison formulas, there are also formulas for comparison of amounts and differences.
3. Amount comparison formula
Number of objects = (number of known ratios/ratios) x number of known objects
4. Difference comparison formula
Difference in objects = (difference in known ratios/ratios) x number of known objects
In order to better understand the comparative material, consider the following example questions.
Examples of Comparison Questions
1. Hendra rides a motorcycle covering a distance of 32 km by spending 4 liters of gasoline. If Hendra has 7 liters of petrol, how far can Hendra travel?
Discussion
From these problems can be made a model of the problem as follows.
| Gas | Mileage |
| 4 liters | 32km |
| 7 liters | x |
This problem is a problem of comparison of worth, so that
4/7 = 32/x
x = (7 x 32)/4 = 56 km
So the distance that can be traveled by Hendra with 7 liters of gasoline is 56km
2. A job if done by 8 people will be completed in 18 days. If 12 people do the work, how many days will it take to complete the work?
Discussion
From these problems can be made a model of the problem as follows.
| Many Workers | Time |
| 8 people | 18 days |
| 12 people | x |
This problem is a reverse value comparison problem, so
8/12 = x/18
x = (8 x 18)/12 = 12 days
So, with 12 people, the work will be completed in 12 days.
3. The ratio of the number of Andika and Bona marbles is 2: 3, while the ratio of the number of Bona and Ciko marbles is 2: 5. If the total number of marbles in the three of them is 75. Find the number of marbles Andika, Bona, and Ciko.
Discussion
The model of the problem is
A: B=2:3
B: C=2:5
————————–
A: B:C=4:6:15
Total ratio = 4 + 6 + 15 = 25
Lots of Andika marbles
4/25 x 75 = 12 marbles
Lots of Bona marbles
6/25 x 75 = 18 marbles
Lots of Ciko's marbles
15/25 x 75 = 45 marbles
So, the number of marbles of Andika, Bona and Ciko are 12, 18 and 45 respectively.
4. There is a tree 10 meters away from you. Behind the tree, there is a multi-storey building that is 50 meters high and 10 meters away from the tree. Calculate the height of the tree using the concept of comparison
Discussion
To do this problem, we have to draw according to the problem. This is to make it easier to understand the problem.
Based on the picture above, we can find the height of the building with the following comparison
20.t = 50.10
t = 25 meters
So, the height of the tree is 25 meters.
5. A shoemaker is able to complete an order in 84 days with 28 workers. Due to the increasing demand, the work must be completed in 56 days. How many workers need to be added to complete the work in 56 days?
Discussion
Just like the problem above, the first time, we have to make a mathematical model either in the form of an image or an equation.
In the problem above, we will make a mathematical model of the number of workers needed using the concept of comparison. However, the concept of comparison used is different.
In this problem, the comparison concept used is linear in nature. That is, the processing speed remains the same both 84 days and 56 days.
Thus, the form of comparison used is as follows.
56x = 28.84
x = 42
The total number of employees needed to work on shoes in 56 days is 42 employees. Meanwhile, currently, the shoe maker has as many as 28 workers. Thus, the need for additional workers is 42-28 = 14 workers.
6. Mother makes 10 cake pans, requires 8 flour. One day, Mother wanted to make 15 cake pans. How much wheat flour do you need?
Discussion
In this case, we can use equivalent comparisons to solve it. The process is the same as question number 1. We need to make a mathematical model first to make it easier to understand.
10 pans → 8 flour
15 pans → y flour
10y = 15.8
y = 12
Mother needs to make 15 cake pans is 12 flour.
7. A bus travels from city M to O in 2 hours at a speed of 60 km/hour. If the bus wants to arrive 30 minutes faster, what speed should the bus be?
Discussion
Comparison of inverse values can be used again to solve this problem. We can create a mathematical model as below.
2 hours → 60 km/hour
1.5 hours → v km/hour
1.5v = 60.2
v = 80 km/hour
If the bus wants to reach town O 30 minutes faster, then the bus speed must be 80 km/hour.
8. A tailor can make 50 pairs of clothes in 20 days. One day the tailor gets an order for 75 pairs of clothes, how long will it take the tailor?
Discussion
To do this problem, we can use a simple equivalent comparison. So the form of the solution is as below.
50 pairs → 20 days
75 pairs → m days
50m= 75.20
m = 30
A tailor can complete 75 pairs of clothes in 30 days.
Conclusion
Comparison (ratio) is a technique or way of comparing two quantities.
There are several types of comparisons such as worth comparisons, reverse value comparisons, multilevel comparisons, and other comparisons.
How to calculate comparisons, namely determining the model, determining the type of comparison, applying the formula to calculate the comparison.
Worth Comparison Formula
a1/a2 = b1/b2
Reverse Value Comparison Formula
a1/a2 = b2/b1
Thus the discussion of comparisons, hopefully it can add to your knowledge about comparisons. Thank You.
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