# 3 Scale Formulas in Basic Mathematics

Scale formulas – Most of the Sinaumed’s probably have difficulty understanding basic math. Now, these subjects may seem trivial to you, but in the past, there was a possibility that you would need to spend quite a bit of time to master one topic.

These topics may include integers and negative numbers, fractions and decimals, plane and geometric shapes, and measuring scale. The topics above are some of the things that have made it difficult for elementary school children, although in the end they will certainly be able to master these topics.

In this article, Sinaumed’s will be reminded of your childhood when studying basic mathematics. Now, we will study the topic of scale, starting from the definition of scale to the scale formula that you will often use.

## Explanation Regarding Scale

If explained simply, scale can be interpreted as a representation or copy of an object that is either larger or smaller than the actual size of the original object. However, usually the scale model is smaller than the original and is used as a guide for creating objects at full size.

So, it can be concluded that one of the greatest uses of scale is to create approximate models before someone creates the actual shape of these objects. These objects can be of various types, ranging from statues, buildings and also houses.

However, it is not uncommon for someone to measure the scale to make a smaller miniature of an object. Their needs also vary, ranging from educating other people or just displaying them. These objects can be vehicles, bridges, or even things that may no longer be categorized as “objects”, such as parks or housing.

Before we go into the next discussion about scales, Sinaumed’s needs to know that scales in mathematics have a fairly broad scope of discussion. Even so, elementary school children usually only learn one type of scale measurement, namely the scale on a map.

This is because the scale on the map has a number of variables which are easier to teach to elementary school children than other types of scale calculations. Not only that, calculating the scale on a map is also not complicated, but it does require precision and patience.

Returning to the explanation of the scale, we can state that the scale uses four ways, namely using words which are also commonly referred to as lexical scales, as ratios, as fractions, or as graphical scales in the form of bar charts.

Therefore, if there is a mention of a scale that is written as “one centimeter per hundred meters”, then Sinaumed’s can write it in the form of numbers such as 1/100 or 1:100 according to the request asked by the question giver or the client.

Topics regarding this scale are usually taught when elementary school children have entered grade 5, where many subjects have a higher level of difficulty. The book ” Summary of Material and Practice Math Questions for Grade 5 SD/MI ” can help Sinaumed’s’ children, cousins, or nephews who have entered grade 5 elementary school so they are not left behind in mathematics.

## Scale formula

Usually, when there are questions that discuss the topic of scale, you won’t be asked to just calculate the scale. Apart from the scale, elementary school children will generally be asked to calculate other things related to the scale such as the actual distance or the distance on the map.

For this reason, before we enter into the discussion of scale formulas, Sinaumed’s must first know the form of these formulas as a whole. Fortunately, this form or format of calculation is also common in other math topics, so learning it shouldn’t be difficult. You will find a more detailed explanation in the image below.

As Sinaumed’s can see above, you can find this triangular model of calculation in other math topics, such as calculating the formula for speed, distance and time. You can apply the same calculation method to the formulas to calculate the scale.

With the above understanding, we will now jointly discuss the formulas for calculating scale, starting from the formula for calculating scale, the formula for calculating actual distance, and the formula for calculating distance on a map.

Not only that, we will also work on several problems regarding the calculation of scale together. The hope is that Sinaumed’s can gain your understanding of the topic of scales and be able to recall one of the topics in this mathematics subject.

## The formula for calculating the scale

Based on the picture above, the position of the scale is below the distance on the map and next to the actual distance. If we apply the formula to calculate the scale using this information, it can be translated as follows:

S = Jp ÷ Jb

Problems example

It is known that the distance between the cities of Jakarta and the cities of Bandung is 150 kilometers (km). If the distance between these two cities is only about 3 centimeters (cm), what scale is used to draw the map?

To get the scale used on the map, what you need to do first is change the distance units to be the same between the two. In this case, we’ll convert kilometers to centimeters to make the calculation easier. 150 km if converted to centimeters must be multiplied by 100,000.

150 km x 100,000 = 15,000,000 cm

After converting km to cm, you only need to enter the variables above into the formula. The variable in question is the actual distance, namely the distance between the cities of Jakarta and Bandung, and the distance on the map. So, the calculation will be more or less like this:

S = Jp ÷ Jb
S = 3 cm ÷ 15,000,000 cm
S = 1 ÷ 5,000,000 cm

Your calculations can end there. With this, Sinaumed’s has found the scale used to draw a map between the City of Jakarta and the City of Bandung, which is 1:5,000,000 or 1/5,000,000. That is, every one cm used to describe the map, is 5,000,000 cm or 50 km in the original distance.

### The formula for calculating the actual distance

Based on the image above, the actual distance position is below the distance on the map and next to the scale. If we apply the formula to calculate the scale using this information, it can be translated as follows:

Js = Jp ÷ S

Problems example

It is known that the distance on the map between Malang City and Surabaya City is 5 centimeters (cm). If the scale used to depict the map is 1:1,800,000, what is the actual distance between these two cities?

Before we go into the discussion of questions, Sinaumed’s needs to know that later you will be faced with calculations using large numbers. However, you don’t need to worry about this. The key is to remain patient, thorough and not panic, because believe it or not these numbers are not difficult numbers to calculate.

Once you are ready, Sinaumed’s can plug the above variables into the formula. The variable in question is the scale used and the distance between cities written on the map. So, the calculation will be more or less like this:

Js = Jp ÷ S
Js = 5 cm ÷ 1:1,800,000 or 1/1,800,000
Js = 5 cm x 1,800,000
Js = 9,000,000 cm

Calculations regarding the actual distance from the two cities can actually stop here. However, generally you are asked to convert distances from centimeters to kilometers as these are the most commonly used units with numbers that large. You just need to divide by 100,000.
9,000,000 cm ÷ 100,000 = 90 km.

After achieving these results, it is a sign that Sinaumed’s’ calculations are completely finished. You no longer need to add or change anything from the results above, so the conclusion is that the actual distance between Malang City and Surabaya City is 90 km.

### Formulas for Calculating Distances on a Map

Based on the picture above, the position of the distance on the map is above the actual distance and also the scale. If we apply the formula to calculate the scale using this information, it can be translated as follows:

Jp = Js x S

Problems example

It is known, the distance between the city of Padang and the city of Medan on the island of Sumatra reaches 770 kilometers (km). Calculate the distance that will be drawn on the map using a scale of 1:11,000,000.

First, Sinaumed’s must realize that these two variables are different from each other, because as discussed earlier, the 1:11,000,000 scale above means “1 cm every 11,000,000 cm at the original distance”. For that, we have to convert one of these variables into the same unit of measure.

Here, Sinaumed’s is advised to convert the original distance in km to cm. This is because we follow the scale used and the scale cannot be changed even if it is only for calculation purposes. To convert km to cm, you need to multiply by 100,000.

770 km x 100,000 = 77,000,000 cm

Only then was Sinaumed’s able to enter the variables above into the formula. The variable in question is the scale used on the map and the actual distance between the city of Padang and the city of Medan. So, the calculation will be more or less like this:

Jp = Js x S
Jp = 77,000,000 cm x 1:11,000,000 or 1/11,000,000
Jp = 77,000,000 cm/11,000,000 or 77,000,000 cm ÷ 11,000,000
Jp = 7 cm

The results above indicate the end of the calculation regarding the distance on the map between the City of Padang and the City of Medan, which is 7 cm long. There’s nothing else that Sinaumed’s needs to do or look for in these calculations.

How about it, Sinaumed’s? The scale formula is not as difficult and complicated as you imagine, right? You only need to read the questions carefully, adjust the variables according to the formulas requested, and finally you can use these formulas according to the purpose of the calculation.

As long as Sinaumed’s is diligent in practicing questions and willing to learn from mistakes, over time you will definitely find math to be fun. As presented in the book ” Why? Mathematics 1 “, a book that allows you to learn about mathematics in an exciting and fun way.

## How to Learn Maths Effectively

The scale formula above not only teaches Sinaumed’s how to calculate scale, but also the basics of multiplication, division, and length conversion. So, basically you can learn many things about mathematics from just one topic.

Even though you can learn many things from there, Sinaumed’s might not be the type of person who can learn many things in one meeting. You may be a person who needs to learn slowly but surely in order to understand a topic.

This is not a problem at all. Because the key to success in learning mathematics is to practice and get used to the existing problems. There is no point in memorizing one formula a day but forgetting it the next day.

As a closing session, Sinaumed’s will learn what things you must pay attention to if you want to study mathematics effectively. Hopefully, these suggestions can make it easier for you to learn math and not be afraid of this subject anymore.

### Understand Formulas Instead of Memorizing

Memorizing the formula for your sign is just remembering the existing formulas. Although this is not wrong, there is a potential that Sinaumed’s can forget the formula more quickly. It’s different if you try to understand the formula, so you can know for sure the written formula.

### Make as many notes as possible

Messy notes, especially in mathematics, will only make it difficult for you to study. Therefore, make notes that are neat and easy to read so that you can study them better. Another alternative that you can try is to borrow a friend’s notes that are tidier.

Sinaumed’s can take the time to ask those who understand mathematical concepts. This includes teachers, lecturers, or friends who have high scores in mathematics. This is one way for you to more quickly understand one of the math concepts you don’t understand.

### Don’t get tired of practicing questions

The formulas you learn will be of no use if you don’t apply them to the problem. Practice practice questions are the best way for you to understand mathematics even deeper. With this, you can find out whether you have been able to work on the questions based on your current knowledge or not.

### Learn Past Mistakes

Mistakes in learning mathematics are very natural. In fact, by making mistakes, you can find out where your weaknesses are so you don’t repeat this in the future. You will understand that what you are doing is not right and know what steps you should take.

As a closing conclusion, the essence of the explanation above is to always be diligent in learning, keep practicing and not be afraid of making mistakes. Don’t let Sinaumed’s stop being consumed by negative emotions. Keep studying and practicing until you master math perfectly.

Don’t just wait for class. Sinaumed’s can also learn mathematics outside of the classroom, whether it’s tutoring from your friends, learning from the internet, reading books, and of course practicing self-taught. The book ” Math Runner: Collection of High School / MA Math Practice Questions ” is a practice book for high school students that can help you practice math problems.

Apart from the recommended books above, Sinaumed’s can find other books according to your interests or even articles you need on the sinaumedia.com website. sinaumedia, #FriendsWithoutLimits , will never get tired of reminding Sinaumed’s to keep reading diligently because you can get knowledge, information, and insights #MoreWithReading .