The Most Frequently Used Mathematical Formulas – Mathematics for some people is considered a subject that makes a headache and belongs to a category that is not too much interested in. Maybe this assumption is due to the unpleasant experience when learning these calculations, starting from the teacher teaching, lots of assignments or homework, classmates laughing at you when you can’t do it, and so on.
The bad experience that was experienced became material for stories from one person to another which could have made other people afraid and considered mathematics as a difficult subject.
Fear of mathematics can make people feel uncomfortable, stressed, and can even lead to paranoia.
The person will feel excessive fear when learning mathematics. Myths like this must be dispelled so that people don’t feel afraid when they have to solve questions related to arithmetic.
Mathematics does have many formulas that are used, but basically most of these formulas are often used. Mathematical formulas that are often used are usually easy to find in life.
List of Most Often Used Mathematical Formulas
No need to memorize math formulas, just understand them carefully because if we apply the method of memorizing formulas it might just evaporate.
Formulas that are interpreted by rote learning models usually do not last long in memory. Imagine that there are tens to hundreds of mathematical formulas that if memorized will definitely make you dizzy and won’t last long to remember.
On the other hand, if you use the comprehension method to remember mathematical formulas, it will be stored longer and appear in a person’s unconscious. Actually, unconsciously formulas in mathematics are often found around us.
One of them is in the field of research where to solve the problems encountered, researchers use a lot of mathematical formulas in order to overcome existing problems.
Then what about mathematical formulas that can be applied in other situations? Below is a list of the most frequently used mathematical formulas in everyday life.
1. Discount formula
Have you ever taken a walk in a shopping center to see nice clothes being sold at one of the outlets that offer discounts of up to 50%?
For those who like shopping, they might be very interested in buying it, but have you ever calculated how much money you have to pay from the discount given. Here you need to use mathematical calculations. The mathematical formula used to calculate the discount is:
Discount Price = (% Discount) x Item Price
In order to better understand the discount formula, consider the following questions.
While shopping at the mall, Raisa saw a nice dress that she wanted. When approached, it turns out that the clothing store is giving a discount of 40%. The clothes are valued at Rp. 120,000.00. How much money does Raisa have to pay to get the shirt?
It is known that:
Discount = 40%
Price of clothes = IDR 120,000.00
Discounted price = (% discount) x Goods price
Discounted price = (40/100) x 120,000.00
Discounted price = 48,000
So, the discounted price of the item is Rp. 48,000.00 so that the total money Raisa has to pay is IDR 120,000.00 – IDR 48,000.00 = IDR 72,000.00.
2. Calculating Interest in the Banking System
The mathematical formula that is often used next is the formula for calculating bank interest. Bank interest is divided into two, namely bank interest and savings interest. Bank interest is the amount of money that must be paid from the customer to the bank as remuneration for using the facilities at the bank.
Meanwhile, interest on savings accounts is the amount of money paid by the bank to customers for saving money in the bank. For those who often save their money in the bank, bank interest and savings interest will be obtained every month. The formula for calculating interest in the banking system is as follows:
Interest per month = (Loan amount/number of months) x % interest
Below is an example of calculating the amount of bank interest.
Agnes plans to open a franchise in the form of a cafe at her college. However, he did not have enough funds, so he planned to borrow some money from the bank to run his business. Agnes borrowed a total of IDR 15,000,000.00 from Bank A and paid it in installments within one year. The bank interest rate set by Bank A is 2% per month. How much installments must Agnes pay each month?
It is known that:
Amount of loan = IDR 15,000,000.00
Installments = 1 year (12 months)
Bank interest rate = 2%
Interest per month = (loan size/number of months) x % interest Interest
per month = (15,000,000/12) x 2/100
Interest per month = 25,000
So, the amount of interest per month is IDR 25,000, so Agnes has to pay monthly installments of IDR 1,250,000.00 + IDR 25,000.00 = IDR 1,275,000.00.
3. Formulas for Speed, Distance, and Time
The third frequently used mathematical formula is about distance, speed, and time. We often encounter its use, for example when we ride a motorcycle from one place to another, we have to take into account how fast the motorcycle is so that we are not late.
Then this formula can also be used to calculate trans bus queues so that every few minutes passengers can be transported from one place to another. The formula used is as follows.
V = S/t
Description:
V : speed (km/hour)
S : distance (km)
t : time (hour)
The formula above is a formula for calculating speed that can be developed to find distance and time.
Time formula:
t = S/V
Distance formula:
S = tx V
To make it easier to understand this formula, consider the following two example questions
Father now works in a well-known company in the city. There is a rule that every employee is prohibited from arriving late. Office time is 07.30 and Dad estimates that he will be at the office at 07.00 so he has to leave at 06.30. Father drives his vehicle at a speed of 50 km / hour. How far is the house from the office?
Given:
Time (t) = 06.30 – 07.30 = 30 minutes (1/2 hour)
Speed (V) = 50 km
S = tx V
S = ½ x 50
S = 25
So the distance between the house and the office where Dad works is 25 km.
The city of Semarang implements a public transportation system called BRT (Bus Rapid Transit) for the people of Semarang. Every 10 minutes there must be a bus that stops at the next stop to transport people. The distance between stops is 10 km. What is the speed of the BRT so that every 10 minutes it can carry passengers at each stop?
Given :
Time (t) = 10 minutes (1/6 hour)
Distance (S) = 10 km
V = S/t
V = 10 / 1/6
V = 60
Then the speed of the BRT so that every 10 minutes it stops at the next stop is 60 km/hour.
4. Permutations and Combinations
The four mathematical formulas that are often used are permutations and combinations. In everyday life, this formula might be useful for you to use. When you are holding a meeting at a meeting, have you ever imagined how to arrange the seats according to the order you have predicted. If you have trouble arranging them, you can use the permutation formula.
As for what is meant by Permutation is a formula used to find out the possibility of something happening based on a predetermined sequence. Meanwhile, the combination formula is used to calculate the probability that an event will occur without regard to the sequence that may occur.
Both permutations and combinations are used to calculate the probability of occurrence of a possibility, the difference is that permutations must pay attention to order, whereas combinations do not pay attention to order. The permutation and combination formulas are:
Permutations :
P (n,r) = n! / (nr)!
Information:
P = permutation
n = total objects overall
r = total objects that are used as sequences
! = factorial
Combination:
nCr = n! / (r! (nr)!)
Information:
C = combination
n = total objects overall
r = total objects observed
! = factorial
To make it easier to understand what the concept of permutations and combinations looks like, consider the example questions below.
A competition was attended by 5 teams A, B, C, D, and E to fight for the champion. The committee provides places for 1st, 2nd and 3rd place winners. What is the probability that the team will win the competition?
It is known that:
n = 5
r = 3
Because it takes order into account, the permutation formula
P (n,r) = n is used! / (nr)!
P(5,3) = 5! / (5-3)!
P(5,3) = 5! / 2!
P(5.3) = 5 x 4 x 3 x 2 x 1 / 2 x 1
P(5.3) = 120/2
P(5.3) = 60
Then there are 60 possible ways the winner will appear in the race.
Clara will depart for Yogyakarta from Semarang today. He will go by bus. There are 6 buses ready to depart. Clara only chose 2 buses that she wanted to take. How many ways does Clara choose the bus?
It is known that:
N = 6
R = 2
Because it does not take into account the order, the combination formula
nCr = n! / (r! (nr)!)
6C2 = 6! / (2! (6-2)!)
6C2 = 6! / (2! x 4!)
6C2 = 15
Then there are 15 ways for Clara to choose which bus she will take.
5. Slice and Join Sets
Slices and unions are mathematical formulas that are often used in solving problems related to sets or calculations. An intersection or intersection is a set of two parts (A and B) or more whose members include members of the same set A or B.
Meanwhile, a union or union is a set whose members come from two sets, set A or set B. As the name implies, a union combines two sets into one. Slices are denoted by the symbol (∩) while the combined symbol is (∪). The following questions make it easier for you to understand what intersections and unions look like.
Set A = {1, 3, 5, 6} while Set B = {1, 3, 4}. What is the intersection set and the combined set of the two?
Given:
A = {1, 3, 5, 6}
B = {1, 3, 4}
The intersection set becomes A ∩ B = {1, 3, 5} while the combined set A ∪ B = {1, 3, 4, 5, 6}
When depicted with a diagram it will become:
Another example is as follows:
A food consumption survey was conducted in grade 12 of a high school in Semarang City. There are 17 students who like to eat meatballs, 23 students like to eat chicken noodles, and 10 students like both. What is the total number of students who took part in the survey?
It is known:
Likes meatballs = 17
Likes chicken noodles = 23
Likes meatballs and chicken noodles = 10 people
When depicted with a diagram it will become:
Because there are 10 people who like meatballs and chicken noodles, to find out students who only like chicken meatballs and noodles are deducted by 10 each.
Only likes meatballs : 17-10 = 7 people
Only likes chicken noodles : 23-10 = 13 people
So the total number of students who took part in the survey was 7+10+13 = 30 students.
6. Arithmetic Line or Series
The last mathematical formula that is often used is arithmetic. In arithmetic, it can be classified into two, namely arithmetic rows and arithmetic series. An arithmetic row is a sequence of numbers whose differences between terms are always the same (consistent).
While the arithmetic series is the sum of the numbers or the total number of terms that are formed in one series. You can find arithmetic lines or series when you compare your pocket money at school.
For example, when you are in grade 1, your pocket money is Rp. 1,000.00, then when you go up to grade two, your pocket money is Rp. 3,000.00. When you are in grade 3 it becomes IDR 5,000.00. That is what is called an arithmetic row.
Your pocket money consistently increases by Rp. 2,000.00 when you go to class. You can find an arithmetic series when you look at cinema seats, where the number of seats is different for each row, for example, the first row has 7 seats, the second row has 9 seats, and the third row has 11 seats. To find out the number of seats left, you just add each row so that there are a total of 27 seats.
If the number of tribes or lines you are looking for is small, you can still count them, but if the number reaches hundreds, it will certainly be a headache and a hassle if you have to add them up one by one. It’s better if you use a formula to make it easier to calculate. The arithmetic row and series formulas are as follows:
Arithmetic Row:
Un = a + (n-1) xb
Information:
Un = line syllable
a = first term
n = many tribes
b = difference or difference in numbers
Arithmetic Series:
Sn = n/2 x (a+Un)
Information:
Sn = number of terms
a = first term
n = many terms
b = difference or difference in numbers
To understand this, consider the following questions.
Chelsea buys marbles every day. On Monday buy 2 marbles, Tuesday 4 marbles, Wednesday 6 marbles, and so on until Sunday. On Sunday how many marbles does Chelsea buy?
Given:
a = 2
b = 2
n = 7 (Monday-Sunday)
Un = a + (n-1) xb
U7 = 2 + (7-1) x 2
U7 = 14
So on Sunday Chelsea will buy 14 marbles.
Dilan works as a cleaning service in a cinema building. He will clean the first building. The first row has 10 seats, the second row has 12 seats, the third row has 14 seats, and so on up to 10 rows. How many seats will Dilan clean?
Given:
a = 10
b = 2
n = 10
Because the number of seats in the 10th row is unknown, first find the seats in the 10th row using the arithmetic row formula
Un = a + (n-1) xb
U10 = 10 + (10-1) x 2
U10 = 28
Sn = n /2 x (a+Un)
Sn = 10/2 x (10+28)
Sn = 190
So, the total seats cleaned by dilan are 190.
7. Flat Build Formulas
a. Rectangle
A square is a type of flat shape. A square has 4 sides. All four sides are the same length. The angles of all four sides are 90° or right angles. The opposite sides of a square are always parallel. To calculate a square, there are two formulas. The formula for the area of a square and the formula for the perimeter of a square.
The formula for the area of a square (side times side), or:
L = s × s
The formula for the perimeter of a square (4s), or:
K = 4 × s
b. Rectangle
A rectangle is almost similar to a square, it has 4 sides. However, the sides of a rectangle are not all the same size. A rectangle has two pairs of parallel sides that are the same length. The four corners of the rectangle are also right angles.
The two pairs of sides in a rectangle consist of the long side and the short side. The short side is the length of the rectangle. While the short side is the width. To calculate a rectangle, there are two formulas. The formula for the area of a rectangle and the formula for the perimeter of a rectangle.
The formula for the area of a rectangle (length X width), or:
L = p × l
The formula for the perimeter of a square (4s) or:
K = 2 × (p + l)
c. Triangle
A triangle is a flat shape that only has 3 sides. In addition, a triangle also has 3 vertices. All the sides and angles in a triangle are different sizes.
Triangles based on the length of the sides are divided into several types. equilateral triangle, isosceles triangle and any triangle. Meanwhile, triangles based on their angles are also divided into 3. Right triangles, obtuse triangles and acute triangles. To calculate a triangle, there are two formulas. Triangle area formula and triangle perimeter formula.
The formula for the area of a triangle (base times height divided by two), or:
L = ½ × a × t
The formula for the perimeter of a triangle (adding all sides), is:
K = a + b + c
d. Trapezoid
A trapezoid is a flat shape that is a quadrilateral but has a pair of parallel sides. The length of the sides can be different. To calculate the trapezoid, there are two formulas. The formula for the area of a trapezoid and the formula for the perimeter of a trapezoid.
The formula for the area of a trapezoid:
L = ½ × (a + b) × t
Trapezoid circumference formula:
K = AB + BC + CD + DA
e. Parallelogram
A parallelogram is a flat shape that has four sides. It is a quadrilateral, opposite sides are parallel and the same length. In addition, a parallelogram has equal and opposite angles. To calculate a parallelogram, there are two formulas. The formula for the area of a parallelogram and the formula for the perimeter of a parallelogram.
The formula for the area of a parallelogram:
L = a × t
The formula for the perimeter of a parallelogram:
K = 2 × (a + b)
f. Kite
Kites are flat shapes that have four sides, or are rectangular in shape. Kites are divided based on the diagonal shape. The two diagonals have different sizes and are perpendicular. Kites have two pairs of sides that are the same length and close together. To calculate kites, there are two formulas. The formula for the area of a kite and the formula for the circumference of a kite.
The formula for the area of a kite:
L = ½ x diagonal (d) 1 x diagonal (d) 2
The way to calculate the diagonal is:
Diagonal 1 (d1) = 2 × L ÷ d2
Diagonal 2 (d2) = d2 = 2 × L ÷ d1
Kite circumference formula:
K = a + b + c + d or Kll = 2 × (a + c)
g. Cut the rice cake
A rhombus is also a flat shape in the form of a quadrilateral. The four sides of a rhombus are the same length. The two diagonals of a rhombus are perpendicular. The lengths of the sides that are opposite are parallel.
Meanwhile, the angles of the opposite rhombus are the same. A rhombus has four corners. The two angles are acute or more closed. While the other two are obtuse angles or more open. To calculate a rhombus, there are two formulas. The formula for the area of a rhombus and the formula for the circumference of a rhombus.
The formula for the area of a rhombus:
L = ½ x diagonal (d) 1 x diagonal (d) 2
The formula for the circumference of a rhombus:
K = s + s + s + s or s × 4
h. Circle
The circle also includes a flat shape. The circle is formed from a set of all the points around it. These points surround a point and have the same distance. The distance is r or radius, or referred to as the radius.
Circles have an infinite number of rotational and folded symmetries. To calculate a circle, there are two formulas. The formula for the area of a circle and the formula for the circumference of a circle.
Circle area formula:
L = π (pi) x radius (r) squared
Circumference formula:
K = π × diameter or π × r 2
8. The formula for building space
a. Cube
The cube is a geometric shape. A cube has a flat side and six square sides. Each side is identical in size on each. The cube has 12 edges that are the same length. 8 corner points, 12 diagonal fields and 4 diagonal spaces. A cube can be measured by measuring its volume.
Cube Volume Formula:
V = sxsxs
b. Beam
A block is one of the geometric shapes, almost like a cube. A beam is a geometric shape consisting of three pairs of rectangular sides. The three sides face each other. Other than that, they are the same size and shape.
A block also has two pairs of sides. One is rectangular and the other is rectangular. A beam is a geometric shape composed of several components. These components are angles, sides, diagonal spaces, diagonal fields and diagonal fields.
Block Volume Formula:
V = pxlxt
c. Prism
Prism is a geometric shape consisting of a base and a top. The base and top are the same size. Inside the prism shape, there is a vertical side with a rectangular shape. In addition, there are also parallelograms and squares.
A prism is a building that depends on the sides of its base and top. Therefore, this prism building consists of several types.
When viewed from the shape of the base and roof, there are rectangular prisms, triangular prisms and so on. When viewed from the perpendicular component, there are upright prisms and oblique prisms.
Prism volume formula:
V = Area of the triangle x height
d. Pyramid
Limas is a geometric shape with flat sides. Composed on an n-shaped base. has triangular sides. The sides will meet at a single top point. The pyramid is composed of 5 sides, 5 vertices and 8 edges.
There are many kinds of pyramid pedestals. Like rectangles, triangles, rhombuses, and so on. Based on the shape of the base there are rectangular pyramids, triangular pyramids, rectangular pyramids and others.
The formula for the volume of a pyramid
V = 1/3 Base Area x Height
e. Cone
A cone is a geometric shape that has curved sides. The cone is composed of a circular base. The circle will be covered by a triangle. A cone has 2 sides and 1 vertex. A cone has no plane diagonal edges or diagonal planes.
Cone volume formula:
V = 1/3 x π xrxrxt
f. Tube
The next room build is a tube. A tube is a geometric shape whose sides are curved. In addition, the tube has a circular base and lid. The sides of the tube are rectangles.
Tubes do not have edges, corners, diagonal planes and even diagonal planes. The sides of the shape are composed of 3 sides. Those sides are 1 rectangle and 2 circles. The height of the tube will be determined from the distance between the center points of the base and top circles.
Cylinder volume formula:
V = π x r2 xt
g. Ball
A sphere is a geometric figure bounded by a curved plane. The ball has no vertices, edges, diagonals and plane diagonals. The definite components in a ball are the radius and diameter.
The radius is the distance from the ball wall towards the center point. The diameter is the distance from one ball wall to another, this distance will pass through the center point.
Sphere volume formula
V = 4/3 x π x r3
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Those are some mathematical formulas that are often used and often encountered in everyday life. In essence, you don’t need to memorize all the formulas in mathematics by heart, you just need to understand how the existing formulas work so that when you forget the details of the formula but you understand how it works it will help you.
Besides being useful for ourselves, we can also help other people who might need help to solve the problems they face. you just need to understand it so you won’t have any trouble if you encounter a problem. Apart from that, you also have to understand units in mathematics and how to convert them, especially if you work in sales, this is very important for you to understand.