Math Formulas

Basic math formulas

Fractions formulas: 

Consumer math formulas:  Discount = list price × discount rate Sale price = list price − discount Discount rate = discount ÷ list price Sales tax = price of item × tax rate Interest = principal × rate of interest × time Tips = cost of meals × tip rate Commission = cost of service × commission rate

Math Projects

How to Make Math Projects

Math projects help students understand a specific math concept or idea. When you are making math projects, you are doing an in-depth study of one of those concepts. Math projects can be done about any type of math concept, from one in kindergarten all the way through high school. Doing a math project is an easy process -- it's the actual concept that might give you trouble.

Focus on the topic for which you are going to do a math concept. It is important that you have a full understanding of the concept so that you can complete the project. If you don't know anything about the concept, or you aren't sure you understand it, get some books or find some information on the Internet about your subject.

Come up with an angle for your project. Even though it is a project about math, there are many different ways for you to do the project. You might write a paper, create a presentation, write a blog, shoot a video or even make a diagram or 3-D model of whatever your math concept or subject is. You'll need to decide which type of project you are doing before you can get started.

Figure out how your concept will fit into the angle you've chosen. For instance, if you are going to write a report, and your concept is fractions, decide if you'd like to write about the history of fractions, how to work with fractions, or even what fractions are used for in real life. If your concept is geometry and your project is going to be a 3-D model, decide which shapes you are going to make your models of, and how the models will help you display the geometric concepts.

Gather the materials you'll need for your specific math project. Things like a computer, pencil and paper will be important if your project is a research paper. You might need clay, plastic or paper mache if you are making models. You will need presentation software or poster board if your project is going to be a presentation.

Find your research and create your project materials. Be sure that you follow your own plan, but also pay attention to what your teacher has assigned and asked you to do so you can be sure you complete it correctly.

Fact

20 Interesting and Amazing Facts About Maths

Words such as formula, equation and calculation sounds boring for those who hate Maths as a subject, whereas it is fun for those who have keen interest towards solving equations/problems.

October 14th is celebrated as World Maths Day. Let us know some interesting and amazing facts about Mathematics.

1. Zero ( 0 ) is the only number which can not be represented by Roman numerals.
2. What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion
3. Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D
4. 2 and 5 are the only primes that end in 2 or 5
5. An icosagon is a shape with 20 sides

6. Among all shapes with the same perimeter a circle has the largest area.

7. Among all shapes with the same area circle has the shortest perimeter 
8. 40 when written "forty" is the only number with letters in alphabetical order, while "one" is the only one with letters in reverse order
9. 'FOUR' is the only number in the English language that is spelt with the same number of letters as the number itself 
10. From 0 to 1,000, the letter "A" only appears in 1,000 ("one thousand")
11. 12,345,678,987,654,321 is the product of 111,111,111 x 111,111,111. Notice the sequence of the numbers 1 to 9 and back to 1.

12. Have you ever noticed that the opposite sides a die always add up to seven (7)
13. Trigonometry is the study of the relationship between the angles of triangles and their sides
14. Abacus is considered the origin of the calculator
15. Here is an interesting trick to check divisibility of any number by number 3.A number is divisible by three if the sum of its digits is divisible by three (3)
16. Do you know the magic of no. nine (9)? Multiply any number with nine (9 ) and then sum all individual digits of the result (product) to make it single digit, the sum of all these individual digits would always be nine (9).
17. If you add up the numbers 1-100 consecutively (1+2+3+4+5...) the total is 5050
18. A 'jiffy' is an actual unit of time for 1/100th of a second
19. Have you heard about a Palindrome Number? It is a number that reads the same backwards and forward, e.g. 12421
20. Have you heard about Fibonacci? It is the sequence of numbers wherein a number is the result of adding the two numbers before it! Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on

Math Concepts

10 MATH CONCEPTS YOU CAN’T IGNORE

• Sets and set theory: A set is a collection of objects. The objects, called elements of the set, can be tangible (shoes, bobcats, people, jellybeans, and so forth) or intangible (fictional characters, ideas, numbers, and the like). Sets are such a simple and flexible way of organizing the world that you can define all of math in terms of them.
  Mathematicians first define sets very carefully to avoid weird problems – for example, a set can include another set, but it can’t include itself. After the whole concept of a set is well-defined, sets are used to define numbers and operations, such as addition and subtraction, which is the starting point for the math you already know and love.
• Prime numbers: A prime number is any counting number that has exactly two divisors (numbers that divide into it evenly) — 1 and the number itself. Prime numbers go on forever — that is, the list is infinite — but here are the first ten:

  2 3 5 7 11 13 17 19 23 29 . . .

• Zero: Zero may look like a big nothing, but it’s actually one of the greatest inventions of all time. Like all inventions, it didn’t exist until someone thought of it. (The Greeks and Romans, who knew so much about math and logic, knew nothing about zero.)
  The concept of zero as a number arose independently in several different places. In South America, the number system that the Mayans used included a symbol for zero. And the Hindu-Arabic system used throughout most of the world today developed from an earlier Arabic system that used zero as a placeholder. In fact, zero isn’t really nothing — it’s simply a way to express nothing mathematically. And that’s really something.
• Pi (π): The symbol π (pronounced pie) is a Greek letter that stands for the ratio of the circumference of a circle to its diameter. Here’s the approximate value of π:

  π ≈ 3.1415926535…

• Although π is just a number — or, in algebraic terms, a constant — it’s important for several reasons:
  • Geometry just wouldn’t be the same without it. Circles are one of the most basic shapes in geometry, and you need π to measure the area and the circumference of a circle.
  • Pi is an irrational number, which means that no fraction that equals it exactly exists. Beyond this, π is a transcendental number, which means that it’s never the value of x in a polynomial equation (the most basic type of algebraic equation).
  • Pi is everywhere in math. It shows up constantly (no pun intended) where you least expect it. One example is trigonometry, the study of triangles. Triangles obviously aren’t circles, but trig uses circles to measure the size of angles, and you can’t swing a compass without hitting π.
• Equals signs and equations: The humble equals sign (=) is so common in math that it goes virtually unnoticed. But it represents the concept of equality — when one thing is mathematically the same as another — which is one of the most important math concepts ever created. A mathematical statement with an equals sign is an equation. The equals sign links two mathematical expressions that have the same value and provides a powerful way to connect expressions.
• The xy-graph: Before the xy-graph (also called the Cartesian coordinate system) was invented, algebra and geometry were studied for centuries as two separate and unrelated areas of math. Algebra was exclusively the study of equations, and geometry was solely the study of figures on the plane or in space. The graph, invented by French philosopher and mathematician René Descartes, brought algebra and geometry together, enabling you to draw solutions to equations that include the variables x and y as points, lines, circles, and other geometric shapes on a graph.
• Functions: A function is a mathematical machine that takes in one number (called the input) and gives back exactly one other number (called the output). It’s kind of like a blender because what you get out of it depends on what you put into it. Suppose you invent a function called PlusOne that adds 1 to any number. So when you input the number 2, the number that gets outputted is 3:

  PlusOne(2) = 3

  Similarly, when you input the number 100, the number that gets outputted is 101:

  PlusOne(100) = 101

• The infinite: The very word infinity commands great power. So does the symbol for infinity (∞). Infinity is the very quality of endlessness. And yet mathematicians have tamed infinity to a great extent. In his invention of calculus, Sir Isaac Newton introduced the concept of a limit, which allows you to calculate what happens to numbers as they get very large and approach infinity.
• The real number line: Every point on the number line stands for a number. That sounds pretty obvious, but strange to say, this concept wasn’t fully understood for thousands of years. The Greek philosopher Zeno of Elea posed this problem, called Zeno‘s Paradox: To walk across the room, you have to first walk half the distance across the room. Then you have to go half the remaining distance. After that, you have to go half the distance that still remains). This pattern continues forever, with each value being halved, which means you can never get to the other side of the room. Obviously, in the real world, you can and do walk across rooms all the time. But from the standpoint of math, Zeno’s Paradox and other similar paradoxes remained unanswered for about 2,000 years.
  The basic problem was this one: All the fractions listed in the preceding sequence are between 0 and 1 on the number line. And there are an infinite number of them. But how can you have an infinite number of numbers in a finite space? Mathematicians of the 19th century — Augustin Cauchy, Richard Dedekind, Karl Weierstrass, and Georg Cantor foremost among them — solved this paradox. The result was real analysis, the advanced mathematics of the real number line.
• The imaginary number i: The imaginary numbers(numbers that include the value i = √ – 1) are a set of numbers not found on the real number line. If that idea sounds unbelievable — where else would they be? — don’t worry: For thousands of years, mathematicians didn’t believe in them, either. But real-world applications in electronics, particle physics, and many other areas of science have turned skeptics into believers. So if your summer plans include wiring your secret underground lab or building a flux capacitor for your time machine — or maybe just studying to get a degree in electrical engineering — you’ll find that imaginary numbers are too useful to be ignored.

Use of Maths

What use is maths in everyday life?

What do going out for dinner, choosing a shampoo, or planning a holiday all have in common? You’ve guessed it: maths. Numerical and logical thinking play a part in each of these everyday activities, and in many others. A good understanding of maths in everyday life is essential for making sense of all the numbers and problems life throws at us.

Maths on the menu

It’s your birthday and you’ve decided to go out for a meal with some friends. While you won’t be having fried formulas or a side-order of statistics, maths is involved at every stage.

Looking down at the menu, you eye up the prices. The restaurant owner has worked out how much she needs to charge for her food by creating a business model detailing the cost of raw ingredients, staff wages and so on. She also has to calculate how these costs might change in the future and how many customers she expects. Many restaurants fail within their first year because of poor mathematical planning.

Thankfully this one is still open for business, so you place your order and the chef gets to work. You’d better hope he has a good grasp of maths, because understanding measurement, ratio, and proportion can be the difference between something delicious and something that ends up in the dustbin.

Turns out you’re in luck, and the food is excellent. You just about make room for dessert and it’s time to split the bill. Who had the pizza? Did you have one drink, or two? Did the waiter add everything up correctly? Being able to perform quick mental calculations will get it sorted in no time – and percentages help with leaving a tip!

Math Tricks

10 Math Tricks That               Will Blow  Your Mind

1. Multiplying by 6

If you multiply 6 by an even number, the answer will end with the same digit. The number in the tens place will be half of the number in the ones place.

Example: 6 x 4 = 24

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The Answer Is 2

1. 1.Think of a number.
2. 2.Multiply it by 3.
3. 3.Add 6.
4. 4.Divide this number by 3.
5. Subtract the number from Step 1 from the answer in Step 4.

The answer is 2.

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Same Three Digit Number

1. 1.Think of any three-digit number in which each of the digits is the same. 2.Examples include 333, 666, 777, 999.
2. 3.Add up the digits.
3. 4.Divide the three digit number by the answer in Step 2.

The answer is 37.

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Six Digits Become Three

1. 1.Take any three-digit number and write it twice to make a six digit number. 2.Examples include 371371 or 552552.
2. 3.Divide the number by 7.
3. 4.Divide it by 11.
4. 5.Divide it by 13. (The order in which you do the division is unimportant.)

6.The answer is the three digit number

Examples: 371371 gives you 371 or 552552 gives you 552.

1. A related trick is to take any three-digit number.
2. Multiply it by 7, 11, and 13.

The result will be a six digit number that repeats the three-digit number.

Example: 456 becomes 456456.

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The 11 Rule

This is a quick way to multiply two digit numbers by 11 in your head.

1. 1.Separate the two digits in your mind.
2. 2.Add the two digits together.
3. 3.Place the number from Step 2 between the two digits. If the number from Step 2 is greater than 9, put the ones digit in the space and carry the tens digit.

Examples: 72 x 11 = 792

57 x 11 = 5 _ 7, but 5 + 7 = 12, so put 2 in the space and add the 1 to the 5 to get 627

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Memorizing Pi

To remember the first seven digits of pi, count the number of letters in each word of the sentence:

"How I wish I could calculate pi."

This gives 3.141592

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Contains the Digits 1, 2, 4, 5, 7, 8

1. 1.Select a number from 1 to 6.
2. 2.Multiply the number by 9.
3. 3.Multiply it by 111.
4. 4.Multiply it by 1001.
5. 5.Divide the answer by 7.

The number will contain the digits 1, 2, 4, 5, 7, and 8. 

Example: The number 6 yields the answer 714285.

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Multiply Large Numbers in Your Head

To easily multiply two double digit numbers, use their distance from 100 to simplify the math:

1. 1.Subtract each number from 100.
2. 2.Add these values together.
3. 3.100 minus this number is the first part of the answer.
4. 4.Multiply the digits from Step 1 to get the second part of the answer.

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Super Simple Divisibility Rules

You've got 210 pieces of pizza and want to know whether or not you can split them evenly within your group. Rather than whip out the calculator, use these simple shortcuts to do the math in your head:

• Divisible by 2 if the last digit is a multiple of 2 (210).
• Divisible by 3 if the sum of the digits is divisible by 3 (522 because the digits add up to 9, which is divisible by 3).
• Divisible by 4 if the last two digits are divisible by 4 (2540 because 40 is divisible by 4).
• Divisible by 5 if the last digit is 0 or 5 (9905).
• Divisible by 6 if it passes the rules for both 2 and 3 (408).
• Divisible by 9 if the sum of the digits is divisible by 9 (6390 since 6 + 3 + 9 + 0 = 18, which is divisible by 9).
• Divisible by 10 if the number ends in a 0 (8910).
• Divisible by 12 if the rules for divisibility by 3 and 4 apply.

Example: The 210 slices of pizza may be evenly distributed into groups of 2, 3, 6, 10.

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Finger Multiplication Tables

Everyone knows you can count on your fingers. Did you realize you can use them for multiplication? A simple way to do the "9" multiplication table is to place both hands in front of you with fingers and thumbs extended. To multiply 9 by a number, fold down that number of finger, counting from the left.

Examples: To multiply 9 by 5, fold down the fifth finger from the left. Count fingers on either side of the "fold" to get the answer. In this case, the answer is 45.

To multiply 9 times 6, fold down the sixth finger, giving an answer of 54.

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