Can Geometry be Interesting?

Geometry

Geometry can be interesting if it is introduced with proper examples from the real life and with 3D models. Charts and diagrams play a major role in making Geometry shapes look awesome.

Why to learn Geometry?

  • Geometry learning is necessary for understanding the shape and size of the objects around you in life.
  • Knowledge of Geometry is essential for many professions like navigation, architecture, basic engineering projects, animations, computer imaging, surveying and astronomy.
  • Geometric imaging is useful in medical field as in CT and MRI scans.
  • Geometry learning gives exercise to right side brain.
  • It improves the visual imagination of a person.

How to learn Geometry effectively?

Geometry is basically about shapes and sizes. So, you need to improve your expertise in drawing lines and figures with precision. Having powers of exact calculation is also mandatory for flawless diagrams. Geometry is full of formulas and theorems which need to be memorized for easy doing of sums.

Attending Geometry classes is necessary for following Geometry homework without problem. Geometry homework help from reliable websites is worth considering for fetching good scores without frustration and for getting unique insights in subject areas.

Learning Geometry with an e-tutor is the most effective way of doing the subject since the tutor could introduce topics in a real time background with suitable interactive methods and 3D models. This is especially good for high school students when they learn advanced topics in the subject and struggle to get at their essence.

How to get over the hurdles in doing Geometry assignment?

Geometry assignments are in a way taxing due to sums with formulas and applications of theorems. Students who are not good at the basic skills of the subject may feel overwhelmed while sitting for Geometry assignments. They have to brush up their fundamental skills so as to proceed in their assignment doing. Best assignment help from Geometry scholars is possible via online tutorials. After registering with them, students can gain massive knowledge in Geometry topics, discuss sums and theorems on white board and make their Geometry assignments excellent for great scores.

Learning Geometry with a Math Tutor online makes the subject interesting, hassle free and memorable with unique practices and insights.

Are Today’s Kids Burdened With Too Much Of Homework?

The topic definitely opens up to a lot of discussion and scrutiny today and one can find a lot of comments in this regard on various popular platforms. There is a raging debate ongoing as to whether students are given way too much homework and how it affects their mental makeup and performance at school. There are even books being written about this very topic by parents and teachers alike and given that they are becoming best sellers in no time, one can safely assume the amount of interest this topic has generated in recent times amongst the public. To identify if one’s child is actually being burdened with a lot of homework, one should look for certain signs. Read on to learn all about them.

college algebra students

Is your child being given way too much homework?

The very first sign that your child is being burdened with a lot of work is if he/she starts hating the very idea of school. The recommended level of homework is 10 minutes per grade every night and anything in excess simply means that your child will struggle to cope with it! Given the vociferous arguments one can read about it and given that at least more than 90% of the people feel that children are being taxed with undue amounts of work to be done at home, it does look like the scenario is pretty bad. Read on to learn as to how you can help your child in such a case.

What can you do about it?

Too much of homework adversely affects your kids as they stop being children and start to feel stressed every day. When you feel that the amount of homework given is unreasonable, bring it to the notice of your child’s teacher and ask him/her to reduce the same. Take it up further in meetings at school and bring it to the notice of the principal in case nothing works out. This can be very effective when you have the support of other parents.

Is your child unable to cope with homework due to other factors?

If even after your best efforts, your child is struggling to cope with homework (due to lack of understanding or concentration), it is time for you to get them professional assistance from experts such as online geometry tutors and tutors in other subjects. Check whether your child is taking way too much time with homework just because he/she isn’t able to understand the subject they are studying.

In such a case seeking out experts to help them understand the subject and learn its nuances is a good idea (this is of course when you can’t teach your kids by yourself either due to want of time or due to lack of enough knowledge in the subject). And when it comes to particularly difficult subjects such as geometry or trigonometry, you can help your child out by roping in the best geometry homework help online so as to ease your child’s burden and help him/her learn in a fun filled manner.

Summary

It is indeed true that today children have to cope with higher educational standards, peer pressure, pressure to make it big in the world and of course way too much homework. Parents should put their foot down and bring it to the notice of the teacher in such cases and reduce the amount of homework being thrust on the child. If the child is however struggling with a subject like say geometry and hates doing homework in it simply because he/she finds it difficult, parents should assess the situation and get geometry tutors for geometry assignment help and homework help so as to help them tackle the subject better.

How To Get An A In Geometry With Ease?

Geometry is considered as a tough aspect of Math learning with its formulas and drawings. Once you understand how to pick up the basic concepts of Geometry with a firm   knowledge in its fundamental aspects, you can easily win an A in Geometry exams. Here are some basic steps for you to follow for stress free Geometry.

geometry students

  1. Asking questions

It is good to be interactive in your Geometry classes. When you do not understand an idea in Geometry, make it a point to ask your teacher at once in class. Make use of his office hours for your best learning.

  1. Be regular in your homework

Homework helps you measure your understanding of subject topics. Do it on time and review your understanding of Geometry topics.

  1. Group study

When you put your head together with those of others, you get better insights and clarify doubts without struggle.

  1. Use study tools and online resources

Suppose your text has an integrated website, use it.Use study apps that are available for free. Make use of online resources like online calculators through tutoring centers and lessen your burden in problem solving. Get the services of online Geometry tutors for making flash cards and remembering formulas.

  1. Frame mnemonic techniques to remember formulas

Use the first letters of a sentence to remember basic concepts in Geometry.

  1. Drill the important terms into your mind

Have a sound knowledge of the important Geometry terms. Remember right angles are 90 degrees and complementary angles are those angles which are added to take 90 degrees and supplementary angles make 180 degrees. All such factors should be retained in memory without fail.

  1. Prove the Geometry facts

Always question how a Geometry theorem comes true. Go step by step and prove it. This way, you can arrive at answers in exam papers even when you forget some important element in proving a Geometry concept.

  1. Drawing diagrams

Geometry is all about diagrams. If your want to learn angles, draw them. Use the graphics to your utmost advantage. See relationships like vertical angles through diagrams. It is easier to understand by doing so.

  1. Practicing problem solving

Geometry becomes easy through efficient problem solving. Geometry is a skill as well as treasure trove of knowledge. Practice problems as many as possible and concentrate more on troublesome areas. By doing homework in a systematic manner you can achieve this. This lifts you to an A without hassle.

  1. Teach Geometry to some other person

Ask your parent, friend or sibling to listen to you. Teach Geometry concepts to them. You can understand the concepts better for yourself.

  1. Practice different levels of problems

You need to change the order of problems and choose different sets with varying difficulty level. This helps you face Geometry challenges in the exam hall without fear.

  1. Be attentive in class

Do not deviate your attention from the lecture given by your teacher. You can talk to your friends afterwards.

  1. Study the lesson for the day beforehand

Cover the lesson before the class so as to be ready for clearing your doubts and following your teacher with ease.

  1. Studying every day

This is mandatory. Or you forget Geometry formulas and basic concepts and feel flabbergasted while sitting for exam prep. Make it every day for a straight A.

  1. Build your network with classmates and teachers for emergency help

Get the phone numbers and emails of class teacher and friends for contacting them at any crucial moment of preparation and for clarifying your doubts.

  1. Get a tutor for help

Get reliable online Geometry homework help to stay ahead of others in Geometry classes and exams. Do it at the earliest for a strong foundation in the subject.

Taking the assistance of online tutoring centers for Geometry assignment help lessens your burden and makes you climb up the ladder of success without stress and strain.

Math For Advanced Level; Algebra Geometry And Calculus Advanced

mathclass

Math is a combination of many branches such as Algebra, Geometry and Calculus, but math does not quite stop right there, we have levels to each branch of math such as beginners and advanced. The advanced level math usually needs more attention and practice to master it. If you are confident with the basics and know all your formulas then the advanced level math is the next step to beginner math topics. Today let us look at different advanced level math questions in areas such as Algebra, Geometry and Calculus.

Advanced level Algebra

Algebra consists of different algebraic expressions and equations. Algebra has different kind of questions to solve. Mentioned below are few such questions which will give you an idea about how to use the basics of algebra to solve advanced level questions:

Solving linear equations with one variable:

Find the value for x in equation 4 (2x – 3) = 5 (2x – 8)?

Here the unknown variable is x. Since there are numbers in front of the brackets, distribute the numbers as shown below:

math1

Here we have x on both sides of the equation, bring all like terms to the same side of the equation and solve for x.

math2

As show above the equation reduces to 2x = 28. Divide by 2 on both sides of the given equation. This gives x = 14.

Did you follow the solution to the question above? Now let us look at solving an inequality. Solving inequities play an important role in algebra. An inequality is where there is a comparison and is represented by a less than or greater than symbol. The solution to the inequality are usually represented on a number line, so as to represent all the possible values for the variable. Follow the given example below:

Solve the given inequality 3 (2 x + 8) > 24?

Look at the question we have greater than symbol here. You have to solve for the unknown variable x and find all the possible solutions for it. For the given question above, divide both sides of the equation by 3 as show below:

math3

Now the inequality is reduced to the form 2x + 8 > 16. The next step is to solve for x. follow the steps below:

math4

The inequality is now reduced to x > 4. Look at the symbol separating x and 4 it’s a greater than sign not greater than equal to. This implies that the number 4 is not included in the solution. Hence the solution of x contains all the values greater than 4 such as 5, 6, 7, 8…….. This can be represented on a number line as show below:

math5

The advanced level algebra consists of many other subtopics such as quadratic equations, solving two variable equations using substitution and elimination methods and many more. The key to success for solving all such questions is practice and knowing the basics of Algebra.

Advanced level geometry:

After algebra let us look into geometry and some sample question. Geometry is one of the favorite topic for all the students especially when you are in the elementary school, it could be because of learning different kinds of shapes. But geometry does not quite stop there, as you go to the higher grades you need to tackle the advanced level. Let us look at two examples on how the basics of geometry can be helpful to solve the advanced level geometry question.

 Find the area between the two shapes for the given geometric figure:

math6

The given diagram is a square inscribed in a rectangle. Let us recall the formula for the area of the rectangle = length x width. Using the formula, the area of the rectangle = 10 x 8 = 80 square inches.

Now the area of the square = side x side. Using the formula, the area of the inner square = 4inches x 4inches = 16 square inches.

The area between the two geometric figures is obtained by the difference in the areas.

Hence, the area = (80 – 16) square inches = 64 square inches.

Did you follow the solution? Great! The next question you will see how the sum of the angles can be used to find the missing angles of the triangle.

The sum of all interior angles of a triangle = 180 degrees. This fact is very commonly used in solving many geometrical questions. Knowing the angle measures helps you classify the different kinds of triangles such as equilateral, scalene, and isosceles.

In the given diagram, find the value of v and the angles of the triangle. Classify the triangle?

math7

Sum of all the angles of a triangle = 180 degrees.

Adding all the angles of the triangle v + 2v + 60 = 180. This gives 3v + 60 = 180.

Solve for the variable v, follow the steps below:

math8

The angles of the triangle are v = 40 degrees, 2v = 2 (40) = 80 degrees and the third angle is 60 degrees. Therefore, the angles of the triangle are 40, 60 and 80 degrees. Since all the angles of the triangle are different. The given triangle is a scalene triangle.

Advanced level Calculus

The next branch of mathematics which is very important and plays a major role in high school and college level math is calculus. The students are expected to know pre-calculus before stepping into calculus or advanced calculus. Calculus starts off form the basics of functions, domain, range and steps into differentiation and integration, which are the advanced level topics.

Let us take a quick look at few solved calculus questions:

Find the derivative to the function f (x) = 3x3 – 5x2 + 10?

Here before finding the derivative of the given question there are some formulas of derivatives which are expected to be known. Learn from the diagram below:

math9

Did you recall the formulas? Now apply the power rule to 3x3 and -5x2. Since 10 is a constant the derivative will be zero. Take a look at the diagram below:

math10

The answer f’(x) = 9x2-10x.

Taking a step forward, let us solve a derivative question involving logarithms and exponential functions.

Find the derivative of the function f(x) = x5 + 2ex + 3log x?

For the given question you can apply the power rule to x5, exponential rule for 2 ex and logarithmic rule for 3 log x. Use the formulas as mentioned in the diagram below:

math11

Applying the formulas to the given function:

math12

Hence the solution f’(x) = 5x4 + 2ex + 3/x.

Free Online Math tutor is the easiest way to get solutions for difficult Math problems. Tutor Pace provides effective Math tutoring and assignment help which are personalized and customized to meet student demands in one to one sessions.

How To Apply Concepts Of Algebra To Geometry?

In this particular article we have focused on a few properties determined in Geometry utilizing Algebra mathematics. You can definitely consult some kind of math homework help to know more in depth.

Concepts Of Algebra To Geometry

Give us a chance to take the case of a straight line. What do we watch? A straight line meets the X-Axis or the Y-Axis in any one among the four quadrants. A line can be plotted hanging some place in the center, yet dragging it whichever way would make it unquestionably meet in one of the four quadrants. Which properties are held by a straight line? A straight line converge either the y or x axis with a point. If this line makes a point of 90 degrees with the X-Axis, then it is parallel to the Y pivot or it is the Y-Axis itself. On the other hand if this line makes a point of 90 degrees with the Y-Axis then it runs parallel to the X pivot or can be the X-Axis itself.

Let us assume a point on hold as (X, Y), and explore the relationship in the middle of X and Y. Let us extend the point to the X and the Y pivot separately. Let the line converge the X-Axis at (C1, 0) and the Y-Axis at point (0, C).

Assuming a right triangle between the beginning and the two convergence focuses on the X and the Y axis where the straight line meets the two pivots. Let theta be the point made by the straight line and the X-Axis. By definition tan(theta) is equivalent to stature/base of a right triangle. So tan(theta) for this situation is only C/C1.

At some other point (X, Y) on the straight line tan(theta) is equivalent to Y/C1-X.

Likening both we get Y/C1-X= C/C1 so Y = C(C1-X)/C1 = – XC/C1 + C.

Since theta is the inside point made by the straight line with the X-Axis, the outside edge is equivalent to PI-Theta. Likewise, tan(theta) = – tan(PI-theta).

So if takes after that – C/C1 = tan(exterior point).

Y = tan(exterior point) * X + C. This is only the prevalent mathematical statement Y = M*X + C.


Presently apply some rudimentary variable based math to infer the Pythagoras hypothesis.

Consider a right triangle at the beginning with directions (0, 0), (a,0) and(0,b)

The hypotenuse’s length is only sqrt (a*a + b*b).

This is only the squares’ entirety of the other two sides, which is according to the Pythagoras hypothesis.

Now move to a circle, what are the properties of a circle. Any point along the circle is at a separation of r from the focal point of the circle. Let the focal point of the circle be at the birthplace. Take a point (X, Y) situated at any place on a circle. So the separation of that indicate the middle is sqrt(X *X + Y * Y) which is equivalent to r the span’s length.

So the mathematical statement of a circle is sqrt(X*X + Y*Y) = r or X*X + Y*Y = r*r.

By mixing Geometry with Algebra is presently termed as co-ordinate geometry.

Summing up things…

Both Geometry and Algebra are different branches of Mathematics. However, both share a strong relation in the form of Co-ordinate Geometry that needs to be learned through expert online math tutoring by consulting a well versed online math tutor. Let us know if you have more to share.

9 Must Know Methods for Solving Math Problems

Math has many topics and there are various kinds of questions related to each given topic. To solve a given math problem different kinds of methods and formulas can be used. Today, we will try to learn and understand 9 most basic and useful methods utilized while solving Math questions. Let us get started:

1. Method for calculating the LCM (Least Common Multiple)

Finding the least common multiple for the given numbers. I am pretty sure most of you have observed that LCM are part of problem solving for no matter which math topic you are working on. We need to calculate the LCM’s in simple topics like fractions, decimals and they may be also required to be calculated while solving questions in algebra, geometry and many more. Follow the example below:

What is the LCM of the two numbers 6 and 15?

For finding the LCM (least common multiple) first write the multiples for the given numbers.

Remember the 6 times table? Yes! They are all the multiples of number 6, so you have 6, 12, 18, 24, 30…. .

Now the 15 times table, don’t worry you need to check only till you get the common multiple.

So you have 15, 30, 45……………..

Did it strike a bell? Well look below for more clarity:

LCM

Hence the LCM for 6 and 15 equals to 30. (Sometime there can be more than one common multiple, always pick the least number as the LCM.)

2. Method for calculating the GCF (Greatest Common Factor)

Following the LCM is another interesting method in number theory. You guessed it right! The GCF (The greatest common factor.) For finding the GCF the Tree diagram method is very common. Here is a question: Find the GCF for the numbers 21 and 35? The first step is to write the tree diagram for 21 and 35. Try to follow the tree diagram below: GCF Using this tree method, you will get 21 = 3 x 7 and 35 = 5 x 7. (Note: 1 is always a factor for any given number.) Here 7 is the common factor for 21 and 35, which can be written once as its repeating in both the numbers. The Greatest common factor includes the remaining factors from both the numbers as well. Do not forget to include the 5 and 7. Hence GCF for 21 and 35 equals 3 x 5 x 7 = 105. After the LCM and the GCF, let us look at the method for changing the decimal numbers into fractions. Follow the example carefully:

3. Method of converting the decimal numbers into fractions

Convert the given decimal number 0.3 into a fraction. Here given to us is a decimal number. Count the number of decimal places. The number 0.3 has only one decimal place. Now while changing into a fraction multiply the numerator and the denominator by 10 for every decimal place. Here, since there is only one decimal place multiply by 10. Try to follow the diagrams below: decimal numbers into fractions Hence 0.3 can also be written as 3/10.

4. Method for solving Unit and Total Price word problems

Time to solve a work problem on price and money:

Anna and Ben went to a park. Anna brought 3 balloons and Ben brought 2 balloons. Find the total amount of money spent if each balloon costs $0.25.

For the given question you need to first calculate the total number of balloons Anna and Ben brought = 2+ 3 = 5.

Now comes the crucial point the decimal multiplication. Each balloon costs $0.25, so 5 balloons costs 5 x 0.25. Need help? Look at the diagram below:

Total Price

Hence the total price spent by Anna and Ben = $ 0.75.

Well problem solving is incomplete without equations. The next few methods will help you solve equations.

5. Method for solving one step equation using Addition

Find the value of y in the equation y – 6 = 12?

In the given equation 6 is subtracted from y. So the reciprocal operation needs to be applied to the equation. Add 6 on both sides of the given equation. This gives:

one step equation using Addition

Hence, the value of y = 18.

6. Method for solving one step equation using Subtraction.

Find the value of x in the equation x + 30 = 150? In the given equation 30 is added to x. So the reciprocal operation needs to be applied to the equation. Subtract 30 on both sides of the given equation. This gives: equation using Subtraction Hence the value of x = 120.

7. Method for solving one step equation using Multiplication

Find the value of y in the equation y/2 = 7? In the given equation y is divided by 2. So the reciprocal operation needs to be applied to the equation. Multiply by 2 on both sides of the given equation. This gives: equation using Multiplication Hence the value of y = 14.

8. Method for solving one step equation using Division

Find the value of x in the equation 5x = 45.

The given question has the equation with one variable x. I believe, by now did you get a hold of this method? The reciprocal operation of multiplication is division. Divide both sides of the equation by 5. This gives:

equation using Division

Hence the answer to the given equation is x = 9.

9. Method for solving Expressions using substitution

Now, what if there is an expression with more than one variables and you need to find the value of the expression. Here is what needs to be done:

Evaluate the value for the expression 4x – y, when x = 1 and y = 2.

Here for this question the method of substitution can be applied. You are given the value of x = 1 and y = 2. Hence substitute the values in the given equation to solve the question.

Not really sure how! Try to follow the diagram below:

Expressions using substitution

Much better, isn’t it! So after substitution here is how the expression will look like: 4(1) – 2 = 4 – 2 = 2. Hence the solution = 2.

We are not done yet! These were just few methods to get you started on solving math problems. To know more chat with a live Math tutor online and get more interesting details about the topic.

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Geometry for Special Education Students With Emerging Math Skills

Geometry for Pre Kindergarten and Primary Grade kids concentrates on some essential subject skills like recognizing, naming plane figures and naming their properties. Plane shapes are two dimensional shapes that are on a flat plane. They include curved shapes like ovals and circles and many sided shapes like polygons.

Children with disabilities find learning and applying vocabulary hard. They should be trained to use their acquired skills without hassle.

geometry shapes

Sorting shapes

Sorting shapes is the beginning place. Instead of using geometric shapes to sort colors, you can name a sort. This will help children with limited knowledge understand shapes with ease. You can say: “We are having the shapes that have the same number of sides” or “Now, we sort curved shapes and shapes with straight sides” This would help them sort shapes better.

Naming shapes

When you name shapes, you should make it clear that all squares are rectangles but all rectangles are not squares. You should make children understand that squares are rectangles with equal sides. A square is a sub category but it is frequently seen as a polygon in life and worksheets. So, students should be able to name it.

In kindergarten and primary grades like 1 and 2, students should be able to name squares, rectangles and circles.

Defining plane figures

Students have to name three specific characteristics of each space

  • Rectangle: A Rectangle has four sides .It has four sides with opposite sides which are equal in length and parallel. A rectangle has four angles in their corners (vertices).
  • Square: A square is a rectangle with four equal sides. It means that the opposite sides in a square are parallel, opposite sides are equal and all vertices are right angles.
  • Triangle; A triangle has three straight sides and three vertices. Its all sides meet to form a closed figure.
  • Circle: A circle is a closed shape with a curved line. All points in the one line are of the same distance from the center point.
  • Oval: An oval is a closed shape created by one curved side. One of the axes of the oval is longer than the other.

Thus teaching geometric shapes is an art. You need to do it with great care and reach out to young kids with proper techniques. If you chat with live Geometry tutor, you can know more strategies about the topics in Geometry and ways to get them across to kids for their better understanding.

Tips for Helping Your Children with Math Homework

Math Homework HelpGetting your child to do their homework can be a lot like trying to pull teeth. There may be a whole lot of resistance from the child but be patient. Learning is about improving ourselves, and even children understand that. They are always going about learning new ways to make this easier, or more intriguing or most of all, fun! So let’s approach the process from that perspective, shall we?

No Pressure

Children often feel a lot of pressure from adults and adults do not even realize when to pump the brakes a bit, but that is all a part of human nature. Children of course do need to be pressured, but in a positive way. What really works to motivate anyone is to show the short-term or long-term benefit to what it is that you are trying to accomplish. If you go in guns blazing trying to force pressure the child into learning the topic and you become frustrated, your child will in turn notice the negativity right away and begin to decide that they are being judged. They are right.
So avoid this tactic. Try to be open and understanding of their own learning process. Explain the logic of math problems in a way that will show them those benefits, how math is all around us, whether we are gauging our speed driving to school, measuring ingredients for a delicious snack or meal or counting the school supplies that we need. Specific examples really help children appreciate why we need to understand the concepts in mathematics, even at a basic level. They will be more enthused by this method and seek new ways to solve problems with more advanced math. A lot of this is just all about attitude and mentality.

Visual and Practical Models Work

Math is taught with great success in many Asian countries and many believe it is because of the way in which students learn the concepts and make the transition. It has been revealed that more visual representation matters to the student when discussing anything from simple basic addition/subtraction/multiplication/division to fractions and beyond. When they make a visual connection to the data, their brain can begin quickly deconstructing the logic behind the problem.
Ask your child to work out the problem aloud with you so you know their line of reasoning as well. This will help you understand their approach so you can teach them some new tricks. Again, be patient. The respect factor is exponentially higher with children when you are on their level and are actually helpful in their eyes. You should also work problems out aloud with them and do the same with everyday scenarios in life as you are going along your day with your kids. Explain concepts in everyday tone and language and relate it back to those school math problems they were working on.

Be Involved

It may seem obvious that you need to be involved in your child’s education, but moreover, try to be involved in their actual math problems and other studies. Make it your problem too. They will be more studious when they feel it is a group activity or game. Make it fun for them if you can by creating mini milestones like a bonus fun game for every successful problem solved or for finishing their homework. Remember how flash cards worked? The more colorful the cards the better by the way.
Being involved in all aspects of a child’s life is a great way to keep them involved in positive life activities as well. Your child will feel supported and confident knowing that their parents are there for them to help them when things get really tough. In math, when a problem is tough to understand, they may feel comfort in knowing that Mom or Dad can help guide them through it so they may understand it better. This helps a child’s confidence and self-esteem like no other.

Rewarding the Triumph

Children; just like pets, wild animals and grown adult humans; need to see the immediate benefits to the work behind learning a new skill, one that may seem mundane or useless in the form of numbers, symbols or expressions on a piece of paper or computer tablet screen.
When your child solves a problem, be sure to remember to try to challenge them to think of a way that problem can be implemented in the real world, or even better their world! When the child begins to unravel mysteries, not only will it excite and motivate them, they will be rewarded with pride and wisdom. They are never too young to understand this!

Get Access to free math lessons and math homework help online from basic math to algebra, geometry and beyond with the best online math tutors. Students, parents, teachers find these lesson plans to be very useful.

9 Secrets To Know About Speed And Mental Math Tricks And Techniques

Math is definitely challenging but what makes learning math fun and interesting is that, there are some tricks and techniques which can actually make the calculations easy to solve. Today, we will try to learn some math tricks which can be applied in solving different kinds of questions.

Speed And Mental Math Tricks

Multiplying a given number by 2

We all know the 2 times table. But what if 2 is being multiplied to a bigger number, there is a trick to make the multiplication quick and accurate. Think about it, multiplying by 2 it is nothing but doubling the given quantity. So to speed the calculations the given number can be added twice instead of multiplying by 2. For example 6 x 2 = 12.

This can also be got by 6 + 6 = 12. Now, if there is 32 x 2 = 64. This can also be got by 32 + 32 = 64.

Now applying this trick to bigger numbers multiplied by 2.

Find the value of 98340 x 2?

One method is the usual way of multiplying the given number by 2. But let us solve the same question with the trick of addition:

math 1

Hence 98340 x 2 = 1,96,680

Multiplying numbers which are multiples of 10

Did you know 10 is a very interesting number when it comes to multiplication? For example, in a question you come across a calculation such as 23 x 10 all you need to do is place a one zero next to 23. That is 23 x 10 = 230.

Can this be applied to bigger numbers as well? Yes it can! Let us look at some more examples:

While multiplying, 45 and 50 one method would be the regular multiplication. By applying the trick here all that needs to be done is 45 x 50, first find the value of 45 x 5 = 225. Since there is 50 which is a multiple of 10 place a zero next to 225.

So we get 45 x 50 = 2250. Another example would be, 25 x 30. Here first do 25 x 3 = 75. Now since there is 30 place a zero next to 75. This gives 25 x 30 = 750

Question: Sam brought 19 boxes of candies. Each box contains 200 candy bars, find the total number of candy bars in all the boxes.

Number of boxes of candies Sam brought is 19. Each box contains 200 candy bars.

Hence the total number of candy bars equal = 19 x 200.

Try to follow the diagram below for the calculation:

math 2

Multiplying a given number by 11

No matter what number is given to you multiplication with 11 can become quite simple, follow the trick here. Look at eleven, there are two 1’s. Now for example you have 14 x 11. First do 14 x 1 = 14 then to this add 140 which is 14 + 140 = 154?

So we get 14 x 11 = 154

Need a better idea? Follow the example below:

Find the value of 456 x 11?

Here first calculate 456 x 1 = 456 now add 4560 to it so you get 4560 + 456 = 5016

math 3

Adding three or more digit numbers

In some questions, you may have had situations where more than 2 numbers need to be added, it can get more tedious if they are big numbers. Let me share a little secret that can make adding such numbers much easier. For example there is a word problem: Riya spent $ 112 on shoes, $ 216 on bag and $315 on books. Find the total amount of money Riya spent on all the items. Solution: For the given question, the total amount of money spent equals the sum of all the given individual prices = $ 112 + $ 216 + $ 315. Follow the trick here, rather than adding the individual number. Add the hundreds place first. Follow the solution: math 4

Squaring number ending in 5

This rule is applicable from 5 to 95 only (i.e., 5, 15, 25, 35, 45, 55, 65, 75, 65, 75, 85, 95.) and here is how it works! We have 5 x 5 = 25.

The trick is, for a number ending in 5 when squared always has to end in 25. So for a given number example 152 pick the tens place, which is 1. Now the number after 1 is 2. Multiply 1 x 2 = 2. Now place a 25 next to 2. We get 225.

Now for 25 x 25. Here, 2 is in the tens place. What is the number next to 2, 3. So do 2 x 3 = 6. Now place a 25 next to 6. We get, 25 x 25 = 625.

Let us follow the diagram for clarity, take 65 x 65.

math 5

Hence 65 x 65 = 4225

Divisibility rule for number 2

Here is a quick mental math trick to find weather a given number is divisible by 2 or not just by looking at it. If a number is ending with an even number then it is divisible by 2.

What are all the even numbers between 0 and 9 (0, 2, 4, 6, and 8).

Look at an example: 48 here 8 is an even number so it is divisible by 2. Now 51 is not divisible by 2 as 1 is an odd number. Apply the same for big numbers.

Find out if 4576 is divisible by 2? Prove it!

Here 4576 is ending with number 6. Since 6 is an even number the given number is divisible by 2. Follow the diagram for a quick check:

math 6

Divisibility rule for number 4

Now that you are familiar with the divisibility rule for 2. Let us quickly check the divisibility rule for number 4. When it comes to 4 always check whether the last 2 numbers are divisible by 4. Consider 324 here it’s clearly know that 24 is divisible by 4 so 324 will be divisible by 4. Now let me give you another example:

Find out whether 5608 is divisible by 4? Check your answer.

Here again use the trick and figure it your mind. 08 are the last two numbers of the given number. Since 08 is divisible by 4, 5608 is divisible by 4. Let’s check if we got it right look at the diagram below:

math 7

Divisibility rule for number 5

Did your math calculations get faster on the divisibility part? Now let us follow the trick for checking divisibility with number 5. For number 5, the given number should end either with 0 or 5. Take an example of 560 it is divisible by 5 since its ending in 0. Whereas 432 is not divisible by 5 since its ending with 2 not 0 or 5. Look at the following question.

Find out if 890 is divisible by 5? Check your answer.

Here the given number 890 is ending in 0, so it is divisible by 5. Let us check the answer, follow the diagram below:

math 8

Combining the like terms

Many students find adding and subtracting like terms very confusing. Let us look at a simple way of solving this kind of a question. Did you know there is a trick with which you can solve the combining like terms in your mind? Here is what can be done:

Consider a question for finding 5x + 6x.

A like term is a term which have the same variable. Here it is x. Now for adding 5x and 6x since x is the same, just find 5 + 6 = 11. Hence 5x + 6x = 11x.

Did you follow the solution? Follow the next example:

Find the value of 3x + 7x + 10x?

All that needs to be done is add the numbers and place the common variable x next to the sum. Take a look at the diagram below:

math 9

Hence the solution is 20x.

Therefore, practice these tricks and apply them in your math calculations. You will be amazed how they will aid in speeding your calculations. If you still need help, chat with a Live Math Tutor Online Now!

Tips To Remember How Math Logarithmic Notation Works

Logarithms are really fun and interesting, but I have seen many students find changing logarithmic notation to exponential notation and vice versa quite confusing. Well here are some useful tips to make you remember that this conversion is simpler than you have expected.

The exponential form is where we have the base number multiplied according the exponent to get the answer. Here is an example from online math tutor:

When you multiply 2 four times you get 16. That is 2 x 2 x 2 x 2 = 16.

This can be written in the exponential form as 24 = 16. Let’s look deeper into this notation:

log1

Let’s now try to follow how we can convert the exponential notation to the logarithmic notation:

log2

As show above, both the exponential notation and the logarithmic notation have the same base number. Next, there is an exchange in the exponent and answer while writing it in the logarithmic notation.

This can be better understood with an example:

Convert 34 = 81 from an exponential notation to logarithmic notation.

Here 3 is the base number which will remain the same even in the logarithmic form.

We have 4 as the exponent and 81is the answer which can be written as:

log3

Did you get a little hold of this method? Good let me show you one more example:

Convert 52 = 25 from exponential form to logarithmic form.

Everyone likes the 5 times table, for some reason it’s quite easy to memorize.

Here observe 5 is the base number and 2 happens to be the exponent. Multiplying 5 x 5 gives 25 as the answer. Now converting the exponential form to logarithmic form:

4-1hp6teb

Taking a step further, let us now convert the logarithmic notation into exponential notation applying the same process backwards.

Convert log4 64 = 3 from logarithmic notation to exponential notation.

Here the given logarithmic notation can be changed to exponential notation by keeping the base number 4 the same. Follow the steps below:

log5

Hence the exponential notation for the given question is 43 = 64.

Good so far! Now, have you ever observed some logarithms written without a base?

For example, notations like log 5, log 16 or log 150. Are they really without any base number? The answer is NO! They have a base number which is 10 it’s called the common base.

Hence, logarithms with base number 10 are called common logarithms. This can be shown as below:

log6

Convert the given exponential form 103 = 1000 to logarithmic form?

Here we have the base number for the exponential form as 10, so the final answer will be a common logarithm. Hence we can write the given question into a logarithmic notation as follows:

log7

So the final answer is log (1000) = 3. [Not to forget it still has a base 10.]

Now you are familiar with the logarithmic notation and ready to change exponential notation into logarithmic notation. But remember logarithms does not stop here, these are just few useful tips to get you started with the logarithmic notation.

Read more – Solving Logarithmic Equations

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