# 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.

### 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:

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:

### 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

### 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:

### 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.

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:

### 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:

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:

### 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.

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

### 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.

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:

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:

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

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:

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:

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:

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:

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:

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

# Perfect Square Trinomial Calculator – For Some Fun With Algebra

Algebra is mind whirling and messy to many and it would most certainly be a surprise when hears the word fun associated with algebra. You can have just that with a perfect square trinomial calculator. Using this online tool, it is ever so easy to find the trinomial expression corresponding to a binomial that is a perfect square. Learning this important concept in a fun way can ensure complete understanding and retention and given its uses, it will do the learner a world of good!

Algebra is quite an important branch of study in math and finds applications in varied branches of science and math. It is a fundamental subject that is used in trigonometry, calculus, geometry and many other branches of math as well. Its use in subjects pertaining to science streams such as physics, chemistry and astrology need no expounding upon. It is thus important to learn the subject well. Thus, learning the subject well is of immense importance!

A perfect square trinomial calculator is a fun way to learn an important concept in algebra! Read on to find out more.

### What is a perfect square trinomial?

A perfect square trinomial is simply a trinomial that is obtained from a binomial that is a perfect square.

For instance, if a trinomial: Ax2+Bx+C is a trinomial and can be expressed as (x +D)2, then it is said to be a perfect square trinomial.

Note: A,B and C are non zero constants here.

An online perfect square trinomial calculator can help evaluate either the trinomial expression or arrive at the perfect square binomial. If you specify A,B and C in the equation, the calculator will give the (x +D)2 and when you specify D, it will give you the Ax2+Bx+C equation.

Let us understand this with the help of a few examples.

Example 1: Evaluate expression (x+15)2.

Solution:

D = 15. We need to find A,B and C.

Theoretically, we will work it out as follows:

(a + b)2 = a2+2ab+b2

Hence, (x+15)2 = x2 + 2(x)(15) + 152 = x2 + 30x + 225

Example 2: Evaluate the binomial expression from the trinomial x2 + 8x + 16

Solution:

A=1, B=8, C=16

C can be written as 4*4 = 42

B can be written as 2*1*4 = 2*a*b where a=1, the coefficient of x2 and b=4 corresponding to a2+ 2ab + b2

Thus, x2 + 8x + 16 can be written as (x+4)2

With an online perfect square trinomial calculator, you needn’t indulge in all these calculations! Just feed the value of the coefficients in the problem and you will arrive at the solutions instantly!

Algebra is a no fun and nightmarish subject for many. Learning algebra can be made fun with online tools such as a perfect square trinomial calculator. By just feeding the value of the coefficients, one can find the corresponding perfect square binomial to the given trinomial expression and vice-versa. Simply put, this calculator makes homework and algebra so much easier for students and is a fun way of learning the associated concepts.