Become An Amazing Math Tutor: The Secret To Metal Math

Math is a very interesting and innovative subject, we start learning it from a very young age and use it all our lives. The secret to metal math can be understood when you want to solve questions much faster and efficiently. This can be applied for both the students and tutors. Often we wonder why the same question is solved by different people in different ways. This is the beauty of math, there are many ways and approaches to get to the same answer. One method can take more time and many steps whereas another method can take less time and fewer steps to reach the final answer. The thing to realize here is all the different approaches are right and you can follow which ever method best suits your ability to understand the given question.

Let us now take a look at some mental math tricks which will help you while solving different math homework help questions.

While changing the percentages to fractions, divide by 100 and for changing a given fraction to percentage multiply by 100. Here are some examples:

Betty went to trekking with her friends. She drank 75% of the protein shake she brought with her after trekking for 3 hours. What fraction of the protein shake does she have left?

For the above question we are given that 75% of the protein shake is finished. This implies the remaining amount is equal to 100% – 75% = 25%.

Therefore, the amount of protein shake Betty has = 25%. For converting the given percentage into a fraction divide by 100. math help 1 Hence Betty still has 1/4 of the protein shake remaining during her trekking.

Did you find the example quite interesting? Now let us look at another example for changing fractions to percentages.

Samuel finished 1/5 of his homework. What percentage of his homework is still to be completed?

Here you are given that 1/5 of the homework is completed. This implies the amount of homework to be completed is 1 – 1/5 = 4/5.

Now for converting the fraction into a percentage multiply by 100. Follow the diagram given below and try to visualize the calculations mentally:

math help 2

This method mentioned above is very useful because percentage are used almost in every branch of mathematics. Let us look at some quick applications of what we have just learned:

Percentage to fraction:

math help 3

The above examples are for percent to fractions which can be quickly solved in your mind. Practice similar questions to realize how you will become much faster and efficient in your calculations.

Fractions to percent: Below examples are for quick conversion from fractions to percentages. math help 4 After the percentages, let us take a look at how the fractions can be changed to decimals. Do you feel you already know them? Well remember, we are trying to learn the metal math. Here is how you can convert them in your mind. Take a look at the following questions:

Fractions to decimals: Change the fraction 2/5 into a decimal number. Here the given fraction is 2/5. The mental math trick is, for changing any given fraction to decimal number try to have 10 or multiples of 10 in the denominator. Multiply the numerator and denominator if the fraction 2/5 by 2. Follow the diagram below: math help 5 Did you follow the method? This trick has limitation though it can only be applied to the numbers which get 10 or multiples of 10 in the denominator via multiplication. Let us look at more examples to perfect this method.

Convert 7/25 into a decimal number.

Look at the denominator here its 25, which can be changed to 100 on multiplication by 4. Hence multiplying and diving the given fraction by 4. Follow the diagram below, this needs to be visualized mentally.

math help 6

Therefore the fraction 7/25 can be written as 0.28 in the decimal form.

Let me share another branch of math, Algebra where mental math tricks can be applied.

Adding the exponents: Combine the expression 3x4 (x5) Here for the given expression we have multiplication between the same variable x which needs to be combined. Since the base variable is the same for the given exponents add the powers. Here is the rule: math help 7 Subtracting the exponents: Combine the expression 2x11/ x9. Here for the given expression we have division between the same variable x which needs to be combined. Since the base variable is the same for the given expressions subtract the exponents of x. Here is the rule: math help 8 Multiplying the exponents: Combine the expression (x3)5? Here for the given expression we can combine exponents of the variable x by multiplying since they are raised to the same base. Follow the diagram below: math help 9

Therefore, today we looked through different methods and examples for solving math mentally. Use these methods to solve different questions whenever and wherever applicable. For more info you can chat with live math tutor online and get your math assignment help from amazing math tutors.

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:


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.


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!

6 Milestones on the Road to College

6 Milestones on the Road to CollegeFinding out the best & getting into the preferred college is one of the biggest challenges for parents and their children after the high school education. It’s not an easy task for everyone to achieve desired goal without any skill and knowledge. Thus, it is very important to preparing during high school education both academically and financially to deal successfully with college days challenges. To reduce some stress & overcome upcoming difficulties, you can arrange a meeting with counselor and discuss all the important courses to take throughout high school, summer tutoring opportunities as well as extracurricular activities. Indeed, students can register for & take SAT subject test, PSAT/ACT and Reasoning test.

Parents can assist their child create well-versed decisions about his/her education, learn about colleges, perform well academically and discover the best possible opportunities for the college education. Usually, people need to pay attention to each critical step as well as plan ahead along their route to college.

Have a look at the 5 important milestones along your way to college that can help you reach at your preferred destination!

Ready to Face Challenges & Become a Skilled College Candidate During high school education in 9th, 10th, 11th and 12th Grade, students get the better opportunity to learn about the different subjects & prepare for college. Meet with career counselor or guidance counselor in the early hours to lay out a plan to get the toughest & challenging academic courses viable for you. Thus, with the aim to become a strong college candidate, take challenging classes of different subjects like Mathematics, Physics, English, Economics, Science, Arts, History, Civics, Chemistry, Geography and a Foreign Language. In this way, you can improve your basics in all important courses and get the top grades during high school education.

Make a Plan & Start Saving for College Education Financing for college is one of the significant & critical situations for parents. Thus, it is advantageous to build up a financial plan as soon as possible by determining an affordable college education cost to pay per year. Along with this, you also need to consider how much total debt is reasonable to carry once your child will graduate, and who will refund it. Also, determine all additional cost and find out the sources like student education loan, students & parent loans, need-based aid as well as scholarships. In order to reach at the final decision, you can arrange a meeting with a financial planner or tax professional. A financial expert can assist you in all ways to determine what you can afford to spend on college education of your child without sacrificing your future. Moreover, you can also explore different ways to save money like investing in mutual funds, open a saving account in a bank, etc.

Register for and Take the Standardized Test

Participating in standardized testing is one of the very efficient ways to show your skill set, knowledge as well as strength. For this, you must register early on and take the PSAT/NMSQT (Preliminary Scholastic Assessment Test/National Merit Scholarship Qualifying Test), ACT (American College Test), SAT Subject Tests, SAT (Scholastic Assessment Test), or any other competitive exams required for admission in your preferred list of the best colleges. If you are not able to pay registration fee, you can contact your counselor with reference to getting a fee waiver.

Attend Summer Opportunity Fairs, Seminars, Interviews & Schedule College Visits

If you want to learn about types of colleges and their opportunities, qualities as well as differences, then it is better to visit career fairs, attend seminars, face interviews and pursue community-based extracurricular activities or summer opportunities according to your knowledge & skill set. Indeed, you can also attend college meetings held by representatives & experts. After comparing all the essential qualities, facts & financial figures, you can easily narrow down the college list & choose the best one as per your preferences and affordability. After selecting your college, prepare & fill your application form or admission form carefully with complete information & required documents. Moreover, follow the given instructions & pay close attention to applicable deadlines in order to form submission.

Investigate the Availability of Financial Aid & Apply for Scholarships

One of the most important milestones along your way to college is conduct an inquiry about the availability of financial aid from state, private, federal, and local sources for college students. For more information & in-depth inquiries, you can meet or contact your guidance counselor. To gather more info, go to the library & try to find directories of scholarships for disabled students, women as well as minorities. You can also apply for scholarships. There are many organizations inside and outside the colleges offer scholarships such as professional associations, corporations, credit unions, religious organizations, and labor unions.

Make a Final List to Apply for College:

Start applying to the colleges that you have sorted on your final list. You can begin the application process by writing application essay, which tend to help colleges get to know you. Pick an essay writing on the topic you are familiar with and confident of writing it down. Complete and then apply to those colleges where you are competitive.

Start getting higher grades from your first day of college. Signed up for an online college tutoring programs today.

How to Solve Algebra Word Problems in 5 Steps

For solving Algebra word problems you need to use your logic and find out answers for the problem. Here are 5 steps that help you solve Algebra problems with ease

  1. Identify the problem
  2. Identify what you know
  3. Make a plan
  4. Carry out the plan
  5. Verify whether your answer makes sense

Step 1

Identify the problem

The steps for identifying the problem are

  • Express the problem question or statement.
  • Identify the unit of the final answer.
  • Express the problem question or statement.

You find Algebra word problems in the form of a question or statement.


Question How many saplings Brown needs to plant? How many televisions Brenda needs to sell to earn $20000?

Statement Find the number of saplings Brown has to plant. Solve for the number of televisions Brenda has to sell to earn $20000.

  • Identify the final unit of the answer

After understanding the purpose of the word problem, try to find out in what unit the answer will be like miles, ounces, pesos, number of trees or number of televisions.

Example for step1

Christiana is making brownies to serve at the family picnic. If the recipe calls for 21/2 cups of cocoa to serve 4 people, how many cups will she need for 60 people who attend the picnic?

  • Identify the problem: how many cups Christiana needs if 60 people attend the picnic?
  • Identify the final unit of answer: Cups

 Step 2

Identify what you know

I need more information What information you have is not adequate and you need more information.

Example for step 2 

Sarah is carpeting a rectangular room in her house. The length of the room is(x+2) feet and the breadth of the room is (x-6) feet and the area of the room is 84 square feet. Find the length and width of the room. Identify what you know

  • Sarah is carpeting a rectangular room
  • The length of the room is x+2
  • The breadth of the room is x-6
  • The area of the room is 84 square feet.
  • The formula for the area of a rectangle is A=lw
  • I need to find x to find the length and breadth of the room.

Step 3

Make a plan

Methods of building your plan

  • Write down your plan
  • Talk about your plan
  • Make a table
  • Draw a bar graph, line or circle
  • Draw any other type of graph
  • Draw a picture

Example for step 3

The Damsels Theater expects 275 patrons every weekend per new movie. How many new movies they will show if they expect 2200 patrons this week end?

  • For every new movie, 275 patrons come to Damsels Theater
  • 1 movie     =275 patrons
  • 2movies =275*2=550 patrons
  • 3 movies=275*3=825 patrons
  • 275*number of movies=2200 or 275*m=2200(m represents the number of movies)
  • Solve for m to find the answer

Step 4

Carry out the plan

Verify whether the plan is sensible. Check whether you have not missed anything or did not approach the problem in the wrong manner.

Example for step 4

Ben and Jack run a combined distance of 28 miles. Ben runs three times as many miles as Jack. How many miles does Jack run?

The plan

  • B+J=28 where B represents the number of miles run by Ben and J represents the miles run by Jack.
  • B=3*J because Ben runs three times as many miles as Jack.
  • Replace B with 3*J in the equation B+J=28

Carry out the plan

  • 3*J+J=28
  • 4*J=28
  • Solve for J: J=7

Step 5

Verify whether your answer makes sense

In the last step you have two red flags that signal wrong answers

  • Your answer is too big or too small
  • The question remains unanswered

Example for step 5

John is driving from his house to his company. On Monday morning John drives 6 miles north on Peter’s road. Then he drives 8 miles east on Willie’s Road to reach his company. On Tuesday morning, John avoids Peter’s and Willie’s Roads. What is the difference between the number of miles John drives on Monday and Tuesday mornings?

John’s drive to his company resembles a right triangle. You can use Pythagorean Theorem.geometry10 miles is the answer

Verify whether your answer makes sense

No. The answer is the direct distance between John’s company and house. It is not the answer for the question what is the difference between the number of miles John drives on Monday and Tues day mornings?

Make a new plan

  • Find the direct distance
  • Add 6 miles and 8 miles to find the total distance traveled on Peter’s and Willie’s Roads
  • Find the difference between the numbers in steps 1 and 2
  • Distance between the company and house is 10 miles
  • Distance traveled on Peter’s and Willie’s Roads is 6+8=14miles
  • Difference between the numbers 14-10= 4 miles

The answer is correct as per arithmetic and it makes sense.

Doing Algebra word problems through step by step approach is logical easy and fun.


Expert Online College Algebra help: Tailored as per Your Convenience

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