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.


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