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## How to Solve Math Problems Faster: 15 Techniques to Show Students

Here are 15 techniques to show students, helping them solve math problems faster:

## Addition and Subtraction

The first step is to add what’s easy. The second step is to add the rest.

With this fast technique, big numbers won’t look as scary now.

## 2. Two-Step Subtraction

There’s a similar method for subtraction.

Remove what’s easy. Then remove what’s left.

Instead of two complex numbers, students will only have to tackle one.

## 3. Subtracting from 1,000

You can give students confidence to handle four-digit integers with this fast technique.

Let’s say students must solve 1,000 – 438. Here are the steps:

This also applies to 10,000, 100,000 and other integers that follow this pattern.

## Multiplication and Division

Using 33 x 48 as an example, here’s the process:

The only prerequisite is understanding the 2 times table.

## 5. Multiplying by Powers of 2

This tactic is a speedy variation of doubling and halving.

Here’s what to do: For each power of 2 that makes up that number, double the other number.

## 6. Multiplying by 9

But there’s an easy tactic to solve this issue, and it has two parts.

Despite more steps, altering the equation this way is usually faster.

There’s an easier way for multiplying two-digit integers by 11.

Let’s say students must find the product of 11 x 34.

It’s multiplication without having to multiply.

## 8. Multiplying Even Numbers by 5

This technique only requires basic division skills.

The result is 30, which is the correct answer.

It’s an ideal, easy technique for students mastering the 5 times table.

## 9. Multiplying Odd Numbers by 5

This is another time-saving tactic that works well when teaching students the 5 times table.

This one has three steps, which 5 x 7 exemplifies.

## 10. Squaring a Two-Digit Number that Ends with 1

Squaring a high two-digit number can be tedious, but there’s a shortcut if 1 is the second digit.

There are four steps to this shortcut, which 812 exemplifies:

- Subtract 1 from the integer: 81 – 1 = 80
- Square the integer, which is now an easier number: 80 x 80 = 6,400
- Add the integer with the resulting square twice: 6,400 + 80 + 80 = 6,560
- Add 1: 6,560 + 1 = 6,561

## 11. Squaring a Two-Digit Numbers that Ends with 5

Squaring numbers ending in 5 is easier, as there are only two parts of the process.

First, students will always make 25 the product’s last digits.

Just like that, a hard problem becomes easy multiplication for many students.

## 12. Calculating Percentages

The result is 113.75, which is indeed the correct answer.

This shortcut is a useful timesaver on tests and quizzes.

## 13. Balancing Averages

With practice, this method may not even require pencil and paper. That’s how easy it is.

## Word Problems

This isn’t a trick. It’s a tactic.

Teach students to look for these buzzwords, and what skill they align with in most contexts:

As a result, they should have an easier time processing word problems .

## 15. Creating Sub-Questions

Each student should ask him or herself:

- What am I looking for? — Students should read the question over and over, looking for buzzwords and identifying important details.
- What information do I need? — Students should determine which facts, figures and variables they need to solve the question. For example, if they determine the question is rooted in subtraction, they need the minuend and subtrahend.
- What information do I have? — Students should be able to create the core equation using the information in the word problem, after determining which details are important.

These sub-questions help students avoid overload.

## Final Thoughts About these Ways to Solve Math Problems Faster

Showing these 15 techniques to students can give them the confidence to tackle tough questions .

A rewarding class equals an engaging class . That’s an easy equation to remember.

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## 10 Ways to Do Fast Math: Tricks and Tips for Doing Math in Your Head

If it’s your job to teach those, here’s a great refresher.

## 10 tricks for doing fast math

## 1. Adding large numbers

650 – 644 = 6 and 240 – 238 = 2

Now, add 6 and 2 together for a total of 8

To find the answer to the original equation, 8 must be subtracted from the 890.

So the answer to 644 +238 is 882.

## 2. Subtracting from 1,000

Step 3: Subtract 6 from 10 = 4

## 3. Multiplying 5 times any number

When multiplying the number 5 by an even number, there is a quick way to find the answer.

- Step 1: Take the number being multiplied by 5 and cut it in half, this makes the number 4 become the number 2.
- Step 2: Add a zero to the number to find the answer. In this case, the answer is 20.

When multiplying an odd number times 5, the formula is a bit different.

- Step 1: Subtract one from the number being multiplied by 5, in this instance the number 3 becomes the number 2.
- Step 2: Now halve the number 2, which makes it the number 1. Make 5 the last digit. The number produced is 15, which is the answer.

## 4. Division tricks

Here’s a quick way to know when a number can be evenly divided by these certain numbers:

- 10 if the number ends in 0
- 9 when the digits are added together and the total is evenly divisible by 9
- 8 if the last three digits are evenly divisible by 8 or are 000
- 6 if it is an even number and when the digits are added together the answer is evenly divisible by 3
- 5 if it ends in a 0 or 5
- 4 if it ends in 00 or a two digit number that is evenly divisible by 4
- 3 when the digits are added together and the result is evenly divisible by the number 3
- 2 if it ends in 0, 2, 4, 6, or 8

## 5. Multiplying by 9

This is an easy method that is helpful for multiplying any number by 9. Here is how it works:

Let’s use the example of 9 x 3.

Step 1 : Subtract 1 from the number that is being multiplied by 9.

The number 2 is the first number in the answer to the equation.

Step 2 : Subtract that number from the number 9.

The number 7 is the second number in the answer to the equation.

## 6. 10 and 11 times tricks

There is also an easy trick for multiplying any two-digit number by 11. Here it is:

Now add those two numbers together and put the result in the center:

There is the answer to 11 x 88: 968

## 7. Percentage

- Step 1: Move the decimal point over by one place, 235 becomes 23.5.
- Step 2: Divide 23.5 by the number 2, the answer is 11.75. That is also the answer to the original equation.

## 8. Quickly square a two-digit number that ends in 5

Let’s use the number 35 as an example.

35 squared = [3 x (3 + 1)] & 25

## 9. Tough multiplication

Step 1: Divide the 20 by 2, which equals 10. Double 120, which equals 240.

Then multiply your two answers together.

The answer to 20 x 120 is 2,400.

## 10. Multiplying numbers that end in zero

Step 1: Multiply the 2 times the 4

Step 2: Put all four of the zeros after the 8

## You may also like to read

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## How to Solve Percent Problems? (+FREE Worksheet!)

Learn how to calculate and solve percent problems using the percent formula.

## Related Topics

- How to Find Percent of Increase and Decrease
- How to Find Discount, Tax, and Tip
- How to Do Percentage Calculations
- How to Solve Simple Interest Problems

## Step by step guide to solve percent problems

- In each percent problem, we are looking for the base, or part or the percent.
- Use the following equations to find each missing section. Base \(= \color{black}{Part} \ ÷ \ \color{blue}{Percent}\) \(\color{ black }{Part} = \color{blue}{Percent} \ ×\) Base \(\color{blue}{Percent} = \color{ black }{Part} \ ÷\) Base

## Percent Problems – Example 1:

\(2.5\) is what percent of \(20\)?

## Percent Problems – Example 2:

\(40\) is \(10\%\) of what number?

## Percent Problems – Example 3:

\(1.2\) is what percent of \(24\)?

## Percent Problems – Example 4:

\(20\) is \(5\%\) of what number?

## Exercises for Calculating Percent Problems

- \(51\) is \(340\%\) of what?
- \(93\%\) of what number is \(97\)?
- \(27\%\) of \(142\) is what number?
- What percent of \(125\) is \(29.3\)?
- \(60\) is what percent of \(126\)?
- \(67\) is \(67\%\) of what?

## Download Percent Problems Worksheet

- \(\color{blue}{15}\)
- \(\color{blue}{104.3}\)
- \(\color{blue}{38.34}\)
- \(\color{blue}{23.44\%}\)
- \(\color{blue}{47.6\%}\)
- \(\color{blue}{100}\)

by: Reza about 3 years ago (category: Articles )

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## How to Solve Math Problems Faster: 12 Techniques to Show Students

Marta Sebos 26/10/2022 Education

## Addition and Subtraction

## 1. Two-Step Addition

You can add 7 to 493 to make it 500 and then subtract 7 from 87. Now add 500 and 80. That is 580.

## 2. Two-Step Subtraction

## 3. Subtracting From Thousand

## 4. Multiply with the power of 2

So, it is a simple method to multiply the numbers in fragments.

## 5. Double and Halve

Here is how you can calculate that simply:

## 6. Multiply even Numbers by 5

## 7. Multiply Odd Numbers by 5

## 8. Multiply with 9

## 9. Square Two-Digit Number That Ends with One

## 10. Calculate the Percentage

## 11. Balance Average

## 12. Know the Buzzwords

- Addition: Sum, a total of, increased by, combined, more than.
- Subtraction: Difference of, less than, fewer than, reduced by.
- Multiplication: The product of times.
- Division: the ratio of, out of, the quotient of, per.

Tags learning Math problems Students Studying Subtracting

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## 1. Break Down Complex Problems

## 2. Master the Basic Math Skills

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## How to Improve Your Mathematical Calculation Skills

Last Updated: September 13, 2022 References Approved

## Practicing the Fundamentals

- You can find speed tests online or in your local school supply store. Typically, there will be 50 problems on a single sheet that you will work through.
- Work as fast as you can to finish and then go back to check your work. The worksheets should take you less than 3 minutes per test page. Set a timer to stick to the 3-minute limit.
- Aim for accuracy above time, but eventually you will only to have to focus on how fast you can get the right answer out.

- Rather than finding multiplication tables to print out, create your own. The practice of writing the table out will start to work the numbers into your memory even sooner. Write them out at least 7 times before sticking to 1 of your sheets to study.
- Keep working on the tables until you just remember what 6 x 13 is, for example. You should not have to work out the math for any of the 256 combinations.
- You can find multiplication speed tests similar to the addition and subtraction ones as well online and in school supply stores. After reviewing the tables sufficiently, work up to the timed tests.

- Having this type of recall will also help you to recognize when a number won’t be evenly divisible. For example, you might see 127 / 14 and remember that this is almost the even division of 126 / 14 = 9. Since the numerator is slightly off, you will know to resort to working out the problem.
- Knowing that 127 is larger than 14 x 9 will help you to immediately realize that the answer is going to be slightly larger than 9!

## Using Other Methods to Calculate

- Instead of dealing with writing down the multiplication and work right-to-left, you can realize that you’re looking for 125 x (10 + 5) = (125 x 10) + (125 x 5) = (125 x 10) + (125 x 10 / 2).
- By breaking the problem down to one simple calculation of 125 x 10, one division by 2, and one addition, you avoid a trickier multiplication.
- Always look for ways to use simpler calculations or memorized multiplication tables, for instance, to simplify a harder calculation.
- Understanding these component parts can then be applied to leaving a 15% tip, for example, and all you have to do is move some decimal places afterward.

- Challenge yourself to work on areas that you notice you struggle in. If fractions tend to give you a hang up when calculating, spend a week or two just doing fraction calculations.
- Even just looking at multiplication tables or worked out problems is beneficial. Eventually, you will start to notice patterns and new ways to deconstruct problems you didn’t see before.

- Although fingers can be a quick way to hold a number aside during a calculation, try to rely on the visual memory or even auditory memory instead.
- Testing yourself by not relying on a calculator or even writing the numbers down will help with your working memory, number recall, and even visual/spatial skills.

## Community Q&A

## You Might Also Like

- ↑ https://education.jlab.org/smadd/
- ↑ https://www.mathsisfun.com/tables.html
- ↑ https://www.manhattanprep.com/gmat/blog/2012/05/09/everyday-ways-to-improve-your-mental-math-skills/
- ↑ https://www.mathsisfun.com/multiplication-tips-tricks.html
- ↑ https://guides.lib.uoguelph.ca/MathWithoutCalculator
- ↑ https://www.ldatschool.ca/evidence-based-interventions-for-math/

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## These four easy steps can make you a math whiz

Assistant Professor of Education Studies, University of Oregon

## Disclosure statement

## Math Pólya’s way

Pólya’s problem solving plan breaks down to four simple steps:

- Make sure you understand the problem.
- Make a plan to solve the problem.
- Carry out the plan.
- Check your work to test your answer.

There it is. Problem solving in the palm of your hand – math reduced to four steps.

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Here are 15 techniques to show students, helping them solve math problems faster: Addition and Subtraction Many students struggle when learning to add integers of three digits or higher together, but changing the process's steps can make it easier. The first step is to add what's easy. The second step is to add the rest.

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This method will solve the problem quickly. For instance, consider 20 x 120 Step 1: Divide the 20 by 2, which equals 10. Double 120, which equals 240. Then multiply your two answers together. 10 x 240 = 2400 The answer to 20 x 120 is 2,400. 10. Multiplying numbers that end in zero Multiplying numbers that end in zero is actually quite simple.

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To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem. en. image/svg+xml. Related Symbolab blog posts.

Taking the time to identify your problem type is essential to finding the best way to solve the problem. [1] 2 Read the problem carefully. Even if the problem seems simple, read it very carefully. Don't just skim the problem and attempt to solve it.

The dirty little secret is that to solve math problems quickly, you must have seen similar problems in the past and memorized the corresponding techniques and tricks. Entirely original solutions are very difficult to come by and are usually made a big deal of.

Step by step guide to solve percent problems. In each percent problem, we are looking for the base, or part or the percent. Use the following equations to find each missing section. Base = Part ÷ Percent = P a r t ÷ P e r c e n t. Part = Percent × P a r t = P e r c e n t × Base. Percent = Part ÷ P e r c e n t = P a r t ÷ Base.

#fastmathtricks#mentalmath#mathtrick Using this math trick for fast calculation you will be able to multiply any pair of three digit numbers with each other ...

How to Calculate Faster than a Calculator - Mental Maths #1 mathOgenius 3.1M views 2 years ago Fast Math Tricks | Multiply 2 Digit No having Same Tens Digit & Ones Digits Sum is 10 | Vedic...

We can follow some easy and simple tricks to get it right. 1. Two-Step Addition Students often face difficulties in adding integers above two digits. In such cases, add a number that makes it easy and then add the rest. For example, a student needs to make a sum of 493 and 87. You can add 7 to 493 to make it 500 and then subtract 7 from 87.

This pre-algebra video tutorial explains the process of solving two step equations with fractions and variables on both sides. It also explains how to solve 2-step equations with parentheses...

There is always an easier way to solve a problem. Go to the heart of any complex mathematical problem by dividing any complex Problem. Try to simplify them by breaking them down to the most basic form. Get Help from the top homework help in Canada to know more about it. 2. Master the Basic Math Skills

FAST Problem Solving Stands for Facts, Action, Solve, Thinking. The students solve all word problems using this method. The students draw four quadrants and fill in each section as necessary. We practice this each day with a word problem and the students solve it in their math journals.

Ever wondered how some people can solve seemingly complex math problems in seconds? Learn their shortcuts, then try it out at https://brilliant.org/arithmeti...

1. Do speed addition and subtraction tests. The more you work with the numbers themselves, the quicker you will recall how they work together. Start back at simple addition and subtraction to ensure the fundamentals are solid. [1] You can find speed tests online or in your local school supply store.

Pólya's problem solving plan breaks down to four simple steps: Make sure you understand the problem. Make a plan to solve the problem. Carry out the plan. Check your work to test your answer ...