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## Math Topics

## Getting to the Root of a Problem Quickly

By the Mind Tools Content Team

## Origins of the 5 Whys Technique

## When to Use a 5 Whys Analysis

## How to Use the 5 Whys

The model follows a very simple seven-step process: [1]

## 1. Assemble a Team

## 2. Define the Problem

## 3. Ask the First "Why?"

## 4. Ask "Why?" Four More Times

The diagram, below, shows an example of 5 Whys in action, following a single lane of inquiry.

Figure 1: 5 Whys Example (Single Lane)

Figure 2: 5 Whys Example (Multiple Lanes)

## Step 5. Know When to Stop

The important point is to stop asking "Why?" when you stop producing useful responses.

## 6. Address the Root Cause(s)

## 7. Monitor Your Measures

## Appreciation

You then continue asking that question until you've drawn all possible conclusions from it.

## 5 Whys Infographic

See our infographic on the 5 Whys and use it to get to the root of your problems!

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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

- Research-Based Math Teaching Strategies
- Tips in Teaching a Hands-On Math Curriculum
- 5 Tips to Help Get Students Engaged in High School Math
- 3 Tips for Running an Elementary School Math Workshop
- Seven Everyday Online Math Resources for Teachers
- Three Tips for Developing Elementary Math Tests
- Online MEd Programs
- Math Teaching Resources
- Online Associate Degrees in Education
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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.

## 7. Multiplying by 11

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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## What Are Heuristics?

These mental shortcuts can help people make decisions more efficiently

## How to Make Better Decisions

## Press Play for Advice On Making Decisions

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## The History and Origins of Heuristics

## How Heuristics Are Used

Here are a few different theories from psychologists about why we rely on heuristics.

- Attribute substitution : People substitute simpler but related questions in place of more complex and difficult questions.
- Effort reduction : People use heuristics as a type of cognitive laziness to reduce the mental effort required to make choices and decisions.
- Fast and frugal : People use heuristics because they can be fast and correct in certain contexts. Some theories argue that heuristics are actually more accurate than they are biased.

Heuristics allow you to think through the possible outcomes quickly and arrive at a solution.

## Are Heuristics Good or Bad?

## Types of Heuristics

## Availability

## Familiarity

## Representativeness

## Trial and Error

## Difference Between Heuristics and Algorithms

Though the terms are often confused, heuristics and algorithms are two distinct terms in psychology.

## How Heuristics Can Lead to Bias

## Identify the Goal

## Process Your Emotions

## Recognize All-or-Nothing Thinking

## 35 problem-solving techniques and methods for solving complex problems

## Design your next session with SessionLab

Join the 100,000+ facilitators using SessionLab.

## Recommended Articles

## How do you identify problems?

How do you identify the right solution.

## Complete problem-solving methods

- Problem-solving techniques to identify and analyze problems
- Problem-solving techniques for developing solutions

## Problem-solving warm-up activities

Closing activities for a problem-solving process.

## Tips for more effective problem solving

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

## Clearly define the problem

## Don’t jump to conclusions

## Try different approaches

## Don’t take it personally

## Get the right people in the room

## Document everything

## Bring a facilitator

## Develop your problem-solving skills

## Design the right agenda

Design Sprint 2.0

## 1. Six Thinking Hats

## 2. Lightning Decision Jam

Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

## 3. Problem Definition Process

Problem Definition #problem solving #idea generation #creativity #online #remote-friendly A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

## 4. The 5 Whys

The 5 Whys #hyperisland #innovation This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

## 5. World Cafe

World Cafe #hyperisland #innovation #issue analysis World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

## 6. Discovery & Action Dialogue (DAD)

Discovery & Action Dialogue (DAD) #idea generation #liberating structures #action #issue analysis #remote-friendly DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

## 7. Design Sprint 2.0

## 8. Open space technology

Open Space Technology #action plan #idea generation #problem solving #issue analysis #large group #online #remote-friendly Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

## Techniques to identify and analyze problems

- The Creativity Dice
- Fishbone Analysis
- Problem Tree
- SWOT Analysis
- Agreement-Certainty Matrix
- The Journalistic Six
- LEGO Challenge
- What, So What, Now What?
- Journalists

Flip It! #gamestorming #problem solving #action Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

## 10. The Creativity Dice

The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

## 11. Fishbone Analysis

Fishbone Analysis #problem solving ##root cause analysis #decision making #online facilitation A process to help identify and understand the origins of problems, issues or observations.

## 12. Problem Tree

Problem tree #define intentions #create #design #issue analysis A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

## 13. SWOT Analysis

SWOT analysis #gamestorming #problem solving #action #meeting facilitation The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

## 14. Agreement-Certainty Matrix

Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

SQUID #gamestorming #project planning #issue analysis #problem solving When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

## 16. Speed Boat

Speed Boat #gamestorming #problem solving #action Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

## 17. The Journalistic Six

The Journalistic Six – Who What When Where Why How #idea generation #issue analysis #problem solving #online #creative thinking #remote-friendly A questioning method for generating, explaining, investigating ideas.

## 18. LEGO Challenge

LEGO Challenge #hyperisland #team A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

## 19. What, So What, Now What?

W³ – What, So What, Now What? #issue analysis #innovation #liberating structures You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

## 20. Journalists

Journalists #vision #big picture #issue analysis #remote-friendly This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

## Problem-solving techniques for developing solutions

## 21. Mindspin

MindSpin #teampedia #idea generation #problem solving #action A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

## 22. Improved Solutions

Improved Solutions #creativity #thiagi #problem solving #action #team You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

## 23. Four Step Sketch

Four-Step Sketch #design sprint #innovation #idea generation #remote-friendly The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper, Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

## 24. 15% Solutions

15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

## 25. How-Now-Wow Matrix

How-Now-Wow Matrix #gamestorming #idea generation #remote-friendly When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

## 26. Impact and Effort Matrix

Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

## 27. Dotmocracy

Dotmocracy #action #decision making #group prioritization #hyperisland #remote-friendly Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

## 28. Check-in / Check-out

Check-in / Check-out #team #opening #closing #hyperisland #remote-friendly Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

## 29. Doodling Together

Doodling Together #collaboration #creativity #teamwork #fun #team #visual methods #energiser #icebreaker #remote-friendly Create wild, weird and often funny postcards together & establish a group’s creative confidence.

## 30. Show and Tell

Show and Tell #gamestorming #action #opening #meeting facilitation Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

## 31. Constellations

Constellations #trust #connection #opening #coaching #patterns #system Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

## 32. Draw a Tree

Draw a Tree #thiagi #opening #perspectives #remote-friendly With this game you can raise awarness about being more mindful, and aware of the environment we live in.

## How do I conclude a problem-solving process?

## 33. One Breath Feedback

One breath feedback #closing #feedback #action This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

## 34. Who What When Matrix

Who/What/When Matrix #gamestorming #action #project planning With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

## 35. Response cards

Response Cards #debriefing #closing #structured sharing #questions and answers #thiagi #action It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

## Over to you

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

## Leave a Comment Cancel reply

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## What are facilitation skills and how to improve them?

## Design your next workshop with SessionLab

Join the 100.000 facilitators using SessionLab

## Reach a solution faster with these problem-solving techniques

This post was originally published on October 18, 2019, and updated most recently on May 20, 2021.

## What is problem-solving?

## How to solve any problem in 5 steps

## 1. Define the problem

## The five whys approach

## 2. Find a solution

## 3. Evaluate your options

## 4. Implement your plan

## 5. Assess the project’s success

## Two problem-solving techniques you need to know

## 1. Creative Problem Solving (CPS)

3 key phases make up the CPS method.

- Brainstorm as many ideas as you can. Don’t evaluate, critique, or prioritize them — just write them all down. The idea is to keep moving. The faster you go, the more you’ll get into your creative flow. If you’re not into brainstorming, a group mind map works just as well.
- Turn all your problems into questions. This encourages the group (or you) to address the situation more creatively and helps remove the burden of blame.
- Keep your language positive and affirmative. Avoid words like ‘no’ and ‘no but’ like the plague. Instead, ask ‘yes and’ to keep the conversation flowing and expand ideas.

## 2. Process-oriented problem solving

- Hurson’s Productive Thinking Model: In his 2007 book Think Better: An Innovator’s Guide to Productive Thinking , Tim Hurson defines six steps intended to give structure to solution planning while maintaining creativity. It involves working together to answer the following questions: 1) What’s going on? 2) What is success? 3) What is the question? 4) Generate answers 5) Create the solution 6) Align resources.
- Means-End Analysis (MEA): This approach is designed to reduce the difference between the problem and the goal. To narrow this gap, teams collect all the information they believe has led them to the problem, then systematically try to eliminate the issues one by one, starting with the biggest.
- Plan Do Check Act (PDCA): A favorite of developers, this iterative technique focuses on continually improving the process, one step at a time. Teams begin by setting out objectives, then implement the plan, compare it against previous results, then define the solution based on the knowledge gained. And then they repeat.

## Common barriers to problem-solving

## Other barriers include:

- Confirmation bias: This is when you search for or interpret information that confirms your existing belief while disregarding data that doesn’t support it.
- Unnecessary constraints: This happens when people get overwhelmed with the drama of a problem and make the situation more confusing than it needs to be. The best way to avoid this is to have a plan in place and a clear schedule to help people work toward a solution.
- Fixedness: This is when people are inflexible and can’t accept different perspectives.
- Groupthink: This happens when people start agreeing with each other because it’s easier than risking the challenge of conflict.
- Rigidity: People naturally want to resist change . It’s important to have self-awareness, so you can spot when you (or your team) are avoiding learning or implementing something new just because it’s never been done before. One way to change perspective is through something called constructive controversy . Split people into two teams and ask one group to play devil’s advocate to refute a solution, while the other defends it. Forcing people to discuss the pros and cons objectively brings any unconscious bias to the surface and helps people think more flexibly.

## Final thoughts

## 6 diagrams to make your marketing processes more visual

## Organize tasks with an issue tracking system

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## How to Solve Math Problems

Last Updated: May 16, 2023 Approved

## Understanding the Problem

- Draw a Venn diagram. A Venn diagram shows the relationships among the numbers in your problem. Venn diagrams can be especially helpful with word problems.
- Draw a graph or chart.
- Arrange the components of the problem on a line.
- Draw simple shapes to represent more complex features of the problem.

## Developing a Plan

## Solving the Problem

## Expert Q&A Did you know you can get expert answers for this article? Unlock expert answers by supporting wikiHow

Support wikiHow by unlocking this expert answer.

- Seek help from your teacher or a math tutor if you get stuck or if you have tried multiple strategies without success. Your teacher or a math tutor may be able to easily identify what is wrong and help you to understand how to correct it. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
- Keep practicing sums and diagrams. Go through the concept your class notes regularly. Write down your understanding of the methods and utilize it. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0

## You Might Also Like

- ↑ Daron Cam. Math Tutor. Expert Interview. 29 May 2020.
- ↑ http://www.interventioncentral.org/academic-interventions/math/math-problem-solving-combining-cognitive-metacognitive-strategies
- ↑ http://tutorial.math.lamar.edu/Extras/StudyMath/ProblemSolving.aspx
- ↑ https://math.berkeley.edu/~gmelvin/polya.pdf

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## Maths Tricks

## 12 Maths Tricks (With Examples)

## 1. Maths Tricks for Addition

- Take 43 + 34
- Split the second number into tens and unit places. 34 = 30 + 4
- Finish the ten’s addition. 43 + 30 = 73
- Finally, add the remaining unit place digit. 73 + 4 = 77.

## 2. Maths Tricks for Subtraction

Here is an example that requires a lot of borrowing

- Consider two numbers say 1000 and 676
- Subtract 1 from both the numbers; we get 999 and 675
- Then subtract 675 from 999, we get 324
- So, 1000 – 676 = 324.

## 3. Quick Multiplication Tricks by Breaking Down Numbers

- Let’s try the numbers 24 and 16
- First split the number 24, which gives 4 x 6
- Then multiply 6 with 16, we get 96
- Finally multiply the number, 96 x 4 = 384
- So, the multiplication of two numbers 24 x 16 gives the solution 384.

## 4. Multiplied By 15

- Consider the multiplication of two numbers say 56 and 15
- Now add zero at the end of the first number, it becomes 560.
- Divide that number by 2; we get 560/2 = 280
- Add the resultant number with 560, so 560 + 280 = 840.
- So the answer for 56 and 15 is 840.

## 5. Multiplication of Two-Digit Numbers

If anyone of the given numbers is an even number, then follow the steps to solve

- Consider an example, 18 x 37
- Here 18 is an even number, then divide the first number in half, so that 18/2 = 9
- Then double the second number. 37 x 2 =74
- Finally, multiply the resultant numbers. It becomes 74 x 9 = 666

## 6. Maths Division Tricks

The numbers that can be evenly divided by certain numbers are:

- If a number is an even number and ends in 0, 2, 4, 6 or 8, it is divided by 2.
- A number is divisible by 3 if the sum of the digits is divisible by 3. Consider the number 12 = 1 + 3 and 3 is divisible by 3.
- A number is divisible by 4 if the last two digits are divisible by 4. Example: 9312. Here the last two digits are 12, and 12 is divisible by 4.
- If the last digit is 0 or 5, it is divisible by 5
- If a number is divisible by 2 and 3, then it is divisible by 6, since 6 is the product of 2 and 3.
- If the number is divisible by 8, the last three digits of the numbers are divisible by 8.
- If a number is divisible by 9, the sum of the digits is divided by 9. Let us consider the example, 4518 = 4 + 5 + 1 + 8 = 18, which is divisible by 9.
- If the final digit of the number is 0, it is divisible by 10.

## 7. Maths Trick to Find Percentage

Let us take; we have to find the percentage of the number 5% of 475, follow the steps.

- For the given number, move the decimal point over by one place. 475 becomes 47.5
- Then divide the number 47.5 by 2, we get 23.75.
- 23.75 is the solution to the given problem.

## 8. Maths Magic tricks to Calculate Squares ending with digit 5

- Let’s consider the number 75 to find its square.
- Start writing the answer of last two digits number that is 25 because any number that ends with 5 is 25
- Take the first digit of the number 75. That is 7 and take the number that follows 7 is 8.
- Now, multiply 7 and 8, we get the number 56.
- Finally, write the number 56 in the prefix and combine with 25 what we already wrote.
- So, the answer is 5625.
- Squares Ending in 5: n5 = n(n + 1)5 2 = n(n + 1)25 , where n is the first digit.
- Example: Let’s consider the number 75 to find its square. Here n = 7,

So, 75 = 7(7 + 1)25 = (7 x 8) 25 = 5625.

## 9. Tricks to Multiply by 2 and 4

## 10. Multiplication by 5

When a number is multiplied by 5, then the resulting value will either end with 0 or 5.

## 11. Multiplication by 10

When a number is multiplied by 10, then the resulting value ends with 0 always.

## 12. Tricks to Memorise Table of 9

It is easy to remember the table of 9. Just we need to focus on the pattern.

09, 18, 27, 36, 45, 54, 63, 72, 81, 90

## Maths Tricks Practice Questions

Find more maths tricks questions for practice here.

- A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship? (A) 11 (B) 10 (C) 12 (D) 15 (E) 17
- 339% of 803 + 77.8% of 1107 = ? (A) 3175 (B) 3320 (C) 3580 (D) 3710 (E) 3950
- 78.54 ÷ 0.03 + 22.8 ÷ 0.8 – 1470 × 1.25 = ? (A) 809 (B) 807.5 (C) 805 (D) 802.5 (E) 801
- The cost of 8 dozen eggs is Rs. 256. Which calculation is needed to find the cost of 9 eggs? (A) (9 × 256) × (8 ÷ 12) (B) (12 × 256) ÷ (8 × 9) (C) (8 × 256) ÷ (9 × 12) (D) (9 × 256) × (8 × 12) (E) (9 × 256) ÷ (8 × 12)

## Maths Tricks Related Articles

## How to multiply 5 with an odd number?

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Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.

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Let's say students must find the sum of 393 and 89. They should quickly see that adding 7 onto 393 will equal 400 — an easier number to work with. To balance the equation, they can then subtract 7 from 89. Broken down, the process is: 393 + 89 (393 + 7) + (89 - 7) 400 + 82; 482; With this fast technique, big numbers won't look as scary now.

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Draw a graph or chart. Arrange the components of the problem on a line. Draw simple shapes to represent more complex features of the problem. 5. Look for patterns. Sometimes you can identify a pattern or patterns in a math problem simply by reading the problem carefully.

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Maths tricks are the ways to solve complex mathematical problems easily and quickly. Mathematics is not only limited to learning from textbooks, there are different learning styles that make mathematics easier. Simple Maths magic tricks help us with fast calculations and improve our mathematical skills. For example, the multiplication tricks will help students to learn maths tables and quick ...

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