Division is splitting into equal parts or groups.

It is the result of "fair sharing"., example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates.

Answer: 12 divided by 3 is 4. They get 4 each.

We use the ÷ symbol, or sometimes the / symbol to mean divide:

Let's use both symbols here so we get used to them.

More Examples

Here are some more examples:

Opposite of Multiplying

Division is the opposite of multiplying . When we know a multiplication fact we can find a division fact:

Example: 3 × 5 = 15, so 15 / 5 = 3.

Also 15 / 3 = 5.

Why? Well, think of the numbers in rows and columns like in this illustration:

So there are four related facts :

Knowing your Multiplication Tables can help you with division!

Example: What is 28 ÷ 7 ?

Searching around the multiplication table we find that 28 is 4 × 7, so 28 divided by 7 must be 4.

Answer: 28 ÷ 7 = 4

There are special names for each number in a division:

dividend ÷ divisor = quotient

Example: in 12 ÷ 3 = 4:

  • 12 is the dividend
  • 3 is the divisor
  • 4 is the quotient

But Sometimes It Does Not Work Perfectly!

Sometimes we cannot divide things up exactly ... there may be something left over.

Example: There are 7 bones to share with 2 pups.

But 7 cannot be divided exactly into 2 groups, so each pup gets 3 bones, but there will be 1 left over :

We call that the Remainder .

Read more about this at Division and Remainders

Try these division worksheets .

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Division Worksheets Grade 3 Solving Division Problems

Welcome to our Division Worksheets Grade 3 page.

Here you will find a wide range of free 3rd Grade Division Worksheets, which will help your child learn to solve division problems across a range of different contexts.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

Division Worksheets Grade 3

Solving division problems.

The worksheets on this page have been designed to support your child on their division journey from the start of 3rd grade to the end.

The first two sheets involve drawing out different amounts in groups and solving simple problems which do not require any reasoning skills.

Sheets 3 to 5 involve understanding and working out division word problems that require a little more reasoning and thinking about.

Sheets 6 and 7 are the most complicated and involve division problems with remainders. In order to solve the word problem, the remainder needs to be rounded up or down, depending on the context.

Division Worksheets Grade 3 - Worksheets

Simple division worksheets problems.

  • Division Problems Sheet 3.1
  • PDF version
  • Division Problems Sheet 3.2

Medium Level Division Word Problems

  • Division Problems Sheet 3.3
  • Division Problems Sheet 3.4
  • Division Problems Sheet 3.5

Harder Division Problems (interpreting remainders)

  • Division Problems Sheet 3.6
  • Division Problems Sheet 3.7

Looking for some harder Division worksheets

Our 4th grade division worksheets are similar to those on this page but at a more challenging level.

The links below will take you to our division worksheets for 4th grade.

These sheets involve solving a range of division problems.

  • Division Worksheets Grade 4 Word Problems
  • Divding by Multiples of 10 and 100 Worksheets
  • 4th Grade Long Division Worksheets

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Division Worksheets

  • Divide a 2 digit number by a single digit;
  • Use remainders when dividing;
  • Calculate division facts related to multiplication facts.
  • Division Facts to 10x10 Worksheets
  • Long Division Worksheets 3rd Grade
  • Division Facts Worksheets (randomly generated)

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All the 3rd grade sheets in this section support Elementary math benchmarks.

These sheets involve solving one or two more challenging longer problems.

  • 3rd Grade Math Problems

These sheets involve solving many 'real-life' problems involving data.

  • Math Word Problems for kids 3rd Grade
  • 3rd Grade Addition and Subtraction Word Problems (3- and 4-digits)

These sheets involve solving a range of multiplciation problems.

  • Multiplication Word Problem Worksheets 3rd Grade
  • Third Grade Math Games

Here you will find a range of free printable Third Grade Math games. All children like to play Math games, and you will find a good range of 3rd Grade Math Games here for your child to play and enjoy.

The following games involve different Third Grade Math activities which you and your child can enjoy together.

All the free Third Grade Math sheets in this section are informed by the Elementary Math Benchmarks for Third Grade.

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Arithmetic (all content)

Course: arithmetic (all content)   >   unit 3.

  • The idea of division

Intro to division

  • Division with groups of objects
  • Divide with visuals
  • Ways to represent division

problem solving dividing by 3

What is division?

Equal groups.

  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
  • (Choice A)   4 ÷ 16 ‍   A 4 ÷ 16 ‍  
  • (Choice B)   16 ÷ 4 ‍   B 16 ÷ 4 ‍  
  • (Choice C)   16 × 4 ‍   C 16 × 4 ‍  

Using arrays

Practice problem 2.

  • (Choice A)   7 ÷ 4 ‍   A 7 ÷ 4 ‍  
  • (Choice B)   7 ÷ 28 ‍   B 7 ÷ 28 ‍  
  • (Choice C)   28 ÷ 7 ‍   C 28 ÷ 7 ‍  

Practice problem 3

Equal shares.

  • (Choice A)   4 ‍   A 4 ‍  
  • (Choice B)   20 ‍   B 20 ‍  

Let's try another problem

  • (Choice A)   20 ÷ 10 ‍   A 20 ÷ 10 ‍  
  • (Choice B)   10 ÷ 20 ‍   B 10 ÷ 20 ‍  
  • (Choice C)   20 ÷ 20 ‍   C 20 ÷ 20 ‍  
  • (Choice A)   A
  • (Choice B)   B

Connecting division and multiplication

Let's try another one..

  • (Choice A)   3 × 9 = 27 ‍   A 3 × 9 = 27 ‍  
  • (Choice B)   27 ÷ 3 = 9 ‍   B 27 ÷ 3 = 9 ‍  
  • (Choice C)   9 + 3 = 12 ‍   C 9 + 3 = 12 ‍  

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How to Divide by 3

problem solving dividing by 3

Dividing by 3

Method 1: grouping.

Key Point:

9 ÷ 3 = 3 ✅

Method 2: Repeated Subtraction

Dividing by 3 - Example 1 Method 2

Method 3: Using Multiplication

9 ÷ 3 = ? 3 × ? = 9

Another Example

Dividing by 3 - Example 2 Method 1

Dividing By 3 Facts

30 ÷ 3 = 10

Lesson Streak

problem solving dividing by 3

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problem solving dividing by 3

Common Core - State Standards Initiative

Knowing how to divide numbers is an essential basic math skill. The free games and other educational resources offered by Math Games help kids to perfect that skill and ensure they have fun in the process!

Whether using our online games, apps, printable worksheets, or digital textbook, students can use our site to practice:

  • Understanding, identifying and comparing fractions of numbers and shapes
  • Making equivalent fractions and reducing fractions
  • Performing calculations with fractions and mixed numbers
  • Converting between fractions, percents, decimals and mixed numbers

Other resources for teachers and parents include downloadable worksheets and apps, and a digital textbook. We have activities for every grade and ability level, and all of them are aligned with the Common Core State Standards for Mathematics. Choose a skill to start playing!

Long Division Calculator – with Steps to Solve

Enter the divisor and dividend below to calculate the quotient and remainder using long division. The results and steps to solve it are shown below.

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On this page:

  • Long Division Calculator

How to Do Long Division with Remainders

Parts of a long division problem, steps to calculate a long division problem, how to get the quotient and remainder as a decimal, how to do long division without division, frequently asked questions.

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Ethan has a PhD in astrophysics and is currently a satellite imaging scientist. He specializes in math, science, and astrophysics.

Learning long division is a crucial milestone in understanding essential math skills and a rite of passage to completing elementary school. It strikes fear in elementary school students and parents alike.

A recent study found that the understanding of long division and fractions in elementary school is directly linked to the student’s ability to learn and understand algebra later in school. [1]

Have no fear!

Learning long division can be easy, and in just a few easy steps, you can solve any long division problem. Follow along as we break it down, but first, we need to cover the anatomy of a long division problem.

diagram showing the parts of a long division math problem

There are a few parts to a long division problem, as shown in the image above.

The dividend is the number being divided and appears to the right and under the division line.

The divisor is the number being divided by and appears to the left of the division line.

The quotient is the solution and is shown above the dividend over the division line. Often in long division, the quotient is referred to as just the whole number part of the solution.

The remainder is the remaining part of the solution, or what’s leftover, that doesn’t fit evenly into the quotient.

There are a few main steps to solving a long division problem: divide, multiply, subtract, bringing the number down, and repeating the process.

Step One: Set up the Expression

The first step in solving a long division problem is to draw the equation that needs to be solved. If the problem is already in long division form, then skip along to step two.

If it’s not, this is how to draw the long division problem.

Start by drawing a vertical bar to separate the divisor and dividend and an overbar to separate the dividend and quotient.

Place the dividend to the right of the vertical bar and under the overbar. Place the divisor to the left of the vertical bar.

For example , to divide 75 by 4, the long division problem should look like this:

diagram showing how to write a long division proble

Step Two: Divide

With the long division problem drawn, start by dividing the first digit in the dividend by the divisor.

You can also think about this as counting the number of times the divisor will evenly fit into this digit in the dividend.

If the divisor does not fit into the first digit an even number of times, drop the remainder or decimal portion of the result and write the whole number portion of the result in the quotient above the overline directly above the digit in the dividend.

For example , the divisor “4” goes evenly into the first digit of the dividend “7” one time, so a “1” can be added to the quotient above the 7.

diagram illustrating how to divide the first digit of the dividend by the divisor to solve the first digit of the quotient

Step Three: Multiply

The next step is to multiply the divisor by the digit just added to the quotient. Write the result below the digit in the dividend.

This step forms the part of the expression for the next step.

Continuing with our example, multiplying the divisor “4” by “1”, which we found in the previous step, equals “4”. So, add a “4” below the first digit in the dividend.

diagram illustrating how to multiply the divisor by the first digit of the quotient in the solution of a long division problem

Step Four: Subtract

Now, add a minus sign “-” before the number added in the previous step and draw a line below it to form a subtraction expression.

Continuing the example above, add a “-” before the “4” and a subtraction line below it.

diagram illustrating where to add the minus sign and subtraction line in a long division problem

Now that you have created a subtraction problem, it’s time to solve it.

To solve, subtract “7” minus “4”, which equals “3”, so write a “3” below the subtraction line.

diagram showing how to solve the subtraction portion of the long division problem where 7 minus 4 equals 3

Note: if the resulting value of the subtraction problem is greater than the divisor, then you made a mistake in step 2 and should double-check your work.

If the long division problem has a dividend that is a single digit, then hooray, you’re done! The remaining number that is the result of the subtraction problem is the remainder , and the number above the dividend is the whole number quotient.

If more digits are remaining in the dividend, then proceed to the next step.

Step Five: Pull Down the Next Number

At this point in the process, it’s time to operate on the next number in the dividend. To do this, pull down the next digit in the dividend and place it directly to the right of the result from the subtraction problem above.

The next digit in the dividend is “5”. So, pull “5” down and write it next to the “3” found in the previous step.

diagram showing how to pull down the next digit in the dividend in a long division problem

Step Six: Repeat

At this point, you might be wondering where to go from here. Repeat steps two to five until all the digits in the dividend have been pulled down, divided, multiplied, and subtracted.

When dividing, use the result of the subtraction problem combined with the pulled-down digit as the dividend and divide the divisor into it.

Continuing the examples above, divide the result of the subtraction problem and the pulled-down digit by the divisor. Thus, the next step is to divide 35 by 4. The result is “8”, so add “8” to the quotient.

diagram showing how to divide 35 by 4 to find the next digit in the quotient

Next, multiply the quotient digit “8” by the divisor “4”, which equals 32. Add “32” to the long division problem and place a negative sign in front of it.

diagram showing how to multiply 8 by 4 equalling 32

Next, repeat the subtraction process, subtracting 32 from 35, which equals 3. Add a “3” below the subtraction line. Since there are no longer any remaining digits in the dividend, this is the remainder portion of the solution.

diagram showing how to subtract 32 from 35 to find the remainder in the long division problem

Therefore, 75 divided by 4 is 18 with a remainder of 3. As you practice these steps, use the calculator above to confirm your answer and validate your steps solving long division problems.

If you’ve gotten this far, then you should have a good idea of how to solve a long division problem, but you might be stuck if you need to get the quotient as a decimal rather than a whole number with a remainder.

To calculate the quotient in decimal form, follow the steps above the get the whole number and remainder.

Next, divide the remainder by the divisor to get the remainder as a decimal. Finally, add the decimal to the quotient to get the quotient in decimal form.

For example , 75 ÷ 4 is 18 with a remainder of 3.

Divide 3 by 4 to get the decimal 0.75. 3 ÷ 4 = 0.75

Then, add 0.75 to 18 to get the quotient as a decimal. 0.75 + 18 = 18.75

Thus, the decimal form of 75 ÷ 4 equals 18.75.

While it defeats the purpose of actually learning how to do long division, there is technically a way to perform long division without actually doing any division. The way to do this is as follows.

Set up the long division expression the exact same way as you would normally.

Graphic showing the first step of setting up the expression for the subtraction method of doing long division

Step Two: Repeatedly Subtract the Divisor

Now, subtract the divisor from the dividend. Afterward, subtract the divisor again from the remaining value. Do this repeatedly until the remaining value is less than the divisor.

Graphic showing the second step of repeatedly subtracting for the subtraction method of doing long division

Step Three: Count the Number of Subtractions

Finally, to find the quotient, simply count the number of times you subtracted the divisor. This is the whole number portion of the quotient, and the final remaining value is the remainder.

Graphic showing the final step of calculating the quotient and remainder for the subtraction method of doing long division

Note: While this method of solving long division problems may seem easier, it is often very impractical to do so. For example, in the above example of 75 divided by 4, you would need to repeat the subtraction 18 times!

Therefore, traditional long division is the vastly superior method.

Why is long division important?

Long division is important not just because it is a tool that allows us to solve difficult division problems, but because it helps to teach logical thinking that will prepare students to excel in solving future mathematical problems.

Why do we still teach long division?

We still teach long division because it teaches students how to think logically, a valuable skill that is shown not just to improve future understanding of algebraic concepts, but also to help solve problems in all aspects of their lives.

How do you check a long division answer?

Just like subtraction is the opposite of addition, multiplication is the opposite of division. Therefore, to check a long division answer, multiply the quotient by the divisor, and if it equals the dividend, then the answer is correct!

Can you do long division on a calculator?

While a calculator can solve division problems, it will not list out the steps used in evaluating a long division problem, and will therefore not improve your understanding of how to perform long division.

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  • Carnegie Mellon University, Press Release: Carnegie Mellon-Led Research Team Finds Knowledge Of Fractions and Long Division Predicts Long-Term Math Success, https://www.cmu.edu/news/stories/archives/2012/june/june15_mathsuccess.html

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Division Word Problem Worksheets

This page contains extensive division word problems replete with engaging scenarios that involve two-digit and three-digit dividends and single digit divisors; three-digit dividends and two-digit divisors; and advanced division worksheets (four-digit and five-digit dividends). Thumb through some of these worksheets for free!

Division Word Problems for Beginners

Division Word Problems for Beginners

These printable worksheets feature simple division word problems. The divisors are in the range 2 to 9. The quotients are in the range 2 to 10. These worksheets are building blocks for children.

  • Download the set

Division: Two-digit by Single-digit (without Remainder)

Division: Two-digit by Single-digit (without Remainder)

This set of word problems involves dividing a two-digit number by a single-digit number to arrive at a quotient. The division leaves no remainder. Answer key is included in each worksheet.

Division: Two-digit by Single-digit (with Remainder)

Division: Two-digit by Single-digit (with Remainder)

These word problems require the learner to divide the two-digit dividend by the single-digit divisor and write down both the quotient and the remainder. Three pdf worksheets with 15 scenarios are featured here.

Theme based Word Problems

Theme based Word Problems

Each worksheet has five word problems related to the given theme. Supermarket, School and Halloween party are the themes used here.

Three-digit by Single-digit Word Problems

Three-digit by Single-digit Word Problems

These printable worksheets involve division word problems with three-digit dividends and single digit divisors. Apply long division method to solve each problem.

Three-digit by Two-digit Word Problems

Three-digit by Two-digit Word Problems

This set of word problems will require the student to perform division operations involving three-digit numbers and two-digit numbers. Verify your answer with the answer key provided in the worksheet.

Division: Four or Five-digit by Single-digit

Division: Four or Five-digit by Single-digit

Interesting scenarios are presented in these advanced worksheet pdfs that involve four-digit and five-digit dividends and single digit divisors. Use long division method to find the quotient.

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Divide by 3 Games

Division games make learning math facts and division by 3 a blast! Dividing by 3 means sharing equally among three. Like splitting 9 cookies among 3 friends, each gets 3. It's about distributing things evenly into three parts. Explore our variety of fun math games for kids and play now!

All Divide by 3 Games

problem solving dividing by 3

Taterz Quiz-O-Rama | Divide by 3 Game

Practice division with Taterz! Help her by choosing the right answers in this division by 3 game.

problem solving dividing by 3

Numberman's Pizza Party | Divide by 3 Game

Master division by 3 and make it fun with Numberman's Pizza Party!

problem solving dividing by 3

Boofus Quiz-O-Rama | Divide by 3 Game

earn division with Boofus! Help him ace his quiz by selecting the correct answers to divide by 3.

problem solving dividing by 3

Dino Soar | Divide by 3 Game

Navigate through the prehistoric wilderness and boost your division by 3 skills with Dino Soar!

problem solving dividing by 3

Ice Cream Bonanza | Divide by 3 Game

Save the day with Waffle in Ice Cream Bonanza! Click on the ice creams with the correct division by 3 answer and save them from melting.

problem solving dividing by 3

Dino Eggs | Divide by 3 Game

Help baby dinos break free from their eggs by solving division problems! Learn to divide by 3 and set them free.

problem solving dividing by 3

Fast Food | Divide by 3 Game

Digest division by 3 as you race your favorite fast food items to the stomach in this hilarious game!

problem solving dividing by 3

Space Race | Divide by 3 Game

Blast your character through space by mastering division by 3 in this exciting math game!

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Division Workbook

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Division Worksheets

Division worksheets for grade 3 through grade 6.

Our free division worksheets start with practicing simple division facts (e.g. 10 ÷2 = 5) and progress to long division with divisors up to 99. Exercises with and without remainders and with missing divisors or dividends are included.

Choose your grade / topic:

Grade 3 division worksheets, grade 4 mental division worksheets, grade 4 long division worksheets, grade 5 division worksheets, grade 6 division worksheets.

Division facts: drills and practice

Long division: drills and practice

Division flashcards

Topics include:

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Word Problems on Division

Word problems on division for fourth grade students are solved here step by step.

Consider the following examples on word problems involving division: 1. $5,876 are distributed equally among 26 men. How much money will each person get? Solution: Money received by 26 men = 5876 So, money received by one man = 5876 ÷ 26 = 226

Word Problem on Division

Each man will get $226. 

2.  If 9975 kg of wheat is packed in 95 bags, how much wheat will each bag contain?

Since 95 bags contain wheat 9975 kg Therefore, 1 bag contains wheat (9975 ÷ 95) kg = 105 kg

Division Word Problem

Each bag contains wheat = 105 kg In a problem sum involving division, we have to be careful about using the remainder.

3. 89 people have been invited to a banquet. The caterer is arranging tables. Each table can seat 12 people. How many tables are needed? Solution: To answer this question, we need to divide 89 by 12 89 ÷ 12

Division Word Problems

Quotient -  7 

Remainder -  5

If the caterer arranges 7 tables, then 5 people will have no place to sit.  So he needs to arrange 7 + 1 = 8 tables. 

4.  How many hours are there in 1200 minutes? 

Solution: We know that there are 60 minutes in 1 hour.Divide the number of minutes by the number of minutes in 1 hour. We get, divide 1200 by 601200 ÷ 60 = 20

So there are 20 hours in 1200 minutes.

Answer: 20 hours. 

5. A bus can hold 108 passengers. If there are 12 rows of seats on the bus, how many seats are in each row? 

Solution: Total number of passengers = 108

There are 12 rows of seats on the bus.

To find how many seats are there in each row, divide the total number of passengers by the number of rows of seats on the bus.

We get, divide 108 by 12

108 ÷ 12 = 9

Therefore, there are 9 seats in each row.

Answer: 9 seats.

6. Tom had 63 apples. He divides all apples evenly among 9 friends. How many apples did Tom give to each of his friends?

Solution: Total number of apples = 63

There are 9 friends of seats on the bus.

To find how many apples Tom gave to each of his friends, divide the total number of apples by the number of friends. 

We get, divide 63 by 9

Therefore, Tom gives 7 apples to each of his friends.

Answer: 7 Apples

7. Mark baked 195 cookies and divided them equally into 13 packs. How many cookies did Mark put in each packet?

Solution: Total number of cookies = 195

There are 13 packs.

To find how many cookies did Mark put in each packet, divide the total number of cookies by the number of packs.

We get, divide 195 by 13

195 ÷ 13 = 15

Therefore, Mark put 15 cookies in each pack.

Answer: 15 cookies.

9. Nancy needs 5 lemons to make a glass of orange juice. If Nancy has 250 oranges, how many glasses of orange juice can she make?

Solution: Total number of oranges = 250

She needs 5 lemons to make a glass of orange juice.

To find how many glasses of orange juice can Nancy make, divide the total number of oranges by the number of oranges needed for each glass of orange juice.

We get, divide 250 by 5

250 ÷ 5 = 50

Therefore, Nancy can make 50 glasses of orange juice.

Answer: 50 glasses of orange juice.

10. In your classes you counted 120 hands. How many students were at the class?

Solution: Total number of hands = 120

We have 2 hands.

To find how many students were at the class, divide the total number of hands by the number of hands we have.

We get, divide 120 by 2

220 ÷ 2 = 60

Therefore, there were 60 students at the class.

Answer: 60 students.

11. The total train fare for 20 persons is 7540 rupees. What is the fare for 1 person.

12. A milk container can store 8 litres of milk. How many containers are required to stare 6,408 litres of milk?

Capacity of one container = 8 lites of milk

Required number of containers = 6408 ÷  8

Hence, 801 containers are required.

Word Problems on Division

13. A farmer produced 29800 kg of wheat. How many bags will be buy store the wheat if one bag can hold 70 kg?

Produced = 29890 kg

Number of bags needed = 29899 ÷  70

Therefore, 427 bags are needed to hold 29890 kg of wheat.

Division Word Problem

These are the basic word problems on division.

Questions and Answers on Word Problems on Division:

1. 92 bags of cement can be loaded in a truck. How many such trucks will be needed to load 2208 bags?

Answer: 24  trucks

2. The total train fare for 11 persons was $3850. What was the fare for one person?

Answer:  $350

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Formation of Greatest and Smallest Numbers | Arranging the Numbers

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Related Concept

● Word Problems on Addition

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● Word Problems Involving Addition and Subtraction

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● Estimating Products

● Word Problems on Multiplication

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● Division of Two-Digit by a One-Digit Numbers

● Division of Four-Digit by a One-Digit Numbers

● Division by 10 and 100 and 1000

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You're a mastermind if you can solve this tricky brain teaser without a calculator

Try this brain teaser without a calculator to see how fast you can solve this mathematical puzzle..

Mathematical brain teasers are a great way to challenge our thinking and sharpen our problem-solving skills. Today, we delve into a seemingly simple yet tricky expression: ( 6^2/3(2)/6 \). At first glance, it might appear straightforward, but let's break it down step by step to uncover its true value.

Brain teaser: Scroll down to see the answer. (X/@Brainy_Bits_Hub)

Check out the brain teaser here:

The comments are varied with many saying 4 and others saying 1

Step-by-Step Solution

Step 1: understand the expression.

The given expression is:

[ 6^2 / 3(2) / 6 ]

Here, we need to carefully consider the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).

Step 2: Evaluate the exponent

First, calculate the exponent (6^2):

[ 6^2 = 36 ]

So, the expression now looks like:

[ 36 / 3(2) / 6 ]

Step 3: Handle multiplication and division from left to right

Next, we move on to the division and multiplication operations. According to PEMDAS, we handle multiplication and division from left to right.

First, divide 36 by 3:

[ 36 / 3 = 12]

The expression now is:

[ 12*2 / 6 ]

Then, multiply 12 by 2:

[12*2 = 24]

Now, we have:

Finally, divide 24 by 6:

[ 24 / 6 = 4 ]

Final answer

The value of the expression ( 6^2 / 3(2) / 6 \) is 4.

This brain teaser is a great example of why it’s essential to follow the order of operations carefully. Missing a step or misinterpreting the sequence can lead to incorrect results. By breaking down the problem systematically, we can confidently solve it and reinforce our understanding of fundamental principles in Mathematics. (Also Read: You’re a puzzle master if you can solve this age-related brain teaser in just five seconds )

Feel free to share this brain teaser with friends and see how many of them can get the correct answer.

Brain teaser: You only have 30 seconds to solve this intriguing maths puzzle. Can you solve it?

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Oxford geoscience professor myles allen on solving the problem of climate change.

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This week I had the pleasure of meeting Myles Allen . He is Head of Atmospheric, Oceanic and Planetary Physics in the Department of Physics, University of Oxford, and Professor of Geoscience in the School of Geography and Environment. He’s been studying how human and natural influences contribute to climate change since the early 1990s, served on the UN Intergovernmental Panel on Climate Change (IPCC) for its 3rd, 4th and 5th Assessments, and was a Coordinating Lead Author for its special report on 'the impacts of global warming of 1.5 °C above pre-industrial levels,’ and has been dubbed by the BBC “ the physicist behind net zero ”. In short, his scientific credentials regarding climate change are superb.

Professor Myles Allen Delivering The Gresham Lecture on May 21, 2024

But unlike many science professors, Professor Allen is bravely wading into the world of climate policy. The timing of my meeting with Professor Allen was fortuitous. It was the day before he gave a lecture on May 21, 2024, in his capacity as the Frank Jackson Professor of the Environment as part of the annual series of lectures hosted by Gresham College in the City of London. Gresham (b. 1519, d. 1579) was an English merchant, financier, and founder of the Royal Exchange. He started these lectures to ensure the emerging merchant classes were culturally enriched, as well as being versed in the latest science and technology.

The title of Professor Allen’s lecture is “ A Just and Inclusive Net Zero .” You can also view it online , which I highly recommend. The lecture is both global in its ideas and local in terms of the climate change debate taking place in the UK. I am less familiar with this than I am in the United States, and it was through this lens that I read and then listened to his lecture. My overall impression is how pragmatic and non-ideological it is. Professor Allen is no more an apologist for the fossil fuel industry than he is a supporter of the fossil fuel haters. Neither group brings value to the discussion of how to address climate change. Professor Allen does.

Sir Thomas Gresham

While I can’t do justice to his full lecture in this brief summary, here are four points that leaped out to me.

The first is he notes that “in the Paris-aligned scenarios of the IPCC, we are still using fossil fuels, at around one-quarter of the current rate, in 2100, long after the date of net zero.” Today’s world population of eight billion people will have grown to nearly 10 billion, with hopefully a larger percentage leading lives closer to what is enjoyed in the developed world. That means a LOT of fossil fuels. Those who harbor the fantasy that we still have time to achieve our climate goals simply by phasing out fossil fuel use need to get real. “One of the most dangerous myths is that achieving net zero is actually going to be really cheap because carbon-free, instantly-dispatchable energy” will soon take care of all of our energy needs. Nope. Even with the best of battery technologies it will be intermittent, and we’ll need natural gas and nuclear for the baseload.

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People also need to be realistic about some of the barriers to reducing fossil fuel use as rapidly as possible, with permitting being the number one in my mind. Environmentalists protesting transmission lines for bringing renewable power into the grid are part of the problem, not part of the solution. A great local example for me is the Northern Pass project for bringing cheap hydro power from Canada to Massachusetts, which I have written about with John Skjervem, the CIO of Utah Retirement Systems. Permitting extends to domestic mining of the cobalt and rare earths for battery and renewable energy technologies in order to ensure energy security and not being dependent on places like China, Russia, and the Democratic Republic of Congo for getting them.

Second, he calls out what he calls the “climate establishment” filled with those who regard themselves as elite experts who know better than the average citizen what needs to be done, such as “the unelected technocrats like the [UK] Climate Change Committee , the Science-Based Targets Initiative , or the Climate Action Tracker. ” Their perceived arrogance (whether it is real or not doesn’t matter) and disregard for which climate policies will be acceptable to those who will be subject to them is, again, part of the problem, not part of the solution. You can add to that bureaucrats in Brussels. As one example, he drolly quotes the Carbon Border Adjustment Mechanism, “or CBAM, is, in a nutshell, the European Union deciding that it has the right to impose punitive tariffs on imports from countries whose climate policies a team of bureaucrats in Brussels have decided aren’t good enough. I recently heard a talk from one such bureaucrat, I’m sure a very well-intentioned and intelligent chap, in which he said ‘of course, the CBAM is not neo-colonialist.’ If you have to assure people your policy is not neo-colonialist, you have a problem.”

Barnards Inn Hall, Gresham College, Where The Gresham Lecture Is Delivered

Professor Allen rightly suggests that these elite experts should “talking to people who wouldn’t normally show up in their social networks, like populist talk-show hosts, livestock farmers – and the executives of fossil fuel companies.” To that I’d like to add conservatives who are dedicating their lives to addressing climate change. On New Year’s Eve of 2023 I wrote about them and keep finding more. The “Eco-Right” has a very important role to play, and the climate establishment needs to show a little humility (yes, conservatives can have some very good ideas!) and be less self-righteous and start talking to them.

Third, while the “climate establishment” likes to talk about a Just Transition, it largely ignores what is just for the average citizen. Not everyone can go out and replace gas with heat pumps and buy an electric car. Yes, we need to think about a Just Transition for emerging markets, but in the U.S., we also need to think about what this means for low and middle income people in both red and blue states. Professor Allen also provocatively suggests “justice for the fossil fuel industry” which extends beyond “protecting workers in carbon intensive industries, or the interests of new fossil fuel producers, in ways that that just happens, surprise, surprise, to suit the fossil fuel industry itself rather well” to the shareholders of fossil fuel companies and people who benefit from their products—which is pretty much every single one of us.

Justice for the fossil fuel industry means acknowledging its right and need to exist but also holding it accountable for the carbon it produces. As Professor Allen notes, “The greatest climate injustice of all, to my mind, is the fact that the most profitable industry the world has ever known is entirely dependent on selling a product that is causing a very serious problem and no one is even asking them to fix it.” So how to fix it? Here are a few ways that spring to my mind of how not to fix it: (1) divesting from fossil fuel stocks in the naïve belief this will keep them from producing their product (but fine to do so if you don’t believe in the long-term value proposition or you’re just not ethically comfortable holding these stocks), (2) yelling at banks who provide them financing, (3) demanding that fossil fuel companies have unrealistic plans for reducing their investments and production, (4) urging them to get into the renewable energy business (their business model and capabilities don’t lend themselves to this), (5) opposing carbon capture storage technologies using the argument they just prolong the life of the fossil fuel industry, (6) thinking that reporting on Scope 3 emissions will somehow reduce the demand of their customers, and (7) filing useless shareholder proposals using the language of “value creation” to mask a basic hatred of the industry (which all the haters depend on).

Professor Myles Allen: “They just told me to write some physics on the board”

Which gets me to my fourth and last point. What is the solution? “There really is only one way to stop fossil fuels from causing global warming before the world stops using fossil fuels: we have to capture the carbon dioxide they generate and dispose of it, permanently, back underground.” The “underground” part is important. Turning fossil carbon into trees, water, and topsoil only delays its release into the atmosphere. The fossil fuel industry should take responsibility for doing this. It can start modestly, say one percent of the carbon it produces and building up to 100% by 2050. Let’s call this number the “geologically stored fraction.” This is what investors should be focused on, not Scope 3 emissions (although Scope 1 and 2 are fair game). Making this happen will require a mix of regulatory and market forces.

Can this be done? Absolutely. While fossil fuel companies don’t know wind and solar, they for sure know geological carbon management. The industry has a history of innovation and deep technological and engineering expertise for getting fossil fuels out of the ground, which often involving injecting stuff back into the ground. No question in my mind that it can figure out effective and cost efficient ways of putting carbon dioxide back underground at the scale required. In the beginning, the costs of doing so may be so small they just become a cost of doing business and preserving its needed license to operate. Ultimately, the costs will be borne by both the industry and its customers, which includes all of us. But if we want less carbon in the atmosphere but still want to enjoy the benefits of generating it, we must all be willing to pay our fair share for getting rid of it.

Robert G. Eccles

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IMAGES

  1. Dividing by 3 (problem solving)

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  2. Dividing large numbers (problem solving) answer sheet

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  3. Dividing 3 digits by 1 digit (problem solving)

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  5. Division Examples For Grade 3

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VIDEO

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    Here are a few ways that spring to my mind of how not to fix it: (1) divesting from fossil fuel stocks in the naïve belief this will keep them from producing their product (but fine to do so if ...