What is Order of Operations

Introduction

Order Of Operations- what are they?! Well, order of operations are pretty much the way we solve problems with more than one operation in them. Let's take a look at an example to understand this better:

Example...

So, let's say that we have 5+3x5-16/2. That looks really complex, but don't worry! All we have to do is use order of operations:

• Divide
• (left to right)
• Multiply
• Add
• (left to right)
• Subtract

That means that we have to divide or multiply and add or subtract depending on which comes first from left to right!

5+3x5-16/2=

5+15-16/2=
5+15-8
20-8=
12

I know that at first it is hard to understand all of this, but trust me, it gets so much easier once you've practiced this thoroughly!

Sheet 1 Practice Order of Operations

Writing Algebraic Expression by using Variables

Introduction...

Just to start off, we need to know what variables are. Well, here's the best way to put it:

Variable: A variable is a quantity that can change or vary and is often represented with a letter.

What that means is that in algebra, we can represent numbers as letters!

How To Write Expressions With Variables...

Well, when you are expressing any situation in algebra, you will need to use variables. Let's take a look at an example of such a situation. So, let's say that we have 23+46=69 and we have to replace 69 with a variable. Remember that variables are just letters, so that means that we can just simply take any one of the twenty-six letters, and replace it with 69. Usually, the variable will be x, but not always! I will use r, for this case. That means that our now algebraic expression is:

23+46= r!

Sheet 1 Practice Problems on Algebraic Expressions

How to Divide by a Whole Number

Introduction

Dividing by a whole number... it's so easy!

When you are dividing by whole numbers, it's simple because you don't have to worry about decimals!

Let's take a look at an example to learn more!

Moving on...

Let's say we have a problem such as 235/5. All you do is do simple division, that's all!

So, that means that we have to do the following problem:

235 = 047 OR 47

5

That means that our quotient equals 47. So that means that 5 goes into 235, 47 times!

 Sheet 1 Practice Problems on Division of Whole Numbers

Dividing Decimals by Thousand Or Large Numbers

Introduction

In our previous posts, we talked about dividing decimals by tens and hundreds. Well, dividing decimals by thousands and even larger numbers is actually pretty much the same thing! Try it out!

Try It Out...

Let's say that we have a problem such as 54.3/1000. Follow these steps to figure out your quotient:

First, put it in proper format:

54.3

1000

Then, just solve by doing this very easy method:

Just move the decimal point the number of zeros in your divisor from right to left (decrease)

That means the we will move the decimal point three places!

54.3 will then become 0.0543 OR .0543!

Now wasn't that easy!

 Sheet 1 Practice Problems on Dividing Decimals

How to Estimate Decimal Quotient

Preview

Learning how to estimate decimal quotients may seem like hard work compared to the size of the title but this chapter is rather simple. Its when you are dividing decimals that you will come across large numbers and it is better to just estimate rather than work your brains off trying to divide!
For example if you get a problem like 63.99/15.89 the first step you would want to do is estimate the numbers after the decimal point. So 63.99 will be rounded off to 64 since .99 is greater than .50, and 15.89 will be rounded off to 16 since .89 is greater than .50. And now we know that since our problem is 64/16 the answer will be 4 since 16x4=64.
To understand this topic better I suggest watching the video

And trying some of these:

Sheet 1 Estimating Decimal Quotients

Dividing a Decimal by Decimal

Preview

In this chapter you will learn how to divide decimals by decimals. To do this all that you have to do is make the divisor into a whole number.
For example if you have 0.35/0.7 you first have to change the divisor which is 0.7 into a whole number. So first I will have to move the decimal point to the right one place value. And since we changed the divisor we will also have to do the same thing we did with the dividend.Our problem will now become 3.5/7 and the answer will be .5 since 0.5*7=3.5.
To understand this topic better I suggest watching the video

And trying some of these:

Sheet 1 Practice Problems on Dividing Decimals

Dividing Decimals by Ten

Introduction

When it comes to decimal division, it can sometimes be pretty frustrating. But it's actually really easy as long as you know your methods. So let's get started! This topic is a piece of cake!

Let's Get Started...

Let's say that we have 3.2/10. How do we solve it? Well, its simple:

3.2{First, put it in proper format}

10

Now, just simply divide:

3.2= 0.32

10

How did I get 0.32?

All I did was move the decimal point once (because there is only one zero in 10) from right to left [decreasing] and I immediately got my quotient!

Was that a piece of cake or what?!

 Sheet 1 Practice Dividing Decimals by Ten

How to Estimate Decimal Quotient

Preview

To estimate a decimal quotient you need to understand that you will have to estimate the dividend and the divisor.So for example if you have the problem 5.66/2.89 all you have to do is estimate the number after the decimal point so 5.66 will be rounded to 6 and the 2.89 will be rounded to 3.Our problem now will become 6/3 and we all know that since 3x2=6 then our answer will be 2.To understand this topic better i suggest you watch the video . . . . . . . . . . . . . . . and try some of these: 

Example

71.99/7.56=

34.78/4.90=

1.98/0.90=

63.69/31.71=

20.57/6.51=

Dividing Decimals by Hundred

Preview

Dividing decimals by hundreds might seem like a complicated title but actually it's really simple. This is the same thing as dividing decimals by ten. So for example if you have the decimal number 6.7/100 all you would have to do is move the decimal point left two place values. So now our answer will be 0.067.
To understand this topic better I suggest you watch the video

And try some of these:

Sheet 1 Practice Problems Dividing Decimals

Multiplying Two Decimals

Preview

In this chapter you will learn how to multiply two decimals and this might be a little complicated to some of you but it's actually pretty simple. First of all, whenever you are multiplying decimals the first thing you would do is just simply multiply the numbers.
For example if you have the problem 6.7*2.3 the first thing you would do is simply multiply so:
    67
  *23
1541

Now all you have to do move the decimal point in 1541 (which is at the end) from right to left (decrease) as many places as the number of digits after the decimals in 6.7 and 2.3 There are only 2 digits after the decimals so 1541 will become 15.41
The product of 6.7*2.3 equals 15.41.
To understand this topic better I suggest you watch the video

And try some of these:

Sheet 1 Practice Problems on Multiplying Two Decimals

                                

                                  

Multiply a Decimal with a Whole Number

Introduction

Multiplying decimals by a whole number might seem tricky but it's actually pretty simple. All you have to do is simple multiplication, actually. Read on to find out more!

Getting Started...

Let's say we have a problem such as 5.6x24. The first thing you do is put this is proper format:

      5.6

   x 24

Now, just do some simple multiplication ( Forget the Decimal Point for Now )

x 56

   24

-------

+ 224

 1120

----------

 1344

Now that we have our product, all we do is add in the decimal point.

Remember, count the number of digits after the decimal point. 

In this case, we have 5.6 which only has 1 digit after the decimal point

Therefore, we'll go from right to left ( decrease ) in our product one decimal place.

That means that we now have 134.4.

I know that it seems a little complex, but you'll figure it out once you've had some good practice!

Sheet 1 Practice Problems on Multiplying Decimals

Multiplying Decimals by Thousands and Larger Numbers

Preview

In this post, we're just going to teach you some basic rules of multiplying decimals by thousands and then we'll jump into some multiplication of more complex numbers. Don't worry, it's really easy!

Let's Get Started!

So, let's start with multiplying decimals by thousands. 

Let's say that we have 2.4 and we have to multiply that by 1,000. The first thing that you will do is put this in proper format:

2.4x1000

Next thing to do, is that you have to count the number of zeros in 1,000. We all know that 1,000 has 3 zeros.

Now, all you have to do is move the decimal point 3 places from left to right.

Remember:

Left to Right: Increases Value

Right to Left:  Decreases Value  

Therefore, 2.4 will become 2400 OR 2,400.
Wasn't that easy!

Moving On... 

So, now that you know how to multiply decimals by thousands, let's move on to larger numbers.

Let's say we have 6.3 and we have to multiply that by 10,000. Now remember these steps:

1. Place in Proper Format
2. Count the Number of Zeros
3. Move the Decimal Point from Left To Right the Amount of Zeros that you Count.

So now we have:

• 6.3x10,000
• 4 Zeros
• 63,000 OR 63,000.

Sheet 1 Practice Problems on Multiplying Decimals

                                                                                                                                                     

      

Estimate Products of Decimals and Whole Number

Preview

In this chapter you will learn how to estimate products of decimals and whole numbers. This will be helpful for someone who has trouble with finding products.
 For example if you have 55.8x7 the first thing you will do is estimate the decimal number which is 55.8 to its nearest place value so that would be 56. Now our problem will become 56x7 and our answer will be 392.
 To understand this topic better I suggest you watch the video

And try some of these:

 Sheet 1 Practice Problems on Multiplying Decimal Numbers

Two Digit Quotients

Introduction

In our previous chapter, we talked about one digit quotients. This is a sequel post to that chapter because this topic is all about two digit quotients. Keep reading to find out more. It's really simple!

More...

Let's say that we have a question like 121/11. To get a two digit quotient, all we do is divide. We know from the times table of 11 that 11x11 is 121. So we'll get the following answer:
121/11= 11

11 is a two digit quotient!

If you want to practice more, which is great, than try out some of these problems by yourself.

Good Luck!

 Sheet 1 Practice Problems on Two Digit Quotients

How to Estimate and Divide larger Numbers

Preview

This chapter will teach how to estimate larger numbers so that you can divide them easily. This will be helpful because some times you come across large numbers to divide and you may get confused.

 So for example if you get a number like 7483/15 the first thing you do is estimate the number 7483 to large number that 15 can evenly go into. Since 83 in 7483 is greater than 50 the number 483 will be rounded to 500 making 7483 turn into 7500 which 15 can easily go into. So 7500/15 will be 500 since 15x5=75. So 15x500=7500.
To understand this topic better I suggest you watch the video...And try some of these:

 Sheet 1 Practice Problems on Dividing with Larger Numbers

One Digit Quotients

Preview

This chapter will teach you exactly how to find one digit quotients and why this chapter is important. So for example if you have 630/90 all you need to do is cut out the zeros to make those numbers shorter because both have zeros. So now we have 63/9 and if you look at the times table of 9 then 9x7=63 so our answer is 7 since 630/90=7.
To understand this topic better I suggest to watch the video

And try some of these:

 Sheet 1 Practice Problems on One Digit Quotients

Dividing Two Digits Divisors by Multiples of Tens

Introduction

In a previous post, we talked about divisors of tens (multiples of ten). This topic is similar except this time you will confront multiples of ten as dividends. So what are you waiting for, keep going!

Moving on...

The types of problems that you will see in this topic will be similar to this: 100/24. To solve this, all you do is simple division! Let's try it out!

Let's try it out!

So, if we look back at our example, 100/24, we can go ahead and solve it together! The first thing that you do is put this in proper format:

100

24

Now solve the problem!

100= 4.167 OR 4.17

24

Now wasn't that easy! If you think so, then try some of these out too!

 Sheet 1 Practice Problems on Dividing by Multiples of Ten

Multiplying Decimals by Hundred

Preview

Multiplying decimals by hundred is pretty much the same thing as doing multiplication of decimals by tens. Whenever you multiply a decimal number by hundred you have to move the decimal point right two place values.
So for example if we have the number 78.92x100 all that we will do is move that decimal point two times to the right making our answer 7,892.
To understand this topic better I suggest to watch the video

And try some of these:

 Sheet 1 Practice Problems on Multiplying Decimals by Hundred

Multiplying Decimals by Ten

Preview

Multiplying decimals by ten is one of the easiest things to learn in math. All you need to know is that you need to change the decimal point in the number by one place to the right. So for example if you have the number 6.7x10 all you have to do to the 6.7 is move the decimal point to the right one place value. So the answer will be 67.
To understand this topic better I suggest you watch the video

And try some of these:

 Sheet 1 Practice Problems on Multiplying Decimals

How to Handle Zeros in Quotients

Preview

When you are dividing you may come across zeros in your dividends and divisors and those zeros may cause you to thinking that the problem is hard itself. But you should know the zeros can be cut to shorten the problem. For example if you have the problem 5600/700 you will first have to look at the smaller number and eliminate a zero in the 700 since it is smaller than 5600 and make that a 70 and you have to do the same thing with 5600 and make that a 560.Now since the 70 still has a zero and is smaller than 560 you can eliminate another zero from both and make the 70 to a 7 and make the 560 to a 56 so now all you have to do divide is 56/7 and since we all know that 7x8=56 then 56/7=8.
To understand this topic better I suggest watching the video

And trying some of these:  

Sheet 1 Practice Problems on Zeros in Quotients

How to Estimate Quotients with Two Digit Divisors

Introduction

The most important thing when estimating quotients with two digit divisors is that you have to keep in mind to round the divisor and the dividend. That means that you have to estimate these numbers to the nearest ten or hundred. Let's take a look at an example to understand it better!

Moving on... 

Well, let's say that we have a problem such as 432/24 and we have to estimate its quotient. Remember, we need to estimate to tens or hundreds. In this case, we have to estimate to the nearest ten. So, that means that 432 will be estimated to 430 and 24 will be estiamted to 20. Now we have 430/20. All we do now is divide!

430 = 21.5 or about 22.

20

To check our estimation, we can always go back to our original problem: 432/24, and find out the actual answer. Then, we'll be able to see if our estimate is reasonable ro not.

432

------- =18

24

18 and 22 are reasonable because if we round them to the nearest ten, then they both would equal 20. Therefore, our answers are reasonable! Wasn't that easy!

Sheet 1 Practice Problems on Dividing with Two Digit Divisors

Dividing by One Digit Divisor

Introduction

Dividing by one digit divisors is the easiest thing in division because you don't really struggle when trying to figure out how many times a number fits into another. Let's take a look at an example to understand this better!

Let's try it out!

So, let's say we have a problem such as 678/2. The first thing we do is write this in proper format:

678

  2 

Now, start dividing the numbers!

678 = 339.

  2

So, that means that the quotient equals 339. Now, wasn't that easy?!

Sheet 1 Practice Problems on Division by One Digit Divisor

How to Estimate Quotients

Preview

Estimating answers is really easy and now I am going to teach you how to estimate quotients. So for example you get a problem like 47/5. First you have to estimate the number 47 to a number that 5 can easily go into.So lets round 47 to 45 because it is the closest number that can be evenly divided by 5 and is in the times table of 5 as well. Now our problem is 45/5 and we all know that 5*9=45 so 45/5=9. Our estimated quotient equals 9. To understand this topic better I suggest you watch the video...And try some of these:

 Sheet 1 Practice Problems on Estimating Quotients

Dividing Multiple of Ten and Hundred

Introduction

When dividing by multiples of ten and hundred, always keep in mind that you can remove any zeros that aren't needed to do the division. What I mean is clearly stated below:

Let's say that we have a problem such as:

2340/10. We can go ahead and remove the zero from 10 and 2340. That means that we now have 234/1. Now we can simply divide to get our quotient!

Let's try it out!

So, let's first figure out our previous example up above: 234/1

That means that now we must divide 234 by 1. It's really simple because anything you divide by 1 always equals the same thing. That means that the quotient to 2340/10 equals 234. Now, wasn't that easy?!

More...

So, now that we have already covered dividing by tens, let's try dividing by hundreds!

For example, if we have 5670/100. Now remember to remove zeros. But we won't remove all the zeros because 5670 only has one zero. Therefore, we'll only remove one zero. So, now we have 567/10. Now just do simple division to receive your quotient. 567 divided by 10 equals 56.7 because when we are dividing by any multiple of ten or hundred, we just simply move the decimal point the amount of zeros in that multiple. So, in this case, we'll just move it once since 10 only has one zero. Therefore, our quotient to the original problem 5670/100 equals 56.7!

 Sheet 1 Practice Problems on Dividing Multiples of Ten and Hundred

How to Multiply Large Numbers

Preview

When I say large numbers I mean numbers like 450 and to make that even more larger lets do 450*23.
Now don't freak out, this problem may look like the hardest thing in math when this is just as simple as doing one digit multiplication! To do this you first have to write this problem vertically like this

450
x23

Now, all you have to do is follow the rule of multiplying numbers, remember you are going to multiply the smaller number by the larger number so lets first do 450x3 because we always start from the right in the smaller number and go to the left.

   450
   x  3    
1,350

Now let's do 450x20:

450
x20
9,000

Now that we have our products, just add them together to get the final answer!

   9000
 +1350
10,350

So our product to 450x23 is 10,350.
 To understand this topic better I suggest you watch the video

And try some of these:

 Sheet 1 Practice Problems on Multiplying Large Numbers

Two Digit by Two Digit Multiplication

Intro...

Two Digit Multiplication-seems kind of complicated, doesn't it?! Well, it's actually pretty easy. Once you've read the rest of this post, you'll think of multiplying like a piece of cake. Trust me, it's super easy!

Moving on...

Two digit multiplication means multiplying two numbers with two digits in them. Let's take a look at an example to understand what I'm trying to say better. So, let's say we have 23x78. This is an example of two digit multiplication! Now, let's see how we can solve this:

First thing's first: Rewrite this problem in vertical form. Then just do some simple multiplication.

      23 

   x 78

    --------

 + 184

  1610

-----------

  1794

I know that the above example isn't very clear, but I did my best :)

However, if you still need some help figuring this topic out, then I recommend watching the video on this topic!

 Sheet 1 Practice Problems on Two Digit Multiplication

One Digit Multiplication

Preview

One digit multiplication! The most easiest thing to learn in 5th grade! If we have to then why not use a shortcut. By revising your multiplication tables.If you know your multiplication tables then its going to be easy as pie going through one digit multiplication and this also counts for two digit by two digit multiplication as well! To learn more about one digit multiplication watch the video...And try to revise as much as possible because after all these are the origins of multiplication:

Times Table

Sheet 1 Practice Problems on One Digit By One Digit Multiplication

What is Distributive Property

Introduction

Distributive Property- what is it? Well, distributive property is a property of algebra. It is used mainly to break up or expand numbers to make them look easier. Let's take a look at an example to understand it better!

Example:

Let's say that I have to quickly multiply the following numbers: 69x3. The first thing that you need to do is, well, use the distributive property! Try writing the following numbers in expanded form like this:

(60x3)+(9x3). I know that it looks even more complex now, but don't worry! I'll help you. The first step to take is that we have to solve the parenthesis. So 60x3 equals 180 and 9x3 equals 27. Now the only thing we have to do to get our final answer is that we have to add our two products together: 180+27 which equals 207. Therefore the answer to our problem, 69x3, equals 207.

I know that the above steps look very complicated, but trust me, you will understand it after practicing.

However, if you are still confused, then here is the most formal way to put this:

Distributive Property: To expand numbers in an equation to figure out the product (we are working with multiplication in this case!)

 Sheet 1 Practice Problems on Distributive Property

What are Exponents

Preview

Exponents are just another way of saying " to the power of ". For example if you get a exponent 6 to the power of 2 all they are asking you to do is to multiply 6 two times so if they would have said 6 to the power of 4 the product would be 6*6*6*6=1,296. So now we know that 6 to the power of 2 is 36 because 6*6=36.
To understand this topic better I suggest watching the video

And trying some of these:

 Sheet 1 Practice Problems on Exponents

Learn How to Estimate Products

Introduction

In this lesson, you will learn how to estimate products. Now, estimating means making an educated math guess to get your answer. To estimate the product means to make an educated math guess on the numbers in your problem to get an answer to a multiplication problem. Easy, right?!

Now that you have an idea of what this lesson is about, let's take a look at an example to understand it better. Trust me, it's easy as ABC's!

Examples

Let's say that we have a problem such as 22*36. The first thing we need to do is that we have to estimate the numbers 22 and 36. Since 22 is less than 25, we will round it to 20. And since 36 is greater than 35, we will round it to 40. Now comes the easy part: Just multiply your estimated numbers 20*40. If you are finding this part a little tricky, which is okay, than just remove the zeros, and multiply 2*4 which equals 8. Now just simply add the two zeros you had removed. That means that the estimated product of 22*36 equals 800. 

I know that the above steps seem like a lot of stuff, but it is really simple once you have had enough practice. So, why not try some of these out?!

 Sheet 1 Practice Problems Estimating Products

Tips and Tricks on Doing Mental Multiplication

Preview

In this chapter you will learn some tips and tricks on doing mental math multiplication.You will learn how to break apart the problem and get the product easily with out getting confused, especially with large numbers!

For doing mental math we also recommend you revising your multiplication tables from 1 to 20.
For example if we get a problem like 30x5x2 we will break apart the problem to for us to understand it better , so now we can do 30x2 first and get 60 then we can do 60x2 and since we know 6x2=12 all we have to do is add  a zero to 12 and make that a 120. To understand this topic better I suggest watching the video

And trying some of these:

 Sheet 1 How to do Mental Multiplication

1ntroduction

ALL ABOUT US

Hi guys! Welcome to Bro and Sis Math Club with Ali and Rida! We're two kids from Charlotte who make videos on YouTube related to mathematics. So far, we have finished 5th grade math, 6th grade math, and 7th grade math videos. We follow the Common Core curriculum and show step by step procedures in each video to give a clear understanding of the math concept. To learn more about each of us, keep reading! 

Rida...

My name is Rida. I am 12 years old and currently in 8th grade. As to my interests and hobbies, I'm a huge reader! If I find any book, I'll pick it up and start reading until someone doesn't snap me out of it! I'm also outgoing because I enjoy doing things such as: kayaking, canoeing, hiking, going on long drives with my family, being outside on a nice day, and many other things that are escaping my mind right now! I also have a passion for doing math. Ever since I can even remember, I have always enjoyed learning and practicing math. For some reason, math is something that comes to me naturally-I really don't need to do anything to understand it. I can always figure it out because math always has some method and logic to it, and I understand it very clearly. That is, by the way, one of the reasons my brother and I started this blog in the first place! So, to get away from all the math-talk, that is pretty much all you need to know about me for now, but I am sure you'll more through our videos! :)

Najaf...

 

 

My name is Najaf, but my friends call me by my last name which is Ali. I am 13 years old and I am in 8th grade just like my sister. I like playing video games and watching TV. My favorite sport is playing soccer. My hobbies are doing water sports. Out of all of those I am most fascinated with math. ''Pure mathematics is, in its way, the poetry of logical ideas'' a quote from Albert Einstein is one way to look at math. So I figure without math, the human race has no way to think up calculations! 

What are Multiplication Properties

Introduction

We all know what multiplication is but we don't really know the rules, or properties of multiplication. Multiplication Properties include the following properties:

• Commutative Property of Multiplication
• Associative Property of Multiplication
• Identity Property of Multiplication
• Zero Property of Multiplication

I know that all of these big and fancy words seem like a lot of stuff, but it's actually pretty easy. Especially once you know what they are and have solved some examples!

Commutative Property of Multiplication

Definition: The order of factors can be changed, but the product stays the same.

Example: 4x3=12
               3x4=12

Associative Property of Multiplication

Definition: You can change the grouping of the factors. The product stays the same.

Example: (6x8)x7=336
                6x(8x7)=336

Identity Property of Multiplication

Definition: When you multiply any number by 1, the product is that number.

Example: 2x1=2

Zero Property of Multiplication

Definition: When you multiply any number by 0, the product is 0.

Example: 3x0=0

More about the Properties of Multiplication

I hope that after reading the above information on the Properties of Multiplication, you got an idea of what each is. Even if you already knew these, this was probably a good review! Also, if you still think you need to practice identifying them, try doing the problems listed below:

 Sheet 1 Practice Problems Multiplication

Learn How to Subtract Decimals

Preview

Subtracting decimals is really easy just like the last chapter on adding decimals. All that you do is arrange the decimal points so that they match each other. Then you just simply subtract. But remember that before you do any subtraction you have to bring the decimal point straight down.

Let's say we have the decimals 5.6-4.6:

 5.6
-4.6
 1.0  OR 1!
 To understand this topic better, I suggest watching the video...and trying some of these:

Sheet 1Practice Problems Subtracting Decimal Numbers

How to Estimate Sums and Differences

Introduction:

In order to estimate sums and differences, you first need to learn the key points. The key points are really the definitions and steps to estimating the sum or the difference between two numbers. Let's get started!

Key Points:

The key points to estimating sums and differences are:

• Estimating means to make an educated and approximate calculation; not exact
• Sum is the answer to an addition problem
• Difference is the answer to a subtraction problem
• When the digit is below 5, 50, 500, etc. you will estimate below that value
• When the digit is above 5, 50, 500, etc. you will estimate above that value

Examples:

Now that you have been introduced to the topic and its key points, let's take a look at an example to understand it better!

Estimate the sum of 48 and 103

Keep in mind that sum means the answer to an addition problem. Therefore,we must add the following numbers: 48+103. Now, you also must remember not to directly add the numbers. The key point is estimate. So, let's see how we can answer this problem using a very easy method!

First, we will look at the last digit of the first number: 48. Since 8 is greater than 5, we must round up to 10. Therefore, now we have 50+103. But remember that we must round both numbers to get our estimate. Since 3 is less than 5, we will round that to 0, so it will become 50+100, which equals 150. That means that the estimate for 48+103 equals 150!

Checking...

It's a good idea to check your answer by finding the direct answer and then determining whether your estimate is reasonable or not. To do that, you just simply add the original problem: 48+103, which will give you an answer of 151. Now, ask yourself, " Is my estimate reasonable, according to the actual answer?"

Well, our estimate is reasonable because 151 is only 1 digit away from 150. Easy, right?!

 Sheet 1 How to Estimate Sums

Sheet 2 How to Estimate Differences

Learn How to Add Decimals

Preview

Learning how to add decimals is as easy as 1, 2, 3's. All you need to know is that whenever you are adding decimals, you have to line up the decimal points. For example, if the two numbers are 2.50+25.7, you will line up the decimal points like this:

    2.50
+25.7
                                                   
 Always add zeros in blank spot to make it easier for you to add.

  02.50
+25.70

Now just add and bring down decimal point just as it is!

  02.50
+25.70
  28.20  OR 28.2!

To under this better I suggest you watch the video...and try some of these!

 Sheet 1 How to Add Decimal Numbers Practice Problems

                                            

How to Round Whole Numbers and Decimals

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Rounding a number is the easiest thing you learn in math once you know the basics of it.
When rounding  a  whole number, first specify if the number is in the ones, tens, hundreds, etc.
Then you have to see whether the number's midpoint is below or above five, fifty, or five hundred, etc.
If the number is above, then round to greater number if the number is below then round to the smaller number.

For example the number is 22, so I know that this number is in the tens and that the midpoint is twenty five. Now the two points I can round 22 is 20 and 30. I know that 22 is less than 25 so I will round below to 20.

Same thing with rounding decimals. If the decimal number is greater than 5 tenths, 5 hundredths, or 5 thousandths etc, then round up. Otherwise, round below. So if I had the decimal number .54 I know it is in hundredths place so I can round to either .50 or .60. $ is less than so we'll round to .50!

To understand this topic better I suggest watching the video......And trying some of these out.

Sheet 1 Rounding Whole Numbers and Decimals

How to do Decimal Mental Math

Tips and Tricks

Decimal mental math is a really simple thing that only you can  perform because it has to deal with how you do math in your head. In order to do decimal mental math, all you need to do is follow some of these super easy steps!

The main thing that you need to focus on when doing decimal mental math is that you have to separate the whole numbers and the decimal numbers. I call this the Separating-Method and what i mean by that in a decimal number the numbers before the decimal point are whole numbers and the numbers after the decimal point are decimal numbers. After doing that, all you do is apply the operation. What I mean by that is that if your operation is addition, then you'll add. If it's subtraction, therefore, you'll subtract. Simple, right?! Now that you have learned and mastered a way to do mental math let's move on. I'll give you an example, and then provide you with some practice problems. 

Examples

Solve 3.4+6.9

Remember, first we must do the Separating-Method. So, that means that we will end up with 3+6 and 4+9. Now, remove the addition signs and make that 36+49. Then add that in your brain. If you are struggling, then use the commutative properties and the associative properties of addition. These make it easier to do mental math. First, separate the compatible numbers, which are 30+40, which equals 70. Then do 6+9, which equals 13. 70+13, therefore equals 83. Now, time to do the final step- adding the decimal point in your answer. If you look back at the original problem and place the answer using place value, you should come up with 8.3. So, the answer to 3.4+6.9 equals 8.3!

I know it looks like a lot of mental math, but trust me, it gets so much easier once you've practiced enough. So, try some of these problems out!

 Sheet 1 Practice Problems Decimal Mental Math

How to Compare and Order Decimals

Introduction

In the last post, we talked about Identifying Decimal Place Value and we also skipped into comparing decimals. If you understood that, then this topic should be a piece of cake for you!!

Let's Get Started

Even though we talked about comparing decimals in the last post, let's just review it one more time.

Comparing Decimals:

When comparing decimals, take a look at the digits on the right side of the decimal point. Those digits are the decimals. Then, just compare by determining which digit is larger in value.

 Easy, right?!

Ordering Decimals:

As you can already assume, ordering decimals is pretty much like comparing decimals. This is because comparing is the key point in ordering decimals. First, you compare the decimals to determine the least and the greatest decimal values. Then, you can order the decimals in least to greatest OR greatest to least order.

 Sheet 1 Practice Problems on Comparing and Ordering Decimals

Identifying Decimal Place Value

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The decimal place value of a number is simply the value of that number defined by the place in which the digit is. To find the place value, first look at the decimal point, for example in the number 6.5. Then you have to put aside the numbers on the left side and the right side of the decimal point. The number or numbers on the left side would be the whole numbers. The numbers on the right side of the decimal point will be the decimals. Then find place values of the whole numbers which is ones, tens, hundreds, etc. Then find decimal place values of the decimal number. Remember they will be decimal place values of tenths, hundredths, thousandths, etc. To understand it better I prefer watching the video. Now try some of these out:

 Sheet 1 Decimal Place Value

Sheet 2 Practice Problems on Decimal Place Value

Place Value: Thousandths

Introduction

Identifying place value in thousandths is the same thing as identifying place value in tenths or hundredths, it's just the usage of a larger number, that's all! In order to find the place value in thousandths, you just look at the fourth digit from right to left of the number. Let's take a look at some examples to understand it better. It's really easy!!

Example

Determine the thousandths place value of the number 0.564. Remember the first digit to the right of the decimal point is tenths, second digit is hundredths, and the third is thousandths place value. So the third digit is 4 so the digit 4 is the thousandths place value.

 Sheet 1 Thousandths Place Value

Sheet 2 Find the Thousandths Place Value

Define Place Value

Definition of Place Value:

Place value is the numerical value that a digit holds in a certain position in a number.

In other words...
Place value is the value of a digit in a number!

Examples:

What is the value of 3 in 4,236?

Answer: Since 3 is the second digit from right to left in the number, let's take a look at the Place Value Chart to determine its value. It's simple!

1. Ones
2. Tens
3. Hundreds
4. Thousands
5. Ten Thousands
6. Hundred Thousands
7. So on... ( keep multiplying the previous value by 10 to get next value 100,000x10=1,000,000)

So, as you can see, the second value of a number is ten. Therefore the value of 3 in 4,236 equals 3 tens or 30!

I know it looks like a lot of work, but trust me, it's very easy once you practice a few problems. You'll have Place Value mastered in no time!

Identifying Tenths and Hundredths

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To find your way through tenths and hundredths, you need to learn that tenths and hundredths are simply parts broken into place values of decimals. Tenths is the first place value after the decimals point and hundredths is the second place value after the decimals point. These place values can also be written as fractions. 5 tenths is the same thing as 5/10. 6 hundredths is the same thing as 6/100.

You can turn the place values into fractions by using the number on the right side of the decimal point  and putting that on top of the line (make that a numerator) and you take the decimal point and make that a one and then count each digit after the point and put the same number of zeros after the one. These digits will become the denominators.
.43 ( 43 hundredths)
Numerator: 43
Denominator: 100

 To understand it better, I suggest watching the video

Then trying some of these:

Sheet 1 Identifying Tenths and Hundredths

Sheet 2 Practice Problems for Identifying Tenths and Hundredths