Khan Academy on a Stick
Arithmetic properties
This tutorial will help us make sure we can go deep on arithmetic. We'll explore various ways to represent whole numbers, place value, order of operations, rounding and various other properties of arithmetic.
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Finding a number's place value
When finding the place value of a particular number, it helps to write out exactly what the number means. Listen as we explain in this video.
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Writing a number in standard form
Here's a BIG number that needs to be expressed in standard form. Can you do this example with us? I bet you can!
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Writing a number in expanded form
What is the "expanded" form of a number? Take a big number and break it down to its ones, tens, hundreds, and other place values and you have expanded form. Not sure what we mean? No worries. We'll explain.
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Representing numbers
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Comparing place values
When asked to compare the place values in a number, remember this simple fact: each step up in place value results in an increase of a factor of ten. Watch this great explanation and become a pro.
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Understanding place value 1 exercise
Here we have a few example exercises in which we are asked to compare place values and determine which are larger or smaller, and by what factor of ten. Let's do it together.
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Place value relationships example
Place value
You've been counting for a while now. It's second nature to go from "9" to "10" or "99" to "100", but what are you really doing when you add another digit? How do we represent so many numbers (really as many as we want) with only 10 number symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)? In this tutorial you'll learn about place value. This is key to better understanding what you're really doing when you count, carry, regroup, multiply and divide with mult-digit numbers. If you really think about it, it might change your worldview forever!
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Rounding whole numbers example 1
Here's a whole numbers rounding exercise. Let's do this example together.
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Rounding whole numbers example 2
Another rounding exercise using whole numbers. Having fun yet? We are!
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Rounding whole numbers 3
You're becoming a pro at rounding whole numbers. Here's another example exercise. Can you do it first before watching the end of the video?
Rounding whole numbers
If you're looking to create an army of robot dogs, will it really make a difference if you have 10,300 dogs, 9,997 dogs or 10,005 dogs? Probably not. All you really care about is how many dogs you have to, say, the nearest thousand (10,000 dogs). In this tutorial, you'll learn about conventions for rounding whole numbers. Very useful when you might not need to (or cannot) be completely precise.
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Regrouping numbers intro various place values
Thinking about numbers as expressions of different place values is really helpful. In this example we'll look at regrouping a number by different place values.
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Comparing whole number place values
Which number is bigger? Which number is smaller? Are they equal? Use your knowledge of place value to find the answer.
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Creating the largest possible number
Taking numbers and moving them into different place values to create the highest (and lowest) numbers possible.
Understanding whole number representations
Whether with words or numbers, we'll try to understand multiple ways of representing a whole number quantity. We'll even play with place value a good bit to make sure that everything is clicking!
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Regrouping whole numbers
A number like 675 is really an addition problem. Each place value is added together to form the sum (the number). If we regroup the numbers thereby changing the individual place values, we still don't change the outcome. It's still the same number!
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Regrouping whole numbers example 1
This example problem gets the ole noggin working. We're regrouping numbers and having to determine how each place value shakes out.
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Regrouping whole numbers example 2
Let's work this example together. It will make clear the whole idea of regrouping whole numbers.
Regrouping whole numbers
Regrouping involves taking value from one place and giving it to another. It is a great way to make sure you understand place value. It is also super useful when subtracting multi-digit numbers (the process is often called "borrowing" even though you never really "pay back" the value taken from one place and given to another).
Counting 1 exerciseCounting
How many times do you need to cut a cake? How many fence posts do you need? These life altering decisions will be based on how well you count.
Introduction to rational and irrational numbers
Recognizing irrational numbers
Approximating irrational number exercise exampleRational and irrational numbers
More numbers than you probably imagine can be represented as the ratio of two integers. We call these rational numbers. But there are also really amazing numbers that can't. As you can guess, we call them irrational numbers.
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Introduction to order of operations
This example clarifies the purpose of order of operations: to have ONE way to interpret a mathamaical statement.
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Order of operations example
We're throwing everything but the kitchen sink in this one: addition, subtraction, multiplication, and division. Better remember your order of operations, ya hear!
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Order of operations example: putting it all together
Let's simplify this tricky expression according to the order of operations. Remember: PEMDAS!
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Order of operations: PEMDAS
Have you heard of PEMDAS? No, it's not some fatal illness. We'll explain here and challenge you with a more complicated example.
Order of operations
If you have the expression "3 + 4 x 5", do you add the 3 to the 4 first or multiply the 4 and 5 first? To clear up confusion here, the math world has defined which operation should get priority over others. This is super important. You won't really be able to do any involved math if you don't get this clear. But don't worry, this tutorial has your back.
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Distributive property explained
This is a thorough explanation of the distributive law (or property) of multiplication over division. Let's see how it works!
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Distributive property practice
Rewiting expressions is a great way to show that you understand the distributive property.
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Distributive property algebraic expressions
Here we have some algebraic expressions to which we need to apply the distributive property. Now we're beginning to see how useful this property can be!
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Distributive property exercise examples
You'll be a pro applying the distributive property once you've solved these exercise examples with us.
The distributive property
The distributive property is an idea that shows up over and over again in mathematics. It is the idea that 5 x (3 + 4) = (5 x 3) + (5 x 4). If that last statement made complete sense, no need to watch this tutorial. If it didn't or you don't know why it's true, then this tutorial might be a good way to pass the time :)
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Commutative law of addition
Commutative Law of Addition
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Commutative property for addition
Commutative Property for Addition
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Commutative law of multiplication
Commutative Law of Multiplication
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Associative law of addition
Associative Law of Addition
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Associative law of multiplication
Associative Law of Multiplication
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CA Algebra I: Number properties and absolute value
1-7, number properties and absolute value equations
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Properties of numbers 1
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Number properties terminology 1
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Identity property of 1
Identity Property of 1
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Identity property of 1 (second example)
Identity property of 1
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Identity property of 0
Identity property of 0
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Inverse property of addition
The simple idea that a number plus its negative is 0
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Inverse property of multiplication
Simple idea that multiplying by a numbers multiplicative inverse gets you back to one
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Properties of numbers 2
Arithmetic properties
2 + 3 = 3 + 2, 6 x 4 = 4 x 6. Adding zero to a number does not change the number. Likewise, multiplying a number by 1 does not change it. You may already know these things from working through other tutorials, but some people (not us) like to give these properties names that sound far more complicated than the property themselves. This tutorial (which we're not a fan of), is here just in case you're asked to identify the "Commutative Law of Multiplication". We believe the important thing isn't the fancy label, but the underlying idea (which isn't that fancy).