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.

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!
Finding place value
Sal finds the place value of 3 in 4356.
Writing a number in standard form
Sal writes six hundred forty-five million, five hundred eighty-four thousand, four hundred sixty-two with numbers.
Writing a number in expanded form
Sal writes 14,897 in expanded form.
Intro to place value
Practice thinking about the value of each digit in a number.
Representing numbers
Comparing place values
Sal compares numbers in different place values.
Understanding place value
Sal discusses how a digit in one place represents ten times what it represents in the place to its right.
Place value when multiplying and dividing by 10
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
Place value relationships example

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.
Rounding whole numbers 1
Sal rounds 24,259 to the nearest hundred.
Rounding whole numbers 2
Sal rounds 423,275 to the  nearest thousand.
Rounding whole numbers 3
Sal rounds 1585 to the nearest ten.
Round whole numbers
Practice rounding whole numbers to the nearest hundred or thousand.  

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).
Regrouping whole numbers: 675
Sal regroups 675 into various addition problems.
Regrouping whole numbers: 72,830
Sal regroups 72,830 by its place values.
Regrouping whole numbers: 430
Sal regroups 430 five different ways.
Regroup whole numbers
Regroup numbers in each place value (e.g., regroup 1 ten as 10 ones) to express whole numbers in different ways.

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).
Commutative law of addition
Commutative Law of Addition
Commutative property for addition
Commutative Property for Addition
Commutative law of multiplication
Commutative Law of Multiplication
Associative law of addition
Associative Law of Addition
Associative law of multiplication
Associative Law of Multiplication
CA Algebra I: Number properties and absolute value
1-7, number properties and absolute value equations
Properties of numbers 1
Number properties terminology 1
Identity property of 1
Identity Property of 1
Identity property of 1 (second example)
Identity property of 1
Identity property of 0
Identity property of 0
Inverse property of addition
The simple idea that a number plus its negative is 0
Inverse property of multiplication
Simple idea that multiplying by a numbers multiplicative inverse gets you back to one
Properties of numbers 2