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Solving Linear Equations - Basic Algebra Shortcut Tricks!

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Algebra Basics: Solving Basic Equations Part 2 - Math Antics

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The types of numbers: Natural, Whole, Integers, Rational, Irrational, Real.

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Wordwall - Create better lessons quicker

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1) Which family of numbers begins with the numbers 0, 1, 2, 3, ...? a) Real Numbers b) Rational Numbers c) Integers d) Whole Numbers e) Natural Numbers 2) All integers are... a) irrational b) whole c) natural d) rational 3) The number 1 falls into all of the following families EXCEPT which group?

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Rounding Numbers and Rounding Decimals - The Easy Way!

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Practice rounding whole numbers to the nearest hundred or thousand.

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Commutative Property of Addition.

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Table of important basic rules and properties of algebra are presented with examples and explanations.

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Distributive property with variables (practice) | Khan Academy

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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

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What is addition? Addition is the operation that allows us to group items together. It is one of the first operations we learn in elementary school. Usually, our first experience with addition involves a visual aid. Let's suppose we started out with 3 boxes:

Now, let's say we came across another 2 boxes and we wanted to determine the total number of boxes.

We can count the total number of boxes and we end up with 5. This can be translated into the addition fact: 3 + 2 = 5. After learning via visual cues and object counting, we eventually memorize all of the possible single-digit addition combinations. We can use these addition facts along with a process known as vertical addition to add numbers as large as we would like. When we work with an addition problem, we refer to the numbers being grouped together or added as "addends". The result of the addition operation is referred to as the "sum". In our example featuring the boxes, we added 3 boxes with 2 boxes and got a result of 5 boxes. In other words, the numbers 3 and 2 are being grouped together or added. These numbers (3, 2) are the addends. The result of the addition operation is 5, this is the sum.

Example 1: Label the parts of the addition problem 5 + 7 = 12

The 5 and 7 are being added together, these are the addends. The 12 is the sum or result of the addition operation. Let's take a look at a few properties of addition. These will be useful throughout our study of Algebra.

Identity Property of Zero

The Identity property of zero tells us that adding zero to any number leaves the number unchanged.
Example 2: 17,355 + 0 = ?
The answer here is simple, the number 17,355 will not be changed by adding 0.
17,355 + 0 = 17,355

The Commutative Property of Addition

The commutative property allows us to reorder the addends in an addition problem. The commutative property of addition tells us that we can add numbers in any order and not change the sum.
Example 3: Rewrite 13 + 5 using the commutative property of addition
To complete this problem, we simply change the order of the addends, 5 will be first and 13 will be last.
13 + 5 = 5 + 13
In each case, the result of the addition is 18.
13 + 5 = 18
5 + 13 = 18
Changing the order of the addends (5, 13) did not change the sum (18).

The Associative Property of Addition

The associative property of addition allows us to regroup three or more addends in an addition problem. The associative property of addition tells us that the addition of three or more numbers can be grouped in any order, without changing the sum.
Example 4: Rewrite (9 + 1) + 5 using the associative property of addition
To complete this problem, we simply change the grouping. Notice how parentheses are around the 9 + 1 portion of the problem. In order to complete the problem, we can regroup and place parentheses around 1 + 5:
(9 + 1) + 5 = 9 + (1 + 5)
From the order of operations, we work inside of parentheses first:
(9 + 1) + 5 = 10 + 5 = 15
9 + (1 + 5) = 9 + 6 = 15
Changing the grouping did not change the sum.
In each case, the result of the addition is 15.

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GreeneMath.com | Ace your next Math Test!

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What is addition? Addition is the operation that allows us to group items together. It is one of the first operations we learn in elementary school. Usually, our first experience with addition involves a visual aid. Let's suppose we started out with 3 boxes: Now, let's say we came across another 2 boxes and we wanted to determine the total number of boxes.

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About Properties of Addition:

In our lesson, we learned a few valuable properties of addition. We identify the parts of an addition problem as either: sum or addend. The addends are the numbers being added together or combined through addition. The sum is the result of the addition operation. The commutative property of addition shows us that we can change the order of two or more addends without changing the sum. The associative property of addition shows us that we can change the grouping of three or more addends without changing the sum.

Test Objectives

Demonstrate the ability to rewrite a sum using the commutative and associative properties

Demonstrate the ability to identify the parts of an addition problem as addend or sum

Demonstrate the ability to add using the identity property of zero

Properties of Addition Practice Test:

#1:

Instructions: Rewrite each using the commutative property.

a) 1 + 7

b) 2 + 4

c) 6 + 15

d) 13 + 12

Watch the Step by Step Video Solution | View the Written Solution

#2:

Instructions: Rewrite each using the commutative property.

a) 21 + 1

b) 13 + 9

c) 51 + 7

d) 103 + 2

Watch the Step by Step Video Solution | View the Written Solution

#3:

Instructions: Identify the parts of each addition problem.

a) 9 + 4 = 13

b) 12 + 10 = 22

c) 5 + 4 + 11 + 3 = 23

Instructions: Find each sum.

d) 37 + 0

e) 962 + 0

f) 1,362,373 + 0

Watch the Step by Step Video Solution | View the Written Solution

#4:

Instructions: Rewrite each using the associative property.

a) (3 + 1) + 5

b) 17 + (11 + 2)

c) (9 + 2) + 1

Watch the Step by Step Video Solution | View the Written Solution

#5:

Instructions: Rewrite each using the associative property.

a) (4 + 6) + 7

b) 13 + (2 + 8)

c) (10 + 20) + 15

Watch the Step by Step Video Solution | View the Written Solution

Written Solutions:

#1:

Solutions:

a) 1 + 7 = 7 + 1

b) 2 + 4 = 4 + 2

c) 6 + 15 = 15 + 6

d) 13 + 12 = 12 + 13

Watch the Step by Step Video Solution

#2:

Solutions:

a) 21 + 1 = 1 + 21

b) 13 + 9 = 9 + 13

c) 51 + 7 = 7 + 51

d) 103 + 2 = 2 + 103

Watch the Step by Step Video Solution

#3:

Solutions:

a) 9 - addend, 4 - addend, 13 - sum

b) 12 - addend, 10 - addend, 22 - sum

c) 5 - addend, 4 - addend, 11 - addend, 3 - addend, 23 - sum

d) 37 + 0 = 37

e) 962 + 0 = 962

f) 1,362,373 + 0 = 1,362,373

Watch the Step by Step Video Solution

#4:

Solutions:

a) (3 + 1) + 5 = 3 + (1 + 5)

b) 17 + (11 + 2) = (17 + 11) + 2

c) (9 + 2) + 1 = 9 + (2 + 1)

Watch the Step by Step Video Solution

#5:

Solutions:

a) (4 + 6) + 7 = 4 + (6 + 7)

b) 13 + (2 + 8) = (13 + 2) + 8

c) (10 + 20) + 15 = 10 + (20 + 15)

Watch the Step by Step Video Solution

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GreeneMath.com | Ace your next Math Test!

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In our lesson, we learned a few valuable properties of addition. We identify the parts of an addition problem as either: sum or addend. The addends are the numbers being added together or combined through addition. The sum is the result of the addition operation.

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GreeneMath.com | Ace your next Math Test!

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Properties of Addition Test - Test your knowledge of the Properties of Addition. Do you understand the Commutative and Associative Properties of Addition?...

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What is Subtraction? Subtraction is the mathematical operation of taking away and is normally accompanied by "-" (the subtraction symbol). The main idea is to find out how much is left after one amount is taken away from another. Subtraction is the opposite operation of addition. The subtraction operation is usually the second operation we learn in elementary school, after mastering addition. Let's think about the subtraction concept using an example. Suppose we started out with 6 boxes:

Now, let's suppose we wanted to take away or subtract away 2 boxes. How many boxes would be left? We could simply cross out 2 boxes and count what remains:

We can see from our picture above that we have 4 boxes remaining. This example can be translated into the subtraction problem: 6 - 2 = 4.
There are three parts to a subtraction problem:

Minuend - the starting amount or leftmost number

Subtrahend - the amount being taken or subtracted away from the minuend. This will be the number that comes after the subtraction symbol

Difference - the result of the subtraction operation. We start with the minuend and subtract away the subtrahend, the result is the difference

So using our example, we would label the 6 as the minuend. This was the starting number of boxes. The 2 would be our subtrahend. This was the number of boxes that we removed or subtracted away. The 4 would be the difference. This is the result of subtracting 2 away from 6.
Notice how working backward will give us a related addition problem:
4 + 2 = 6. In other words, the difference added to the subtrahend will give us our minuend back. This should make perfect sense. If we start with an amount such as 6 and we take away an amount such as 2, the result is 4. If we reverse the process and start with 4, and then add back the 2 that was taken away, we will end up with 6 again.
When we first learn to subtract, we utilize counting and related addition problems, until we can memorize the single-digit subtraction facts. Once these are known, we can use the process of vertical subtraction to subtract with numbers that are as large as we would like.

Subtracting Whole Numbers using a Number Line

Recall that we learned how to perform addition with whole numbers using a number line. The same can be done for subtraction. Again this process may seem trivial now, but it will help tremendously when we encounter the addition and subtraction of integers. Before we dive into number line subtraction, let's recall that addition is commutative:
3 + 4 = 7
4 + 3 = 7
Changing the order of the addends does not change the sum. This is not true with subtraction.
7 - 4 = 3
4 - 7 ≠ 3
The main point to understand is that the order matters when we subtract, so there is no commutative property for subtraction.

Subtracting on a Number Line

On the number line, start at the leftmost number of the subtraction problem (the minuend)

Move to the left by the number of units being subtracted away (subtrahend)

Recall that numbers increase moving to the right. Notice how with number line addition we moved right, as the addition of two non-zero whole numbers results in a larger number. The opposite is now true for subtraction. This operation is taking away, so the subtraction of one non-zero whole number from another will result in a smaller number. This means we will move left on the number line. Let's take a look at a few examples:
Example 1: Subtract 9 - 5, using the number line

Start out at the number 9, the leftmost number of the subtraction problem

Move to the left by 5, the number of units being subtracted away

We end up at 4, which is our answer

9 - 5 = 4

Example 2: Subtract 15 - 8, using the number line

Start out at the number 15, the leftmost number of the subtraction problem

Move to the left by 8, the number of units being subtracted away

We end up at 7, which is our answer

15 - 8 = 7

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how to subtract whole numbers using a number line

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GreeneMath.com | Ace your next Math Test!

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What is Subtraction? Subtraction is the mathematical operation of taking away and is normally accompanied by "-" (the subtraction symbol). The main idea is to find out how much is left after one amount is taken away from another. Subtraction is the opposite operation of addition.

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Once we have memorized all of the single-digit subtraction facts, we are ready to subtract with multi-digit whole numbers. In most cases, we will perform multi-digit subtraction using a vertical format. This process is known as vertical subtraction. Vertical Subtraction will allow us to simplify a multi-digit subtraction problem into a series of smaller single-digit subtraction problems.

Vertical Subtraction - Multi-Digit Subtraction without Regrouping (Borrowing)

Arrange the numbers vertically and by place value, the minuend will be on top and the subtrahend will be on the bottom. Remember, subtraction is not commutative, so the order does matter here.

Draw a horizontal line underneath the bottom number and place a "-" to the left of the bottom number

Subtract the digits in the rightmost column, this will contain the ones' place digit for each number. We subtract the bottom number away from the top number.

Place the result directly below the horizontal line

Repeat the subtraction process in each column moving left until there are no more columns to subtract

Example 1: Subtract 59 - 27

1. Arrange the numbers vertically and by place value, the minuend will be on top and the subtrahend will be on the bottom. Remember, subtraction is not commutative, so the order does matter here.

2. Draw a horizontal line underneath the bottom number and place a "-" to the left of the bottom number

3. Subtract the digits in the rightmost column, this will contain the ones' place digit for each number. We subtract the bottom number away from the top number.

4. Place the result directly below the horizontal line

5. Repeat the subtraction process in each column moving left until there are no more columns to subtract

59 - 27 = 32
Example 2: Subtract 996 - 584

1. Arrange the numbers vertically and by place value, the minuend will be on top and the subtrahend will be on the bottom. Remember, subtraction is not commutative, so the order does matter here.

2. Draw a horizontal line underneath the bottom number and place a "-" to the left of the bottom number

3. Subtract the digits in the rightmost column, this will contain the ones' place digit for each number. We subtract the bottom number away from the top number.

4. Place the result directly below the horizontal line

5. Repeat the subtraction process in each column moving left until there are no more columns to subtract

996 - 584 = 412

Vertical Subtraction - Multi-Digit Subtraction with Regrouping (Borrowing)

In many cases, the lower digit of a column is larger than the upper digit. When this occurs, we utilize a procedure known as borrowing. Borrowing is just a way to re-write our number such that the subtraction in a particular column is possible. Let's think about a simple example.
Example 3: Subtract 71 - 35

1. Arrange the numbers vertically and by place value, the minuend will be on top and the subtrahend will be on the bottom. Remember, subtraction is not commutative, so the order does matter here.

2. Draw a horizontal line underneath the bottom number and place a "-" to the left of the bottom number

3. Subtract the digits in the rightmost column, this will contain the ones' place digit for each number. We subtract the bottom number away from the top number.
In this case, the subtraction in the ones' column provides an issue. We can't subtract 1 - 5 since 1 is not large enough to take 5 away. When this occurs, we can borrow from the next digit left. 71 = 7 tens + 1 ones. If we borrow 1 ten or 10 ones from the 7, we could rewrite the number 71 as:
6 tens + 11 ones. This would allow us to subtract in the ones' column since 11 is larger than 5.

Now we can subtract 11 - 5

Place the result directly below the horizontal line

Repeat the subtraction process in each column moving left until there are no more columns to subtract

71 - 35 = 36

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GreeneMath.com | Ace your next Math Test!

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Once we have memorized all of the single-digit subtraction facts, we are ready to subtract with multi-digit whole numbers. In most cases, we will perform multi-digit subtraction using a vertical format. This process is known as vertical subtraction.

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Algebra Basics: Solving Basic Equations Part 1 - Math Antics

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Αρχική_αξιολόγηση_στην_Ενότητα_1_μαθη_ε

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Ενότητα_1_Μαθηματικά_1

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επανάληψη_πενταψήφιοι_αριθμοί

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Τετραψήφιοι_αριθμοi

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Multiple choice exercise for Computer Basics