## Introduction: How to Add

Here is a complete list of how to add anything you may ever want to add, like whole numbers, fractions, radicals, and much much more. Please comment, rate, and ask as many questions as possible. Remember I am only an 9th grade honors student and even though I have a high math average, some things may be incorrect. Please inform me if anything is wrong. Thank You. Please comment and rate.

## Step 1: How to Add Whole Numbers

This is the most basic of the basics. All you need to do is keep counting up. For example, 7+3=10. To learn the concept, you would count up to seven, and then keep counting up three more numbers. Ex, 1,2,3,4,5,6,7 (then the next 3) 8,9,10. There are three more numbers added on to the original seven and that is basically how it works. Obviously, you cant do this when adding big numbers, but there is a better way for that. Line up the numbers vertically and, starting at the right, add together the numbers that line up. Look at the pictures (coming soon) for more detail. If there is a number 10 or greater, place the units value, left, below the line and carry the ten's digit number up and to the left. Next time you just do the same and add on the remainder from last time. If you have any questions or if I have mislabeled or spelled something wrong please leave a comment. Thank You.

TRY IT

1. 2+2

2. 5+8

3. 4+1

4. 9+0

5. 3+5

## Step 2: How to Add Integers

Adding integers is similar to adding whole numbers, but integers can be positive or negative. To add two negetive integers, you add the same way as you would add whole numbers, but place a negative sign in front of the answer. Adding positive and negative integers can get more tricky. To do that, you subtract the larger number from the ,smaller one. Then you keep the sign from the number with the greatest common value. That means the larger number without taking the negetive into account. Ex. |5| (the absolute value of 5) is equal to 5, and |-7| is equal to 7. then you get your answer. Ex, -6+3=-3. subtract 3 from 6 and keep the negative because |-6| is greater than |3|. If you have any questions or if I have mislabeled or spelled something wrong please leave a comment. Thank You.

TRY IT

1. -8+3

2. 3+(-5) (ignore the parenthesis, They just mean it is plus negative 5)

3. -6+(-2)

4. -2+1

5. 5+(-3)

## Step 3: How to Add Fractions

Adding Fractions is once again a basic concept, but occasionally it can get hard. Once you have mastered basic addition-adding up to 12 and 12-and multiplying-up to 12 and 12-you can do this. If you have a basic fraction where the denominators (the bottom part of the fraction) are equal, such as 1/2 + 1/2, you can just add the top numbers and keep the bottom the same. The reason for this is if you have half of a pizza, and your friend has half a pizza, and you put them together what do you get. A whole pizza. if the denominators are not the same, you may need to cross multiply. If you have 1/2 + 1/3 you multiply opposites. 1 x 3 and put it in the upper left. 1 x 2 and put that in the upper right. And multiply the bottoms and that becomes the denominator of both fractions. Now you can add them normally. In order to simplify fractions, you must know how to divide. Divide the numerator (top) and the denominator (bottom) by the same number. This works because 1/1, 2/2, 3/3, and even 99/99 all equal 1. If you divide by one, the number remains the same even though it appears different. If you have any questions or if I have mislabeled or spelled something wrong please leave a comment. Thank You.

TRY IT write each answer in simplest form

ex. 3/8 + 1/8 = 4/8 or **1/2**

1. 2/3 + 1/3

2. 2/7 + 3/7

3. 1/2 + 1/3 (remember cross-multiplying)

4. 1/10 + 1/10

5. 2/5 + 1/5

ANSWERS ARE IN STEP 6

## Step 4: How to Add Radicals

IMPORTANT BELOW IS A PICTURE OF A RADICAL SIGN. I WILL BE SUBSTITUTING THAT SIGN WITH A STAR FOLLOWED BY PARENTHESIS. *(X). This is complex 9th grade algebra so if you don't get it it's OK. A radical is the square root sign, and adding them can get tricky. first, you must simplify. *(40) is not a perfect square and it equals a strange decimal, so what you must do is simplify it. First, find the greatest square divisible into the number. In this case, it is 4. Divide the number under the radical and you should get *(4) x *(10). Now, take the square root of 4 (2) and express it in front of the remaining radical. Yay. You get 2*(10). That is simplified. Now to add you must have the same number under the radical in each one. If you dont try simplifying and if that doesn't work you would be forced to word with uneven decimals. Add the leading number of each one. Addition is not difficult on this, it is trying to get the numbers under the radical equal. Hint-the most common square root to divide by is 4, so always try that first unless it is a large number. Also, if there already is a leading number but the radicand (number under the radical) is divisible by a perfect square, you do the same thing but after you square the leading number you would multiply it by the original leading number. If you have any questions or if I have mislabeled or spelled something wrong please leave a comment. Thank You.

TRY IT

1. 4*(8)+5*(8)

2. *(8)+2*(18)

3. *(44)+ *(44)

4. 2*(32)+ *(50)

5. 3*(20)+ *(45)

## Step 5: ANSWERS

Whole Numbers

1. 4

2. 13

3. 5

4. 9

5. 8

Fractions

1. 1

2. 5/7

3. 5/6

4. 1/5

5. 3/5

Integers

1. -5

2. -2

3. -8

4. -1

5. 2

Radicals

1. 18*(8)

2. 8*(2)

3. 4*(11)

4. 13*(2)

5. 9*(5)

If any of these answers are incorrect please leave a comment and be sure to tell me which one is wrong and what it should be. Thank You.

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Burning Questions Round 6.5