Summer Math Part 2 - 8th Grade

Scroll down to the previous post for help on #1-27.


Okay...it's been more than a few days since the other post, but here is the rest of the summer math examples! Remember, you can always email me if you have any questions. That's what I'm here for.

#28-32. Scientific Notation

Remember, first you multiply the first numbers in parentheses. Then multiply the powers of 10. How you do that is by ADDING the exponents following the rules for adding integers. If your first number is a single digit or has a single digit before a decimal point, you are finished.If your first number is two or more digits, you have to change that. Remember, in scientific notation, your first number has to between 1 and less than 10...one digit before the decimal point. So, if you multiply and get a number greater than 10, such as 24, you have to move the decimal point over until you have only a single number before the pont. So, 24 would change to 2.4. Once you do that, since we moved the decimal over 1 time, ADD one to the exponent with the 10.

Here are two examples. In the first, you don't have to move the decimal point or change the exponent. In the second, you do have to move the decimal point.


For #33-36, remember the rules for multiplying and dividing signed numbers.

If the signs are the same the answer is POSITIVE.

If the signs are different, the answer is NEGATIVE.

If you are multiplying more than two numbers, just count the number of negative signs. If there is an even number of negative signs, it's POSITIVE. If there is an odd number of negative signs, it's NEGATIVE. All you have to do is multiply the numbers.

#37-40 Simple Equations. Here are a few examples. Remember, to solve an equation, you are trying to get the variable by itself.
For #41-43, remember that to add like terms, you combine the terms that have the exact same variable. Numbers without variables are like terms with each other. Do not combine terms that have two different letters. Here are a few examples:

Example 1:



Example 2:




For #44-45, you are using distributive property. You multiply the number on the outside by each of the numbers on the inside.


That's it! Remember to write if you need help and ----

HAVE A GREAT SUMMER! See you in the fall!

Mrs. Swickey

Summer Math Homework - 8th Grade

Hello, 8th grade! Here is the information I promised to help you with your summer homework. Remember, you are only supposed to work half a worksheet a week! First, this will keep you from being overwhelmed at the end of the summer and second, it will keep your math skills up over the summer.

This post has examples or explanations for #1-27. I will post the rest in the next couple of days.

Each form has the same kind of problems, so I'll go through them by number.

Please email me if there is something you don't understand. I am here to help!

#1-7: You should know how to do these.

#8. To round repeating decimals, first write the repeat to one place past the place you are supposed to round. Here is an example:

If you are supposed to round to the nearest ten thousandth, write the repeating numbers until you are one place past the ten thousandth. Then, use that number to round to the ten thousandth. Your final answer will NOT have a repetend, (the little bar), because it will be rounded.


You can click on any image to make it bigger and easier to see.

#9. If you can say the decimal, you can write it as a fraction. Remember to reduce!

#10 & #12. Remember, exponents tell you how many times to multiply a number by itself:



#11 & #13. To write a number as a product of prime numbers using exponents means to do the prime factorization. Use the factor tree. Here is an example:

#14. To find the area of a complex shape, first divide the shape into squares and rectangles. Here is an example:


For #15-18, you are going to plug in the number given for each variable (letter) and find the value of the expression. Here is an example:

#19 - This is just a simple equation. You should know how to solve this!

#20-23 - These are order of operations problems. Remember the order:

Parentheses - Exponents - Multiplication/Division - Addition/Subtraction

Simplify everything inside parentheses or other inclusion symbols, like brackets. Then, simplify exponents (if any). Then do any multiplication OR division - whichever is first from left to right. Then do any addition OR subtraction - again, whichever is first from left to right. Be sure you DO NOT add numbers that still need to be multiplied. That is the biggest mistake students make. Take your time!

Here is an example:



#24-25. For these problems, you will need to know some basic formulas for finding the area and circumference of a circle. I will do a few problems.


If you are given 9 as the diameter, to find the radius, divide by 2. It will be a decimal - 4.5

#26-27. You need to remember the rules for adding signed numbers. If the signs are the same, ADD and keep the same sign. If the signs are different, SUBTRACT, and use the sign of the bigger number. Here is an example: