Chapter 4 Study Guide

Hey guys. Here's a study guide for your Chapter 4 assessment (scheduled for Monday, January 12th). We've taken shorter assessments along the way so far in this chapter, but this assessment will cover everything we've learned from the chapter, so please be sure to study by looking back over your previous assignments from Chp. 4 and your notes. Also, don't forget that Glencoe has a GREAT website for studying. Click here: http://www.glencoe.com/sec/math/msmath/mac04/course1/self_check_quiz/index.php/


You can use the online quizzes and personal tutor videos to look back at what we've learned and to practice what you know.


Hooookay. Let's talk about what we've learned in Chapter 4.


Section 4-1: Multiplying a decimal by a whole number


*Remember, you should not line up the decimals when you are multiplying - only when you're adding or subtracting.*

1) Set the problem up as though you were dealing with plain ol' whole numbers.
2) Solve (ignore the decimals for now - remember, we're pretending they are both whole numbers).
3) To place the decimal in your answer:
    First, count how many numbers after the decimal in the original problem.
    Then, going from right to left in your answer, count that many spaces over and put your decimal there.

Example:

      4.23   ---> There are two numbers after the decimal here. 
   x      6
    2538    ---> Now, going from right to left, put the decimal two places from the end.

Answer: 25.38

Section 4-2: Multiplying decimals

This method is exactly the same as the method for multiplying a decimal by a whole number.

1) Set the problem up.
2) Solve just like they're whole numbers (ignore the decimal).
3)  How many numbers (TOTAL) are there after all the decimals in your problem? Count them up, and then
     place the decimal that many places over in your answer.

Example:

     3.65   ---> There are two numbers after the decimal here. 
x     2.5   ---> There is one number after the decimal here. 
   9125    ---> Now, going from right to left, put the decimal three places from the end, since we counted
                       3 numbers total after decimal points in our problem.

Answer: 9.125


Section 4-3: Dividing decimals by whole numbers


First, carry the decimal straight up. Then divide as with regular numbers. *Don't forget, you may need to annex zeros as you divide.*
Your decimal will already be correctly placed in your answer.




Section 4-4: Dividing by decimals


When dividing any number by a decimal:


1. Turn the outside number into a whole number by moving the decimal.
2. Now go to the inside number and move the decimal the SAME number of spaces.
3. Carry the decimal straight up from its new position & divide using the method we learned in 4-3.




Section 4-5: Perimeter


The formula for the perimeter of a rectangle is 2l + 2w. (Two times the length plus two times the width.)
The formula for the perimeter of a square is 4s (four times the length of one of the sides).
*If in doubt, you can simply add all of the sides together for the perimeter. This is how to find the perimeter of any other figure.*


For example, if you have a rectangle with a length of 18 inches and a width of 11 inches, you can simply substitute the numbers into the formula:


2l + 2w ----> 2 x 18 + 2 x 11    (don't forget order of operations - multiply first)
36 + 22 = 58
So the perimeter of this particular rectangle = 58 in.




Section 4-6: Circumference


Remember that circumference packet we completed? That would be a great tool to use when studying for circumference. Here's a post I made a couple years ago for walking through circumference:
Check out this diagram from kidsmathgamesonline.com:

Diameter (d) is the distance a cross a circle through its center (it goes all the way through). 

Radius (r) is the distance from the center to any point on a circle (it's half of the diameter). 

And, as we said, Circumference (c) is the distance around a circle. 

There's a formula to figure out what the Circumference of a circle is:

C = πd 

This says "Circumference = pi times the diameter"

What is that little symbol? That "pi" thing??? Well, it's not a pie, although I could certainly go for a cherry pie right now. 

tasteofhome.com

Anyway. Pi is a number that we use to find Circumference. Use a calculator to find the real value of pi by pressing the  π  button on your calculator. It goes on forever - so we round it to 3.14. 

Now that we know what pi is, we can find the circumference of any circle as long as we know its diameter. Let's say we have a circle with a diameter of 4.5 inches. All we need to do is plug the numbers into the formula:

C = 3.14 x 4.5

Then, using your calculator or your multiplying decimal method, solve for C:

C = 14.13

We know that the circumference is 14.13 inches. 

There's another way to find Circumference - this time, using radius. Take a look at the circle diagram above. Did you notice that the radius is exactly half the length of a circle's diameter? So to find the Circumference of a circle using the radius, we use the following formula:

C = 2πr

This says "Circumference equals 2 times pi times the radius of a circle."

Again, all we have to do is plug the numbers in. If we have a circle with a radius of 38 ft, we would plug the numbers in like so:

C = 2 x 3.14 x 38

Now solve for C.

C = 238.64 ft.

That about sums it up. As always, please email me if you're having trouble. Look over your notes during the commercials as the Ravens crush the Patriots this weekend.... ;)