|
Learning Objectives:
Student will be able to:
|
Let's start by reviewing fractions.
First, fractions are written as a part/whole. So when you get a fraction like 2/5, what we're really saying is that if you divided the whole into 5 parts, you would have 2 of them. The top number is call the numerator, and the bottom number is called the denominator. The numerator tells you how many parts you have, and the denominator tells you into how many parts the whole was split.
We will start by reviewing how to reduce fractions. The reduction of fractions happens when both the numerator and the denominator have a factor in common. For example, the fraction 3/15 will reduce because both 3 and 15 have a factor of 3. To reduce we divide both the numerator and denominator by that factor. So we have
3
÷
3
= 1
15 3 5
Here are some fractions for you to try and reduce.
ANSWERS:
Now let's review how to multiply fractions. Multiplying fractions is the easiest operation to do with fractions. Here are the steps.
Example 1:
2
. 1
3
4
(2)(1)
(3)(4)
2
12
1
6
Example 2:
5
. 3
8 4
15
32
Dividing fractions is almost as easy. We need to use the reciprocal to divide fractions. The reciprocal is a fraction “flipped:” For example, the reciprocal of 2/3 is 3/2. You take the numerator and put it in the denominator and take the denominator and put it in the numerator. Here are the steps for dividing fractions.
Example 1:
3
÷
4
10 5
Step 1: reciprocal of the second fraction and change division to multiplication
3
. 5
10 4
Steps 2 and 3: multiply numerators and multiply denominators
(3)(5)
(10)(4)
15
40
Step 4: reduce
3
8
Example 2:
_
3
÷
5
4 8
_
3
. 8
4 5
_
24
20
-
6
5
Next, we need to review how to add and subtract fractions. In order to add and subtract fractions we need to make sure we are adding and subtracting equal size parts, so we need to make sure that we have fractions with the same denominator. Here are the steps for adding and subtracting fractions.
Example 1:
4
_ 2
5
3
Step 1: Get a common denominator: Since one fraction has a denominator of 5 and the other has a denominator of 3, we need to find the smallest number that they both go into. The multiples of 5 are 5, 10, 15, 20, 25 ….. The multiples of 3 are 3, 6, 9, 12, 15, 18,..... Since they both have 15 as a multiple, this is going to be our common denominator. We multiply each fraction so that we have 15 on the bottom of both fractions. Be careful because we must multiply both the numerator and the denominator of the fraction by the same number so we don't change the value of the fraction. This is the opposite of reducing.
We know that 5 * 3 = 15, so we multiply the numerator and the denominator of the first fraction by 3/3
4
* 3
= 12
5 3 15
We also know that 3 * 5 = 15, so we multiply the numerator and the denominator of the second fraction by 5
2
* 5
= 10
3 5 15
So now our problem becomes
12
_ 10
15 15
Step 2: Add/subtract the numerators.
12 – 10 = 2
Step 3: Keep the denominator
2
15
Step 4: Reduce
Since 2 and 15 don't have any common factors, this does not reduce, so our answer is 2/15
Example 2:
1
+ 2
2 8
Step 1: Common denominator = 8
1
* 4
= 4
2 4 8
2
* 1
= 2
8 1
8
Step 2:
4 + 2= 6
Step 3:
6
8
Step 4:
3
4
Example 3:
1
+ 1
4 6
1
* 3
+ 1
* 2
4 3 6
2
3
+ 2
12 12
5
12
Let's work on mixed numbers now. We will use the same steps to add, subtract, multiply, and divide mixed numbers, but first we need to change mixed numbers into improper fractions.
Example1: Change 1 5/8 to an improper fraction.
Step 1: Multiply the denominator by the whole number
(8)(1) = 8
Step 2: Add the numerator to the product from step 1
5 + 8 = 13
Step 3: Put the answer to step 2 on top of the denominator
13
8
Example 2: Change 3 ½ to an improper fraction
(2)(3) = 6
6+ 1 = 7
7
2
We also need to change improper fractions back to mixed numbers. The rule is that if the problem gives you mixed numbers, you give your answer as a mixed number. We are going to work backwards from what we just did. Here are the steps.
Example
1: Change 16
into
a mixed number
5
Step 1: Divide the numerator by the denominator.
16 ÷ 5 = 3 R1
Step 2: Take the remainder and put it over the denominator
3 1/5
Example
2: Change 24
into a mixed number
5
24 ÷ 5 = 4 R4
4 4/5
|
Grading for this lesson:
To get a 10: All answers are correct the
first time, or within first revision.
To get a 9: You can have 1 incorrect answer after your original submission. To get an 8: You can have 2 incorrect answers after your original submission. To get a 7: You can have 3 incorrect answers after your original submission. To get a 6: You can have 4 incorrect answers after your original submission. To get a 5: Cheating - Plagiarism - purposeful or mistaken, which will lower your final grade for the course (so be very careful when posting your work!); lack of effort, disrespect, or attitude (we are here to communicate with you if you don't understand something); Note: For this class it is necessary to post the questions over each answer. Failure to do so will result in asking for a revision. No grade will be given for incomplete work. |
Lesson 1 Assignment
Do
the test below. You must successfully complete all of the questions in order
to complete the lesson.
If you get any wrong, you will be asked to
resubmit the wrong answers and show your work. The teacher will then look at
your work and give you advice on what you are doing wrong.