Thursday, November 16, 2017

Dividing Fractions

Dividing fractions is EXACTLY like multiplying fractions with one extra step

COPY CHANGE FLIP

Let's look at a few fraction division problems.








Notice that I COPY the 7/8, CHANGE the divide sign to X, then FLIP the 2nd fraction to be 8/1.  Then multiply like normal.












Here is another example







Here is one more:









This works for all fraction dividing problems including whole numbers and mixed numbers.  With whole numbers, put them over 1.  For example, 12 would be 12/1.  For mixed numbers, change them to improper fractions first.  for 4 1/3 would become 8/3.  Then copy, change and flip as necessary.

Some common mistakes include flipping both numbers, not changing the sign, or not changing whole numbers/mixed numbers appropriately.  BE SURE TO

COPY  CHANGE  THEN FLIP.

Wednesday, November 15, 2017

Multiplying Fractions

When multiplying fractions, we just multiply the numerators together and then the denominators together.  Let's look at an example:

1  *   1  =   1
3       4       12

Here is another example:

2   *   5   =   10  or 5
3        6        18      9

What if you are multiplying a fraction and a whole number?

12 *   1
          4

Every whole number has a denominator of 1, so....

12 *   1   =   12
 1       4         4

Since the fraction bar means divide, we have 12/4 which is 3.  When multiplying fractions, the product will never be larger than the sum.

We can use a brownie pan method to show the same thing.  Here is a blank, square brownie pan.


Let's say that I am selling brownies.  I have only 2/3 of the pan left.  The red section is gone.


Let's say I have a customer who wants to buy 1/4 of what I have left, or 1/4 of 2/3.  I would have to cut my 2/3 into 4th's.  It would look like this.


So now I need to color in 1/4 of what I have here.  The green shows what I would sell.



This represents 2/12 of the whole pan, or 1/6.  Mathematically:

1    *    2   =    2
4          3         12



Modeling Multiplying Fractions

2/3 of 7/10 means 2/3 x 7/10.  The of can be replaced with a multiplication sign.  We begin by drawing a square.




Split the box according to the denominator of the SECOND factor.


Mark off the amount that makes the second factor true.  In this case we marked out 3/10 of the whole because we only have 7/10 of the whole left.

Then split the WHOLE box by the denominator of the FIRST factor.




I labeled the top 1/3 to show that each vertical bar represents 1/3 and the left side 1/10 to show that each horizontal bar represents 1/10.




















I then shaded 2 out of every 3 boxes left over in green.  (sorry the picture is blurry).

The total green boxes represents my numerator.  The TOTAL boxes of the whole becomes my denominator, not just the part leftover.






This shows mathematically why that works.

Tuesday, November 14, 2017

Subtracting/Adding Fractions

We went over adding and subtracting fractions in class.  Here are the 2 ways we discussed.  This also works for adding fractions.

Separate the whole numbers first.  Here, we have 11 - 4 = 7.

Then subtract your fractional parts (we had to find a common denominator first).

Since 1/8 came first, we have to subtract the 1/4 or 2/8 from it.  This give us -1/8.  Now we subtract our two parts

7-1/8.  When the denominator and numerator are the same, we know that it is equal to 1, so 8/8=1




In this method, we changed our mixed numbers into improper fractions.  From there we had to find a common denominator.   Then regular subtraction rules apply.  Once we find our improper fraction, we have to change it back to a mixed number.



Friday, November 10, 2017

Percentages

Here is a chart to memorize for benchmark fractions, decimals, and percentages.


You can take any fraction and divide it to get a decimal.  Let's look at 1/4.


Or you can take any decimal and turn it into a fraction by putting the place value as the denominator and whatever numbers are in your decimal as the numerator.


Or you can take any percentage and turn it into a fraction by placing it over 100 then change it to a decimal from there.

Lastly you can take the benchmarks and use them to your advantage.  In the example, we used 25% which is equal to 1/4.  From there we can get 50 and 75% plus we can do up to any number (we used 20 as a total) to find out each percentage of that number.


In summary, you can use these steps

If you have the part and the total, divide to get a decimal, the multiply by 100 to get the percent.

If you have the percent and the total, multiply to get the part.

Part ÷ Total = Percent

Percent x Total = Part