3TH / VWO §9.1/§9.4 Calculating with fractions

• Wiskunde
• Middelbare school
• havo
• Leerjaar 3

3T havo §9.1 Calculating with fractions

3T vwo §9.4  the same (almost)!

A short recap:

When adding or subtracting fractions, the denominators (noemers) have to be the same. If they're not, let's make them the same! As follows:

​5​​3​​+​7​​6​​=​35​​21​​+​35​​30​​=​35​​51​​

+ Now with variables too!

+ Many times we just multiply the denominators to find the new one.

+ Like here: 5 x 8 = 40

+ another one comes up

+ watch: the 2nd fraction is not changed by us! 

+ 5x is a fine denominator

+ One more.

+ The final result has a sum as numerator.

+ That's because 4 and 3x are not like terms!

Task 1.

Take a scrap paper (or your Notebook) and work out:

Write as one fraction and key in your answer in the next slide:

Answer to task 1:

Solution task 1:

Now about Multiplying and Simplifying!

Do you remember that doing 'times' is much simpler than doing

'plus or minus', with fractions?

 Reason: denominators may be unequal. Who cares?

x             =                    = 

​6​​5​​

​8​​3​​

​48​​15​​

​16​​5​​

Now about Multiplying and Simplifying!

I remember something about making denominators equal. So here I go about the job:

               x                  =                                         x                    =              

            

                

However now I am completely stranded.....         So let's look once more at the right way to do it!

​6​​5​​

​8​​3​​

​48​​15​​

​16​​5​​

​48​​18​​

​48​​40​​

​.....​​75​​

​....​​....​​

Now about Multiplying and Simplifying!

Do you remember that doing 'times' is much simpler than doing

'plus or minus', with fractions?

 Reason: denominators may be unequal. Who cares?

x             =                    = 

​6​​5​​

​8​​3​​

​48​​15​​

​16​​5​​

When multiplying we just multiply numerators and 

denominators. Period!

Simplification is the reverse of multiplication.

Now we divide numerator and denominator by the same number!

2 more examples of simplifications:

The book (where I took this from)

like to write the numbers as 

products of letters and prime numbers

(priemgetallen). This may seem 

unnecessary, but it makes clear

what is really happening when

simplifying! 

Task 2:

Simplify yourself now and key in your answer in the next slide:

Answer task 2:

Solution task 2:

The 2nd step

you may leave out.

There's one more new thing in §9.1....

That's about splitting up a fraction

in 2 new ones.

In exercises 8, 9 and 10 (havo) 

and 32, 33 (vwo) 

you'll discover

this for yourself!

Homework time

I ask you to stay on this Googlemeet a little longer.

In that way you can ask me anything that comes up,

when making: §9.1 Calculating with fractions, yourself.

Send in pics of your results in GoogleClassroom.

Good luck!