1TH/Vwo §8.1 Calculating with numbers

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

§7.1 Calculating with numbers

Homework:  4  t/m  8

Some new words will come up!

It's important to know their meaning.

That's what this LessonUp is for.

§7.1 Calculating with numbers

Homework:  4  t/m  8

Learning goals:

- What is a sum, a difference, a product and a quotient?

- How to do calculations IN THE RIGHT ORDER (aka the order of operations).

The new words:

brackets           product       quotient

           sum          difference          arithmetics      

Try to take in the following information.

Later in this LessonUp there will be several questions about it!

Sum

Adding up two (or more) numbers together,

gives us the Sum of the numbers.  Like  35 + 12 = 47

In fact 'the sum' is our 'de som'!

Indeed, awe-sum!

Difference

When you subtract 2 numbers from each other, 

the result is the Difference.

For example:          45 - 16 = 29,  so 29 is the Difference of 45 and 16.

Product

Multiplying 2 (or more) numbers by each other,

gives us the Product of the numbers.

Like 23 x 3 = 69, so 69 is the Product of 23 and 3.

Quotient

When you divide 2 numbers by each other, the result is called the Quotient of them.

For example:  14 : 7 = 2,  so the Quotient of 14 and 7 is 2.

Mention the most important 4 words from the previous slides.

The Product of 15 and 3 is ......

1. 18
2. 5
3. 45
4. 12

The Product of 15 and 3 ....

means the Multiplication of 15 and 3, so:

15 x 3 = 45

The Sum of 34 and 13 is .........

1. 21
2. 21
3. 57
4. 47

The Sum of 34 and 13 is ...

47, because the Sum means Adding!

The quotient of 27 and 9 is ........

What has to do most with arithmetic?

1. Sam
2. Some
3. Sum
4. Somme

Maybe you remember from your old school ..

that x  and  :  go before  +  and   -.

This is still true.

However, there can be exceptions...

See next slide!

Time for ....

Brackets are the New Things!

Amazing stuff, down here:

Amazing stuff, down here:

So, thanks to the Brackets (=haakjes), the old Priority (=voorrang) is changed.

In the first calculation we do   2 x 5   first,

but in the second calculation we first do 8 + 2 Why?  Because of the Brackets

What is the result of:
(6 + 6) : 3 ?

1. 3
2. 4
3. 9
4. -5

Explanation:       (6 + 6) : 3 =

First work out the Brackets:        (6 + 6) : 3 

                                                                = 12 : 3 

                                                                =4 

Notice that the Brackets have gone now, as they have no meaning any more.

FINALLY:  Try to understand the meaning of the next slide!

In the next slide the meaning is explained!

Here is an example.

Watch how the Calculation is worked out step by step!

The next example is for you to work out and send in in a 'Fotovraag'!

A correct notation is important.

In the next slide, find the mistake!

5 + 5 x 3 = 15 = 5 + 15 = 20

The outcome is good, but the way of writing it all down contains a mistake.

Think hard about this. Which step above is not good?

Some of you get the turn.

Next slide gives the answer.

5 + 5 x 3 = 15 = 5 + 15 = 20

The outcome is good, but the way of writing it all down contains a mistake.

The Mistake:    ' = 15 '

It suggests that 15 is equal to the final outcome, 20.

Why? Well, there are ' = ' signs between every step, so every step must be equal to any other step!

4 : 2 + 7 x 3 - 4 x 2 = .......

1. 31
2. 2 = 2 + 21 = 23 - 8 = 15
3. 2 + 21 - 8 = 15
4. 15

Fotovraag:

1. Work this task out in your Notebook (first copy the task, then write each next step underneath the previous step).

2. Take a picture of this and

3. send it in in the next slide!

4. so show us your Calculations and

5. NOTA = not only the Answer!

Calculate 7 + 3 x 4 : 6 - 5 = .........

Solution:

Homework time

§7.1 :   4 through 8;   for exercises 6 and 7 don't forget to work out the calculations, just like in the 2 examples shown to you.

So you may skip 1, 2 and 3, however do not skip the theories with examples.

Do not forget to check and correct your homework!