Lesson 3ª

 

 

 

 

 

   

 

SOLVING EXCERCISES:

1. Ann has 12 €, Peter has 5 € and Mary has 8 € more than Peter. How many Euros do they have all together?

Solution:

Mary has 8 € + than what Peter has = 8 + 5 = 13

The three of them have: 12 + 5 + 13 = 30 €

2. Imagine that the place you study is 200 metres away from your home. How many kilometres have you walked in a week if you have gone to school 5 days? You go to school in the morning and you go home for lunch. In the afternoon, you do the same thing; another round trip.

Solution:

In the morning, to get to school….............…...………. 200 m.
                       to go back home…………….......…… 200 m.
In the afternoon, to get back to school……………….. 200 m.
                   to go back home………………......……. 200 m.

Total metres walked in a day…….……...… 200   4 = 800 metres
In five days……………………………….. 800   5 = 4000 metres. =  4 Km.

3. How many 5 cent coins are there in 1 €?

Solution:

1 € = 100 cents.

5 cent coins = 100 / 5 = 20 coins.

4. How would you read this number: 123,412,345,678,987,654,321?

Solution:

A. The number is divided in groups of three digits from left to right. Between the first three-digit group and the second group, we write a sub-index 1. Between the second three-digit group and the third group, we write a sub-index 2. Between the third and fourth group, we write a sub-index 3, and so on and so forth.

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B. We begin reading the number from the left. We read quintillion when we reach sub-index 1. We read quadrillion when we reach sub-index 2. We read trillion when we reach sub-index 3. We read billion when we reach sub-index 4. We read million when we reach sub-index 5. We read thousand when we reach sub-index 6. It should read like this:

one hundred twenty-three quintillion, four hundred twelve quadrillion, three hundred forty-five trillion, six hundred seventy-eight billion, nine hundred eighty-seven million, six hundred fifty-four thousand, three hundred twenty-one


GOOGOL

This word should be pronounced like "Google". It was first said (created) by a nine year-old boy when his uncle, a math scholar, asked him, "How would you call a really, REALLY big number?" The boy answered with these words over 60 years ago. Since then, his uncle, the mathmatician, stated it was equivalent to 1 with 100 zeros behind it.

Lets take a look:

                                          aqwd

10 000 0000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000

The name of the reknown search engine GOOGLE, was inspired in GOOGOL.

REMEMBER:

In an operation containing parenthesis, products, sums, subtractions, divisions, brackets etc. there is an order we need to follow. First, we solve the operations inside parenthesis. If there are sums, subtractions, multiplications or divisions inside the parenthesis, you must start with divisions and multiplications. After you have multiplied and divided, you can add and subtract.

Solve the following exercises:

a) 3 + 4 - 6 + 7 x 2 - 13 = 2

b) 4 - 10 + 6 / 2 - 5 + 8 = 0

c) 2 + 4 - 5 + 6 x 9 - 20 = 35

d) 2 (3 - 2) + 1 + 4(1 + 3) - 6 = 13

e) 17 - (5 - 1) + 2(4 - 1) + 10 = 29

f) 2[3 + 2(3 - 1) + 2] = 18

g) 1 + [2 + 4(2 + 4) - 8] = 19

h) [3 + 4 - (8 - 2) + 2[3(3 - 1)] + 9] - 2 = 20

i) 2 [2 + (4 + 2) + 2(3 - 2) + 1] + [2(3 + 1) -1] = 29

Solution to some exercises:

d) 2 x 1 + 1 + 4 x 4 - 6 = 2 + 1 + 16 - 6 = 19 - 6 = 13

h) [3 + 4 - 6 + 2[3 x 2] + 9] - 2 = [1 + 2[6] + 9] - 2 = 1 + 12 + 9 - 2 = 20

f) 2[3 + 2 x 2 + 2] = 2[3 + 4 + 2] = 2[9] = 2 x 9 = 18

i) 2 [2 + 6 + 2 x 1 + 1] + [2 x 4 -1] = 2 [8 + 2 + 1] + [8 -1] = 2[11] + 7 = 22 + 7 = 29