NUMBER PART TWO
Identify Prime Numbers - [L4]
A prime number is a whole number greater than 1. It has only two factors, 1 and itself. The two factors have to be different, which rules out the number 1 being a prime number. The first 10 prime numbers are '2, 3, 5, 7, 11, 13, 17, 19, 23, and 29'. As you progress through the list of natural numbers ...1,2,3,4,5...etc , prime numbers appear less and less often. Very large prime numbers are used in data encryption. Prime numbers are also useful for working out prime factors of numbers, an example of which will be given later in prime factor trees in section 23, a Level 6 topic.
The Sieve of Eratosthenes
Eratosthenes (BC 276 - 194) was a Greek Mathematician (and many other things) who at one point was the head librarian at the famous Library of Alexandria. He devised a method for finding the prime numbers between 1 and 100 called Eratosthenes' Sieve, which sieves out all the natural numbers leaving only the prime numbers. It is based on a table of numbers, see below.
Lets work across the top row of the table from left to right, crossing out the non-primes. Because 1 is not a prime (it has only 1 factor) it is the first to be crossed out on the table. 2 is the first, and only even prime number. So now cross out all the even numbers up to and including 100.
Next is 3, it has only two factors, (1 and 3) so it's a prime number.
Now go through the list and cross out all multiples of three. You can use the three times table or just cross out every third number in the table. Don't forget 87, commonly forgotten as a multiple of 3. Remember all even numbers are crossed out.
So the next is 5 with factors of 1 and 5. Now cross out all multiples of 5 (10, 20 , 30 etc are already crossed out because they were even). So any number ending 5 can be crossed out.
Repeat the process with 7 and 11. The list is now getting quite small. The remaining numbers are prime numbers and you should count 25 of them.
Next is 3, it has only two factors, (1 and 3) so it's a prime number.
Now go through the list and cross out all multiples of three. You can use the three times table or just cross out every third number in the table. Don't forget 87, commonly forgotten as a multiple of 3. Remember all even numbers are crossed out.
So the next is 5 with factors of 1 and 5. Now cross out all multiples of 5 (10, 20 , 30 etc are already crossed out because they were even). So any number ending 5 can be crossed out.
Repeat the process with 7 and 11. The list is now getting quite small. The remaining numbers are prime numbers and you should count 25 of them.
Find Common Factors [l5]
Firstly, factors of a number are those numbers which when multiplied together give you that number. For example, find the factors of 12. Now 1 and 12 are factors of 12 because when multiplied together give 12.
3 and 4 are also factors of 12 because 3 x 4 = 12. Finally, 2 and 6 are factors of 12 because 2 x 6 = 12. So the factors of 12 are:
1,2,3,4,6,12
Find the factors of 18. The factors are 1,2,3,6,9,18
The common factors between 12 and 18 are those factors which appear in both lists. These are 1,2,3, and 6. We are often asked to find the greatest common factor (GCF or highest common factor HCF, they both mean the same thing). In this example the GCF is 6.
3 and 4 are also factors of 12 because 3 x 4 = 12. Finally, 2 and 6 are factors of 12 because 2 x 6 = 12. So the factors of 12 are:
1,2,3,4,6,12
Find the factors of 18. The factors are 1,2,3,6,9,18
The common factors between 12 and 18 are those factors which appear in both lists. These are 1,2,3, and 6. We are often asked to find the greatest common factor (GCF or highest common factor HCF, they both mean the same thing). In this example the GCF is 6.
list the factors of these numbers and find the Greatest common factor
12 =
15 =
15 =
Find Common Multiples [l5]
Firstly, a multiple is a number which is multiplied by 1,2,3... etc. For example, the first 6 multiples of 4 are:
(4 x 1) = 4
(4 x 2) = 8
(4 x 3) = 12
(4 x 4) = 16
(4 x 5) = 20
(4 x 6) = 24
So the answer is 4,8,12,16,20,24 which is probably how you would do it in the first place without even thinking.
The first 6 multiples of 5 are : 5,10,15,20,25,30
Find the common factors between the multiples of 4 and 6 above. You can see that it is 20. This is because 4 x 5 = 20. If the lists were longer there would be more multiples in common.
Find the first 8 multiples of 3 and 4 and find the least common multiple (LCM)
3 = 3,6,9,12,15,18,21,24
4 = 4,8,12,16,20,24,28,32
Here the multiples in common are 12 and 24. The least (smallest) common multiple or LCM is 12.
(4 x 1) = 4
(4 x 2) = 8
(4 x 3) = 12
(4 x 4) = 16
(4 x 5) = 20
(4 x 6) = 24
So the answer is 4,8,12,16,20,24 which is probably how you would do it in the first place without even thinking.
The first 6 multiples of 5 are : 5,10,15,20,25,30
Find the common factors between the multiples of 4 and 6 above. You can see that it is 20. This is because 4 x 5 = 20. If the lists were longer there would be more multiples in common.
Find the first 8 multiples of 3 and 4 and find the least common multiple (LCM)
3 = 3,6,9,12,15,18,21,24
4 = 4,8,12,16,20,24,28,32
Here the multiples in common are 12 and 24. The least (smallest) common multiple or LCM is 12.
list the multiples of these numbers and find the lCM
5=
6=
6=
.
FRACTIONS TEST
PRACTISE FOR THE SUBTRACTION NUMBER TEST
Subtract the following numbers. Focus on layout with columns and then a method that works for you. If you are not sure, learn the "borrow 1000, borrow 100, borrow 10" etc. method.
1) 56.03 - 21.02 [35.01]
2) 108.23 - 9.85 [98.38]
3) 2124 - 1256 [868]
4) 5707 - 2618 [3089]
5) 2007 - 1679 [328]
6) 30010 - 29022 [988]
7) 70700 - 1313 [69387]
8) 4002000 - 5 [4001995]
9) 10001000 - 8 [10000992]
10) 18888 - 9979 [8909]
1) 56.03 - 21.02 [35.01]
2) 108.23 - 9.85 [98.38]
3) 2124 - 1256 [868]
4) 5707 - 2618 [3089]
5) 2007 - 1679 [328]
6) 30010 - 29022 [988]
7) 70700 - 1313 [69387]
8) 4002000 - 5 [4001995]
9) 10001000 - 8 [10000992]
10) 18888 - 9979 [8909]
Subtraction Rules!
1) 78.22 - 21.65 [56.57]
2) 4567 - 2178 [2389]
3) 800100 - 5 [800095]
4) 64006-158 [63848]
5) 2016 - 55 [1961 - when I was born]
1) 78.22 - 21.65 [56.57]
2) 4567 - 2178 [2389]
3) 800100 - 5 [800095]
4) 64006-158 [63848]
5) 2016 - 55 [1961 - when I was born]
Subtractions Test Review:
tTopic 17: Fractions, Decimals and Percentages
17 fractions, decimals and percentages
Getting to know the Fractions to Percentage Conversion Diagram
F D P stands for Fractions, Decimals and Percentages. Arrows indicate the operation to perform when converting from left to right and right to left. We will begin by converting a fraction to decimal using top divided by bottom. See tutorial video.
F D P stands for Fractions, Decimals and Percentages. Arrows indicate the operation to perform when converting from left to right and right to left. We will begin by converting a fraction to decimal using top divided by bottom. See tutorial video.
Converting Fractions to Decimals:
1) 1/2 =
2) 3/8 =
3) 3/5 =
4) 19/20 =
5) 18/100 =
6) 16/1000 =
7) 11/25 =
8) 4/10 =
9) 61/100 =
10) 353/1000 =
1) 1/2 =
2) 3/8 =
3) 3/5 =
4) 19/20 =
5) 18/100 =
6) 16/1000 =
7) 11/25 =
8) 4/10 =
9) 61/100 =
10) 353/1000 =
Converting Decimals to Fractions (Express in Simple Form if you can)
1) 0.4
2) 0.5
3) 0.7
4) 0.35
5) 0.88
6) 0.29
7) 0.99
8) 0.375
9) 0.010
10) 0.685
1) 0.4
2) 0.5
3) 0.7
4) 0.35
5) 0.88
6) 0.29
7) 0.99
8) 0.375
9) 0.010
10) 0.685
Activity 18: Fraction and Percentage of quantity problems
Try working out without a calculator - change fractions into equivalents out of 100.
Try working out without a calculator - change fractions into equivalents out of 100.
.
- Two fifths of the pets in a vet clinic are cats.
What percentage of the pets in the vet clinic are cats?
- 7 out of your 20 friends have iPods.
What percentage of your friends have iPods?
- Last term, there were 50 school days.
Ioane was absent for 3 school days last term.
What percentage of the days was Ioane absent?
- Tana buys his lunch for school 40% of the time.
What fraction of the time does Tana buy his lunch?
- In your class, 12% of the students have blue eyes.
What fraction of your class has blue eyes?
- 65% of the cars on the road are manual.
What fraction of the cars are manual?
Conversions