math for coolcat

Problem:

Work:

Answer:

Feedback:

Example:

Simplify: 62 – 42 ÷ 2

62 – 42 ÷ 2

36-16÷ 2

36-8

28

28

Good!

1. Find all the factors of 210.

If we multiply any two numbers so that result is our required number then we say that these two numbers are factors of required number. e.g.

1Χ210 = 210

1 and 210 are two factors of 210.For more factors we multiply different numbers to get answer 210

2Χ105 = 210

3Χ70 = 210

5Χ42 = 210

6Χ35 = 210

7Χ30 = 210

10Χ21 = 210

14Χ15 = 210

1;2;3;5;6;7;10;14;

15;21;30;35;42;70;105;210

2. Define a Prime number and a Composite Number. Give an Example of each.

Prime Number

31

1Χ31 = 31

31Χ1 = 31

Composite Number

20

1Χ20 = 20

2Χ10 = 20

4Χ5 = 20

Prime Number:

A number which have only two different factors, the number itself and 1

Example:

Number 31

Factors of 31 = 1, 31

Composite Number:

A number which have three or more than three different factors.

Example:

Number 20

Factors of 20= 1, 2, 4, 5, 10, 20

3. Determine whether the number 15 is prime, composite, or neither.

1Χ15 = 15

3Χ5 = 15

5Χ3 = 15

15Χ1 =15

As

Factors of 15= 1, 3, 5, 15.

Therefore 15 is composite number

4. Determine whether the number 41 is prime, composite, or neither

1Χ41 = 41

41Χ1 = 41

As

Factors of 41=1, 41

Therefore 41 is prime number

5. Determine whether the number 1 is prime, composite, or neither.

1 is neither Prime nor composite number because it has only one factor not two, three and more than three.

neither Prime nor composite number

6. Define Prime factorization.

Prime Factorization:

When we break down a number to its prime factors, we call that the Prime Factorization of that number

7. Find the prime factorization of the number 66.

Using the division method of Prime factorization

2 66

3 33

11 11

1

Prime factors of 33 are

2, 3, 11

8. Find the prime factorization of the number 81.

Using the division method of Prime factorization

3 81

3 27

3 9

3 3

1

Prime factors of 81 are

3, 3, 3, 3

9. Determine 348 is divisible by 3.

According to divisibility test for 3

if sum of digits of number is divisible by 3, then this number is said to be divisible by 3

i.e. 3+4+8=15

and 15 is divisible by 3

348 is divisible by 3 because

· 3+4+8=15

· 15 is divisible by 3

10. Determine 2842 is divisible by 6.

According to divisibility test for 6:

A number is divisible by 6 if it is divisible by 2 and 3 both.

i.e.

· The last digit of number is even.

· Sum of digits of number is divisible by 3.

As

2+8+4+2=16

And 16 is not divisible by 3 so number 2842 is also not divisible by 3.

11. Determine 4933 is divisible by 9.

According to divisibility test for 9

If sum of digits of number is divisible by 9, then this number is said to be divisible by 9.

As

4+9+3+3=19

Also; 1+9=10

And 10 is not divisible by 9

So 4933 is not divisible by 9.

12. Identify the numerator and the denominator of 9/12?

The number below the line fraction is called Denominator and other is called numerator.

Numerator = 9 Denominator=12

13. What is a ratio and how does it relate to fraction?

Ratio:

An expression which compares quantities relative to each other for example 3 man of 4 women

Written as 3:4

Fraction:

An expression in which two numbers are related in a part to whole relationship. For example

3 slices of cake out of 12 slices.

Written as 3/12.

Ratio:

An expression which compares quantities relative to each other for example 3 man of 4 women

Written as 3:4

Relation:

Ratio making comparisons of the amount of one thing to another thing. While fractions deal with a certain amount of whole thing

14. In 2008, there were 325 mammals considered to be endangered.  Of these, 69 were in the U.S.  What was the ratio of endangered U.S. mammals to total endangered mammals?  What was the ratio of endangered foreign mammals to total endangered mammals?

Total endangered considered mammals = 325

Endanger mammals in U.S = 69

Endangered mammals not in U.S = 325-69

= 256

Endangered mammals not in U.S= foreign mammals

Ratio of endangered U.S mammal to total mammal = 69:325

Ratio of endangered foreign mammals to total mammals = 256:325

15. What number can we never divided by? Why not?

ZERO (0), because it was just being the same so that’s why there is no point.

16. Simplify: 5/(10-10)

5/0

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17. Simplify: 20/4

20/4= 10/2=5

5

18 Simplify: 8/48

8/48 = 4/24 = 2/12 = 1/6

1/6

19. Simplify: 0/17

When zero is divide to any number its answer is zero

0

20. Simplify 30/252

30/252 = 15/126 = 5/42

5/42

21. Multiply and simplify: 1/2 *3/4

1*3 /2*4= 3/8

3/8

22. Multiply and simplify: 5/6 *3/20

5*3 /6*20= 15/120 = 1/8

1/8

23. Multiply and simplify: 1/3 *9/10

1*9 /3*10 = 9/30 = 3/10

3/10

24. Multiply and simplify: 4* 1/9

(4*1)/ 9 = 4/9

4/9

25. Find the reciprocal: 3/8

To get the reciprocal of a number divide 1 by the number. 1 / (3/8) =8/3

8/3

26. Find the reciprocal: 7

1/7

1/7

27. Divide and simplify: 1/3 % 1/6

1/3 * 6/1 = 2

2

28. Divide and simplify: 6% 2/3

6 * 3/2 =18/2 = 9

9

29. Solve for t. (2/3)*t=18

2t= (18*3) =54/2 = 27

T=27

30. Evaluate and simplify: 1/4 * 3/8 % 3/4

1*3 / 4*8 * 4/3= 3/32 * 4/3 3*4 / 32*3 =12/96 =1/8

1/8

31. Evaluate and simplify: (1/2)^2

1/(2*2) = 1/4

1/4

32. At North Spring College there are 576 students, and  1/9 of them are registered for December graduation.  How many are registered to graduate in December?

576 * 1/9= 576/9 = 64

64

33. A piece of ribbon 3/5 m long is cut into 4 equal pieces. How long is each piece?

(3/5) / 4 =3/(5*4) = 3/20

3/20

34. A gas tank held 24 gal when it was 4/5

Full. How much gas could it hold when full?

24 * (4/5 ) = 96/5

96 /5

35. After driving 180 miles, Larry notes that he has completed 3/5

Of his trip. How far is his trip?

180* (3/5)= 540/5 = 108

108

Part II

 Cross off all multiples of prime numbers from a grid of numbers.  When you are done, the remaining numbers will be prime.

2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

2. List the first 10 multiples of 2 in the space:

Now, highlight these numbers blue from the grid.  Continue highlighting multiples of 2 blue until you reach the end of the grid.

First 10 multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

3.

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

4. Write the list of prime numbers less than 100 in the space below:

Prime numbers less than 100 are 2, 3, 5, 7, 11, 13, 17, 19, 21, 23, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

5.

Need text book

6.

In the Sieve of Eratosthenes method we can easily find the prime and composite number without forgetting and neglecting any number. Each and every number is under consideration.