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Divisibility

and GCF

Primes, Composites and Rational #

Scientific Notation

Simplifying Fractions and Problems

Exponents

Divisibility and GCF for $100

Is 68,301 divisible by 9?

Answer

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Yes, because 6+8+3+0+1 = 18 and 18 is divisible by 9

Divisibility and GCF for $200

List the factors of 70

1, 2, 5, 7, 10, 14, 35, 70

Answer

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Divisibility and GCF for $300

Write a 5 digit number that is divisible by 3

Answers vary, but the sum of the digits must be divisible by 3. i.e. 31,260 = 3+1+2+6+0 = 12. Since 12 is divisible by 3, 31,260 is also divisible by 3.

Answer

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Divisibility and GCF for $400

Find the GCF of 200 and 145

Factor trees!200 = 100*2 = 5*20*2 = 5*5*4*2

= 5*5*2*2*2145 = 5 * 29Thus the GCF is 5 (only factor

in common)

Answer

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Divisibility and GCF for $500

Find the GCF of 56x2y3 and 16x4y

Answer

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56x2y3 = 2*2*2*7 *x*x*y*y*y16x4y = 2*2*2*2*x*x*x*x*y

Top and bottom have 2, 2, 2, x, x, y in common, so the GCF is 8x2y

Primes, Composites, and Rational Numbers for $100

Is 57 prime, composite or neither?

Composite – 57 has 1, 3, 19, and 57 as factors.

Answer

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Primes, Composites, and Rational Numbers for $200

Write two numbers that are neither prime, nor composite

Answer1 and 0

1 only has 1 factor0 cannot be made by

multiplying 2 non-zero numbers together.

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Primes, Composites, and Rational Numbers for $300

Graph the number (5/7) on a number line

Answer

(5/7)

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Primes, Composites, and Rational Numbers for $400

Evaluate for a = -3 and b = 5:

a-2 * (4b2 – 10)

a-2 * (4b2 – 10) = (-3)-2 * (4*52 – 10)

= (1/9) * (100-10) = (1/9) * 90 = 10

Answer

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Primes, Composites, and Rational Numbers for $500

Explain how to find all of the prime numbers less than a certain number.

AnswerWrite out all the numbers 1 to the

number. Then, find all the prime numbers less than the square root of the number. Then cross off all the multiples of the primes less than the square root. The numbers left are prime numbers.

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Simplifying Fractions and Problems for $100

Simplify:

21/33

Answer

21/33 = (7*3)/(11*3) = 7/11

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Simplifying Fractions and Problems for $200

Simplify: xy/y

Answer

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xy/y = x

Simplifying Fractions and Problems for $300

Simplify:

45yz2

36xy2

45yz2 = 3*3*5*y*z*z

36xy2 = 2*2*3*3*x*y*y

3, 3, and y cancel out:

5z2

4xy

Answer

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Simplifying Fractions and Problems for $400

Crystal wants to put a fence around her vegetable garden. Her garden is 5 ft wide and 4 ft long. She plans to put a post at each corner and at every foot. How many fence posts will Crystal need?

There will be 6 posts on each width and 5 posts on each length = 6+6+5+5 = 22. However, this means the four corners are repeated, so 22-4 = 18 posts.

Answer

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Simplifying Fractions and Problems for $500

Jane has 5 marbles in her pocket. She has one blue, one orange, one yellow, one green and one red. If she chooses two without looking, how many possibilities are there?

Answer

Possibilities are B,O,Y,G,R, SoBO, BY, BG, GR, OY, OG, OR,

YG, YR, GR. = 10 possibilitiesOr, n(n-1)/2

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Exponents for $100

Simplify: 450 *423

Answer

450 * 423 = 450 + 23 = 473

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Exponents for $200

Simplify: (2y4)3

(2y4)3 = 23 * y4*3 = 8y12

Answer

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Exponents for $300

Simplify: (8x2)/(16x5)

(8x2)/(16x5) = (8/16)(x2/x5) = (1/2)(x2-5) = (1/2)(x-3) = (x-3)/2 or 1/(2x3)

Answer

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Exponents for $400

Simplify:

(x4 * x3 * x5)3

Answer

(x4 * x3 * x5)3

= (x4+3+5)3 = (x12)3 = x12*3 = x36

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Exponents for $500

Simplify and write the answer without using a division symbol:

35x5y2

7x7y

Answer

Back

35x5y2 = (35/7)(x5/x7)(y2/y) = 5x-2y7x7y

Scientific Notation for $100

Write the following number using standard notation:

4.56 x 107

Answer

4.56 x 107 => the 107 causes the decimal to move to the right 7 places

45,600,000

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Scientific Notation for $200

Write the following number using scientific notation:

2355000

Answer

2355000 => The decimal point goes between the 2 and 3 because it goes after the first non zero number. This moves it 6 places from the original spot, so. = 2.355 x 106

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Scientific Notation for $300

Write 0.0000045 in scientific notation.

Answer0.0000045

= 4.5 x 10-6

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Scientific Notation for $400

Write in scientific notation:

35.2 x 1010

Answer

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35.2 x 1010 = 3.52 x 1011

Scientific Notation for $500

Simplify – Write your answer using scientific Notation:

(3 x 104) x (5 x 10-8)

Answer

Back

(3 x 104) x (5 x 10-8) = (3*5) * (104 x 10-8)= 15 x 10-4

= 1.5 x 10-3