Prime Time
Fractions
Decimals and Percentages
Area, Volume, etc.
Mystery Math
100
What does it mean if two numbers are relatively prime? Provide an example.
The two numbers, which are not necessarily prime themselves, do not share any common factors other than 1. Ex. 8 and 9
100
What is the denominator of every integer (whole number)?
1
100
Express the following fractions as decimals: 33/100 and 1/3
33/100 = .33, 1/3 = .333333 (repeating)
100
Write an algebraic expression for the area of a rectangle, and write another algebraic expression for the perimeter of a rectangle. No points will be given unless both are correct!
A = L*W . . . P = 2*L + 2*W
100
What is the algebraic formula for the nth even number?
y = 2n
200
What is the prime factorization of 640?
640 = 10 * 64 = 5 * 2 * 8 * 8 = 5 * 2 * 4 * 2 * 4 * 2 = 5 * 2 * 2 * 2 * 2 * 2 * 2 * 2 . . . 5x2x2x2x2x2x2x2 = 5x2^7
200
How can we simplify the multiplication of two fractions?
Cross-cancel!
200
Express the following fraction as a decimal and as a percent: 1/16 For your decimal answer, round to the nearest thousandth. For your percent answer, round to the nearest tenth.
1/16 = .0625 = .063 (decimal) . . . 1/16 = .0625 = 6.25% = 6.3%
200
How many faces does a hexagonal prism have? Hint: Try to do a drawing if you get stuck!
6 sides + 2 bases = 8 faces
200
Write the following numbers in Roman numerals. . . 73 257 590
73 = LXXIII . . . 257 = CCLVII . . . 590 = DXC
300
What is the Greatest Common Factor (GCF) of 24 and 16? Solve using prime factorizations.
24 = 3x2x2x2 . . . 16 = 2x2x2x2 . . . GCF = 2x2x2 = 8
300
Write the answer to this multiplication problem IN ITS MOST SIMPLIFIED FORM as a mixed number AND as an improper fraction: 17/16 * 24/7
17/16 * 24/7 = 17/2 * 3/7 = 51/14 (improper fraction) = 3 9/14 (mixed number)
300
You must do BOTH of the following calculations correctly to receive full credit on this problem! .62 x .7 . . . 1 / 8
.434 .125
300
Pete's Pizza Parlor sells cheese pizzas that each have a DIAMETER of 16 inches. If I buy half of a cheese pizza, what is the area of the pizza I have bought? What is the perimeter of the pizza I have bought? Don't forget your units!
Area = (pi*r^2)/2 = (3.14*(8^2))/2 = 100.48 inches^2 . . . Perimeter = ((2*pi*r)/2)+diameter = pi*r + diameter = 3.14*8 + 16 = 41.12 inches
300
What is the Roman numeral between 1 and 100 that is written with the greatest number of letters?
88 = LXXXVIII
400
What is the Least (or Lowest) Common Multiple (LCM) of 16 and 24? Solve using prime factorizations
24 = 3x2x2x2 . . . 16 = 2x2x2x2 . . . LCM = 3x2x2x2x2 = 48
400
72/16 * 54/18 * 3/10 * 180/3 =
Simplify the individual fractions first: 9/2 * 3/1 * 3/10 * 60/1 = 9/1 * 3/1 * 3/1 * 3/1 = 243
400
How do you convert a percent to a decimal? to a fraction?
Decimal: divide by 100 (move the decimal point two places to the LEFT) . . . Fraction: numerator = percentage, denominator = 100, then SIMPLIFY!
400
What is the volume of a rectangular solid with side lengths x, 2x, and x+3 when x = 3 inches? Don't forget your units!
Volume = L * W * H = (x)(2x)(x+3) = (2x^2)(x+3) = 2x^3 + 6x^2 . . . 2*3^3 + 6*3^2 = 108 inches^3
400
Simplify and solve the following problem: (2 * (1/4 + 3/8) + 17)
1/4 + 3/8 = 2/8 + 3/8 = 5/8 *2 = 5/4 = 1¼ + 17 = 18¼
500
Mark is selling hot dogs and hamburgers in Central Park this summer. He buys hot dogs in packs of 12, hot dog buns in packs of 10, hamburgers in packs of 16, and hamburger buns in packs of 9. What is the least number of PACKS OF HOT DOG BUNS he could buy if he wants to have the same number of each item?
We need to find the LCM of 12, 10, 16, and 9. . . . 12 = 3x2x2 . . . 10 = 5x2 . . . 16 = 2x2x2x2 . . . 9 = 3x3 . . . LCM = 3x2x2x5x2x2x3 = 720 . . . 720 hot dog buns = 72 packs
500
Sylvester runs a shelter that cares for 402 cats. 1/3 of his cats are orange, 1/8 of his cats have white spots (could be orange with white spots), and 1/2 of his cats are female. If none of his orange cats are female, how many of his cats are male but NOT orange?
The white spots are irrelevant! (red herring) . . . If none of the orange cats are female, the total number of male, non-orange cats = 1 - 1/3 - 1/2 = 1 - 2/6 - 3/6 = 1 - 5/6 = 1/6 . . . 1/6 x 402 = 67 male, non-orange cats
500
Mr. Tayler is running a lemonade stand at the beach. He sells both regular lemonade and pink lemonade. He sells 15% MORE regular lemonade than pink lemonade. If he sells 645 lemonades IN TOTAL, how many PINK lemonades does he sell?
x + 1.15x = 645, where x = number of pink lemonades sold . . . 2.15x = 645, x = 300 pink lemonades
500
What is the surface area of a rectangular solid with side lengths x, 2x, and x+3 when x = 3 inches? Hint: Draw a picture and label your side lengths!
2 * (x)(2x) . . . + 2 * (2x)(x+3) . . . + 2 * (x+3)(x) = 2 * (2x^2) + 2 * (2x^2 + 6x) + 2 * (x^2 + 3x) = 4x^2 + 4x^2 + 12x + 2x^2 + 6x = 10x^2 + 18x . . . = 10*(3^2) + 18*(3) = 144 inches^2
500
Solve the given equation for x where r = 6: 45 = 2.5x + 3r
3r = 3*6 = 18, so 45 = 2.5x + 18 . . . 27 = 2.5x, x = 10.8
M
e
n
u