Prime Numbers
What is a composite number?
A composite number is a number greater than 1 that has more than 2 distinct factors and is divisible by itself.
What is a 3/2 - 1/4? Express your answer as a simplified improper fraction.
5/4
What is the commutative property for multiplication?
It does not matter what order you multiply numbers in.
Example:
5*4*3*2 = 2*4*5*3 = 4*5*2*3...
What are the three types of triangles in terms of side lengths?
Scalene, Isosceles, Equilateral
From 51 to 60, how many primes are there, inclusive, and what are they?
2 primes. 53 and 59.
What is a prime number?
A prime number is a number greater than 1 that factors to 1 and itself.
What is 7/4 + 1/6? Express your answer as an improper fraction.
23/12
What is 3 x 4?
12
Why is a square both a rectangle and a rhombus?
Because a square both has all angles as right angles, making it a rectangle, and has all sides equal to one another, making it a rhombus.
900 degrees
Why is 1 and 0 neither prime nor composite? (Explain both to earn points)
1 has only one factor, which is itself, and 0 multiplies with every number by itself to get itself. Furthermore, 0 divided by 0 is not defined, so therefore, 0 is not composite.
If you and your sister have a half of a dozen of cupcakes, and your sister bakes a third of a dozen of cupcakes more, and your brother eats a fourth of a dozen of cupcakes, how many cupcakes do you and your sister have left altogether?
dozen = 12
7 cupcakes
What is the distributive property for multiplication?
The distributive property for multiplication is a property where you can distribute the multiplication across numbers when parentheses are involved
Example:
5 * (4 + 3) = 5 * 4 + 5 * 3
For a circle, what is the ratio of the circumference to its diameter and what are the first 3 digits of that ratio?
pi,3.14
What is 2553/23?
These numbers have only 3 distinct factors. What are they?
Squares of primes. (aka a prime multiplied by itself)
What is 13/11 + 11/13? Express your answer as an improper fraction.
290/143
Solve using Order of Operations:
5*(3+2)-(10+2)/3*2
17
A prism has a base that is 300 cm squared. It is 1 feet long. What is the volume of the prism, in centimeters cubed? (Note: 1 foot = 30.44 cm)
9,132 centimeters cubed
What is 1/2 * 2/3 * 3/4 * 4/5 * 5/6 ... 2024/2025 * 2025/2026
1/2026
Which two prime numbers less than 100 have the property that reversing their digits gives the other prime (example, 79 and 97), and reversing the digits of their positions in the sequence of prime numbers (2 is the 1st prime,3 is the 2nd,5 is the 3rd,and so on...) also gives the other's position?
37 and 73
(37 is the 12th prime, 73 is the 21st prime)
You are riding your dirt bike to the grocery store at 12 miles every 42 minutes. You start at your friend's house, 30 miles away from the grocery store. You take 40 minutes to finish shopping once you arrive. Then you ride 20 miles back to your house. How many hours did you take, expressed as a simplified mixed fraction?
3 and 7/12 hours
A reciprocal of a number is the number 1 divided by the original number. For example, the reciprocal of 2 is 1/2. Alice says if you multiply the number by the reciprocal of another number, it is the same as if you divided the same number by the original other number. Is she right? If so, why?
Yes, because a/1 * 1/b = (a*1)/(b*1)=a/b, and a/b = a/b
If you have a pool for your pet mouse that is 20 inches wide, 15 inches long, and 5 inches tall, but suddenly, at 3 PM, due to some plot armor issues, it starts leaking 9 cubic inches per minute, until eventually, all the water has drained away. What time was it when all the water was finally gone? (round down to the nearest minute)
5:46 PM
A special triangular prism has a base being a triangle with the triangle's bottom being the first prime number divided by the second prime number, the height being the third prime number divided by the fourth prime number, and the length of the prism is the fifth prime number divided by the sixth prime number. What is the volume, in units cubed? (Express your answer as a proper fraction)
55/273