1.
If you have to buy multiple items in order to have enough...should you use GCF or LCM to figure it out?
Correct Answer
B. LCM
Explanation
When you need to buy multiple items in order to have enough, you should use the LCM (Least Common Multiple) to figure it out. The LCM represents the smallest common multiple of the given numbers, which means it will give you the minimum number of items needed to have enough of each item. The GCF (Greatest Common Factor) is used to find the largest common factor between numbers, which is not relevant in this scenario.
2.
If you want to figure out when something will happen again at the same time in the future...should you use GCF or LCM to figure it out?
Correct Answer
B. LCM
Explanation
To figure out when something will happen again at the same time in the future, you should use LCM (Least Common Multiple). LCM is the smallest multiple that two or more numbers have in common. It helps determine the next occurrence of an event happening simultaneously. On the other hand, GCF (Greatest Common Factor) is used to find the largest number that divides evenly into two or more numbers. While GCF is useful for other calculations, it is not applicable in this scenario.
3.
A __________ is a number that divides evenly into another number.
Correct Answer
factor
Factor
Explanation
A factor is a number that divides evenly into another number. Factors are the numbers that can be multiplied together to get a given number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because they can divide 12 without leaving a remainder. The term "factor" is used in mathematics to describe the numbers that divide a given number evenly.
4.
Is 7 a PRIME FACTOR of 84?
Correct Answer
A. True
Explanation
The number 7 is a prime factor of 84 because it is a prime number that divides 84 without leaving a remainder. When 84 is divided by 7, the quotient is 12, which is a whole number. Therefore, 7 is one of the prime factors that compose the number 84.
5.
The PRIME FACTORS of 18 are 2 and 3.
Correct Answer
B. False
Explanation
The statement "The prime factors of 18 are 2 and 3" is false.
The prime factorization of 18 is 2×3×32×3×3.
Here's the breakdown:
18 can be divided by 2, resulting in 2×92×9.
Then, 9 can be divided by 3, resulting in 2×3×32×3×3.
So, the prime factors of 18 are 2 and 3, but there are two 3s, not just one. Therefore, the correct answer is false.
6.
Which set of numbers are all PRIME NUMBERS?
Correct Answer
C. 5, 23, 11, 37
Explanation
The set of numbers 5, 23, 11, 37 are all prime numbers because they can only be divided evenly by 1 and themselves. Prime numbers are numbers that have no other factors except for 1 and themselves.
7.
What are the first three prime numbers?
Correct Answer
C. 2, 3, 5
Explanation
The first three prime numbers are 2, 3, and 5. Prime numbers are numbers that are only divisible by 1 and themselves. 0 and 1 are not prime numbers because they have factors other than 1 and themselves. Therefore, the correct answer is 2, 3, 5.
8.
A Prime Number has only how many FACTORS:
Correct Answer
B. 2
Explanation
A prime number has only two factors, which are 1 and the number itself. This means that it cannot be divided evenly by any other number except for those two. Therefore, the correct answer is 2.
9.
9 is a Prime Factor of 81.
Correct Answer
B. False
Explanation
The statement "9 is a prime factor of 81" is false because 9 is not a prime number. A prime factor is a prime number that divides another number exactly without leaving a remainder. However, 9 is a composite number because it can be divided evenly by numbers other than 1 and itself, such as 3. Therefore, 9 cannot be a prime factor of 81.
10.
3 is the ONLY prime factor of 81.
Correct Answer
A. True
Explanation
The statement is true because prime factorization breaks down a number into its prime factors. In the case of 81, the prime factorization is 34, indicating that 3 is the only prime factor of 81, and it appears four times in the factorization. This demonstrates that 81 can be expressed as the product of only one prime factor, reinforcing the fact that 3 is the sole prime factor of 81.
11.
A _____ number is a natural number that's not a prime number.
Correct Answer
composite
COMPOSITE
Explanation
A composite number is a natural number that is not a prime number. It can be divided evenly by at least one number other than 1 and itself. In this question, both "composite" and "COMPOSITE" are correct answers as they both refer to the same concept of a non-prime natural number.
12.
Is 23 a prime number?
Correct Answer
A. Yes
Explanation
Yes, 23 is a prime number. A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. In the case of 23, it does not have any divisors other than 1 and 23, which meets the definition of a prime number.
13.
Select ALL the numbers that are prime numbers.
Correct Answer(s)
A. 7
C. 13
Explanation
The prime numbers among the given options are:
1. 7
2. 13
Explanation: Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves.
7 and 13 fit this definition, as they cannot be divided evenly by any other positive integer except 1 and themselves.
21 and 10, however, are not prime numbers.
21 is divisible by 1, 3, 7, and 21, so it's not a prime number.
10 is divisible by 1, 2, 5, and 10, so it's also not a prime number.
14.
Is 35 a prime number?
Correct Answer
B. No
Explanation
No, 35 is not a prime number.
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
In the case of 35, it has divisors other than 1 and itself. Specifically, it can be divided evenly by 1, 5, 7, and 35.
Since 35 has more than two distinct positive divisors, it does not meet the criteria to be classified as a prime number. Therefore, 35 is a composite number.
15.
7^{5} = 7 x 5
Correct Answer
B. False
Explanation
The equation (75 = 7 times 5) is not accurate.
(75) represents "7 raised to the power of 5," which means multiplying 7 by itself 5 times.
So, (75 = 7 x 7 x 7 x 7 x 7 = 16807).
It's important to understand that exponentiation (raising a number to a power) involves multiplying the base (in this case, 7) by itself the number of times indicated by the exponent (in this case, 5).
16.
9^{ 4} = 9 x 9 x 9 x 9
Correct Answer
A. True
Explanation
The given equation states that 9 raised to the power of 4 is equal to 9 multiplied by itself four times. This is true because raising a number to a power means multiplying it by itself the number of times indicated by the power. In this case, 9 raised to the power of 4 means multiplying 9 by itself four times, resulting in the same value as 9 x 9 x 9 x 9. Therefore, the answer is true.
17.
What is the PRIME FACTORIZATION of 45?
Correct Answer
A. 3 x 3 x 5
Explanation
The prime factorization of 45 is 3 x 3 x 5. This means that 45 can be broken down into its prime factors, which are 3 and 5. Multiplying these prime factors together gives the original number 45.
18.
2^{3} x 3 =
Answer with a WHOLE NUMBER
Correct Answer
24
Explanation
The expression (23 times 3) involves two operations: exponentiation and multiplication.
1. Exponentiation: (23) means "2 raised to the power of 3," which is equivalent to multiplying 2 by itself three times. So, (23 = 2 times 2 times 2 = 8).
2. Multiplication: Once we have the result of (23), which is 8, we then multiply it by 3, as indicated by the expression. So, (8 times 3 = 24).
Therefore, (23 times 3) equals (24).
19.
What is the PRIME FACTORIZATION of 56?
Correct Answer
C. 2 x 2 x 2 x 7
Explanation
The prime factorization of 56 is 2 x 2 x 2 x 7. This means that 56 can be expressed as the product of these prime numbers. The number 2 is repeated three times because it is a prime factor of 56, and the number 7 is also a prime factor.
20.
Is 16 prime or composite?
answer with one of the words:
prime
composite
Correct Answer
composite
Explanation
The number 16 is composite because it has factors other than 1 and itself. In this case, 16 can be divided evenly by 2, 4, and 8, in addition to 1 and 16. Therefore, it does not meet the criteria to be classified as a prime number.
21.
Which part of this question is most related to the "L" in the LCM?
Ben exercises every 12 days and Isabel every 8 days. Ben and Isabel both exercised today. How many days will it be until they exercise together again?
Correct Answer
A. the soonest time they will exercise together again
Explanation
The "L" in LCM stands for "least", which refers to the smallest common multiple. In this question, the "L" is related to the phrase "the soonest time they will exercise together again". The LCM of 12 and 8 is 24, which means that they will exercise together again after 24 days, which is the soonest time they will exercise together again.
22.
Which part of this question is most related to the "M" in the LCM?
Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be the same height?
Correct Answer
C. 12 inch tall boxes are being stacked next to boxes that are 18 inches tall
Explanation
The part of the question that is most related to the "M" in the LCM is "12 inch tall boxes are being stacked next to boxes that are 18 inches tall". This is because the LCM (Least Common Multiple) is the smallest number that is divisible by both 12 and 18. In this case, the LCM represents the shortest height at which the two stacks will be the same height.
23.
Which part of this question is most related to the "C" in the GCF?
Samantha has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are “as wide as possible”. How wide should she cut the strips?
Correct Answer
B. Cut equal strips from both the 72 and 90 wide strips
Explanation
The part of the question that is most related to the "C" in the GCF is "cut equal strips from both the 72 and 90 wide strips". This is because finding the greatest common factor (GCF) involves finding the largest number that divides evenly into both 72 and 90. In this case, cutting equal strips from both the 72 and 90 wide strips would require finding the width that evenly divides into both measurements, which is the purpose of finding the GCF.
24.
Which part of this question is most related to the "F" in the GCF?
Shannon is making identical balloon arrangements for a party. She has 32 maroon balloons, 24 white balloons, and 16 orange balloons. She wants each arrangement to have the same number of each color. What is the greatest number of arrangements that she can make if every balloon is used?
Correct Answer
C. Dividing the balloons into the same number of each color
Explanation
The part of the question that is most related to the "F" in the GCF is "dividing the balloons into the same number of each color". This is because finding the greatest number of arrangements depends on dividing the total number of balloons evenly among the different colors. To do this, Shannon needs to determine the greatest common factor (GCF) of the total number of each color of balloons.
25.
Which one of the following uses UNITS as a way to describe what you are talking about?
Correct Answer
A. Rate
Explanation
A rate is a comparison of two quantities that have different units. It is used to describe how one quantity changes in relation to another quantity. For example, miles per hour is a rate that describes how many miles are traveled in one hour. Therefore, the correct answer is rate because it uses units to describe what you are talking about.
26.
4 apples per 6 oranges is a ratio but NOT a rate
Correct Answer
B. False
Explanation
A ratio compares two quantities and can be expressed in the form of a fraction, like 4:6. In this case, the ratio of 4 apples to 6 oranges means that for every 4 apples, there are 6 oranges. On the other hand, a rate compares two quantities with different units and is expressed in terms of a unit rate, such as "apples per oranges." Since the given statement mentions "apples per oranges," it is actually describing a rate rather than a ratio. Therefore, the correct answer is False.
27.
The correct way to say 34 km/hr is 34 kilometers _______ hour
Correct Answer
per
Explanation
The correct way to say 34 km/hr is 34 kilometers per hour. "Per" is the appropriate preposition to express the relationship between kilometers and hours in this context. It indicates the rate of speed or distance traveled in a specific time frame.
28.
Imagine that you can eat 4 donuts in 5 minutes. How would you explain the rate of donuts you eat per ONE minute?
Correct Answer
C. 0.8 donuts per minute
Explanation
The rate of donuts eaten per one minute can be calculated by dividing the total number of donuts (4) by the total time taken (5 minutes). In this case, 4 divided by 5 equals 0.8. Therefore, the correct answer is 0.8 donuts per minute.
29.
Mr.Brzezinski can dribble a basketball 140 times in 60 seconds. How many times can he dribble in 10 seconds?
Answer: write only the number and round your answer to the tenths decimal place.
Hint: think proportionally!
Correct Answer
23.3
Explanation
Mr. Brzezinski can dribble a basketball 140 times in 60 seconds. To find out how many times he can dribble in 10 seconds, we can set up a proportion. Since the time is decreasing from 60 seconds to 10 seconds, the number of dribbles will also decrease proportionally. By cross-multiplying and dividing, we find that he can dribble approximately 23.3 times in 10 seconds.
30.
When we had our Bubble Blowing Contest, why was a Unit Rate so important and easy to use?
Check ALL the answers that you think are correct.
Correct Answer(s)
B. The Unit Rate helped us COMPARE many students rates
C. The Unit Rate was always Proportional to the student's ORIGINAL rate!!!
Explanation
A unit rate is important and easy to use in a bubble blowing contest because it allows us to compare the rates of different students. By using the same denominator, we can easily determine which student blew the most bubbles per minute. Additionally, the unit rate is always proportional to the student's original rate, meaning that it accurately reflects their performance in the contest.
31.
Write the ratio of 96 runners to 216 swimmers in simplest form.
Correct Answer
C. 4/9
Explanation
The ratio of 96 runners to 216 swimmers can be simplified by dividing both numbers by their greatest common divisor, which is 24. 96 divided by 24 is 4, and 216 divided by 24 is 9. Therefore, the simplified ratio is 4/9.
32.
Which ratios are equivalent to 4 : 32?
Correct Answer
B. 12 : 96; 2 : 16
Explanation
The given ratio is 4 : 32. To find equivalent ratios, we need to find ratios that have the same value when simplified. The ratio 12 : 96 can be simplified by dividing both the numerator and denominator by 12 to get 1 : 8. Similarly, the ratio 2 : 16 can be simplified by dividing both the numerator and denominator by 2 to get 1 : 8. Therefore, the ratios 12 : 96 and 2 : 16 are equivalent to 4 : 32.
33.
The American flag is usually made with its width and length in the ratio of 10 to 19. Which dimensions are in the correct ratio for the flag?
Correct Answer
D. 30 in. by 57 in.
Explanation
The correct answer is 30 in. by 57 in. because the ratio of width to length is 10:19, which can be simplified to 30:57.
34.
Maria tossed a coin 20 times and got 12 heads. What is the first step to find the ratio of the number of tails to the total number of tosses?
Correct Answer
B. Subtract 12 from 20
Explanation
To find the ratio of the number of tails to the total number of tosses, we need to subtract the number of heads (12) from the total number of tosses (20). The result will give us the number of tails.
35.
TRUE or FALSE
16 to 3 equals 27 to 5.
Correct Answer
B. False
Explanation
The statement "16 to 3 equals 27 to 5" is false. The expression "16 to 3" means 16 raised to the power of 3, which is equal to 4096. On the other hand, "27 to 5" means 27 raised to the power of 5, which is equal to 143,489. Therefore, 16 to 3 is not equal to 27 to 5.
36.
There are 17 girls and 15 boys in a class. What is the ratio of boys to the whole class?
Correct Answer
C. 15 : 32
Explanation
To find the ratio of boys to the whole class, we need to express the number of boys as a fraction of the total number of students in the class.
Total number of students = Number of girls + Number of boys
Total number of students = 17 (girls) + 15 (boys) = 32 students
So, the ratio of boys to the whole class is 15 : 32.
Therefore, the correct option is: 15 : 32.
37.
Which of the following ratios is equivalent to the ratio 25 / 35?
Correct Answer
D. 5 / 7
Explanation
The ratio 25/35 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 5. This simplifies the ratio to 5/7.
38.
Rico and Lamar split a profit in the ratio 3 : 4.
Rico received $60.
How much money did Lamar receive?
Correct Answer
B. $80
Explanation
Rico and Lamar split the profit in a ratio of 3:4. Since Rico received $60, we can assume that this represents 3 parts of the ratio. To find out how much each part is worth, we divide $60 by 3, which gives us $20 per part. Since Lamar's share is 4 parts of the ratio, we multiply $20 by 4, which gives us $80. Therefore, Lamar received $80.
39.
For the Proportion.... If a:72 = 30:41, then a =
Write your answer to the tenths decimal place.
Correct Answer
52.7
Explanation
The given proportion states that the ratio of a to 72 is equal to the ratio of 30 to 41. To find the value of a, we can set up a proportion by cross-multiplying. Cross-multiplying gives us 30 * 72 = 41 * a. Simplifying this equation, we get 2160 = 41a. Dividing both sides by 41, we find that a is equal to 52.7 to the tenths decimal place.
40.
At the local zoo, there are 4 penguins, 8 parrots, and 3 monkeys. What is the ratio of monkeys to total animals?
Correct Answer
A. 3/15
Explanation
The ratio of monkeys to total animals can be found by dividing the number of monkeys (3) by the total number of animals (4 penguins + 8 parrots + 3 monkeys = 15 animals). So, the ratio is 3/15.
41.
What ratio is equal in proportion to 8:12
Correct Answer
B. 2:3
Explanation
The ratio 8:12 can be simplified by dividing both numbers by their greatest common divisor, which is 4. This gives us the simplified ratio of 2:3. Therefore, any ratio that is equal in proportion to 8:12 must also have the same simplified ratio of 2:3. The only answer choice that matches this is 2:3.
42.
A car can travel 300 miles on 30 gallons of gas. How much gas will it need to go 260 miles?
Correct Answer
B. 26
Explanation
Set a proportion box. You would have gone 10 miles on 1 gallon of gas. The scale factor would be 26 because 10x26= 260. The amount of gas need would be (B) 26 beacause 1x26=26.
43.
A Unit Rate describes the cost of MORE THAN one item?
Correct Answer
B. False
Explanation
A unit rate describes the cost (or other measure) of one item or unit. It represents the amount of a quantity (such as cost, distance, time) per one unit. For example, if you buy 3 items for $15, the unit rate would be $5 per item. Therefore, a unit rate describes the cost of one item, not more than one item.
44.
2 oranges for $0.50
What is the unit rate?
Correct Answer
C. $.25 per orange
Explanation
The unit rate is $.25 per orange because the given information states that 2 oranges can be bought for $0.50. To find the unit rate, we divide the cost of the oranges by the number of oranges. In this case, $0.50 divided by 2 equals $.25, which means that each orange costs $.25.
45.
5 cases of soda for $15.50.
Find the unit rate.
Correct Answer
A. $3.10
Explanation
The unit rate can be found by dividing the total cost of the soda ($15.50) by the number of cases (5). This gives us a unit rate of $3.10 per case.
46.
TRUE or FALSE
The two triangles above are PROPORTIONAL to each other.
Correct Answer
A. True
Explanation
The statement is true because two triangles are proportional when their corresponding sides are in proportion. In the given question, it is not mentioned explicitly, but it can be assumed that the two triangles are similar. If two triangles are similar, then their corresponding sides are proportional, making the statement true.
47.
What is the largest number of people that could share 72 apples and 54 bananas?
Correct Answer
18
Explanation
To find the largest number of people who can share 72 apples and 54 bananas equally, we need to determine the greatest common divisor (GCD) of 72 and 54.
First, let's find the prime factorization of both numbers:
- 72 = 2^3 * 3^2
- 54 = 2 * 3^3
Next, we identify the common factors:
- Both have 2 and 3 as factors, but the smallest power of 2 is 2^1 and the smallest power of 3 is 3^2.
The GCD is the product of these common factors:
GCD(72, 54) = 2^1 * 3^2 = 2 * 9 = 18
So, the largest number of people who can share 72 apples and 54 bananas equally is 18.
48.
Which is the GCF of 18 and 24?
Correct Answer
B. 6
Explanation
The greatest common factor (GCF) is the largest number that divides both 18 and 24 without leaving a remainder. To find the GCF, we can list the factors of both numbers and find the largest one they have in common. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The largest number they have in common is 6, so the GCF of 18 and 24 is 6.
49.
What is the GCF of 10 and 21?
Correct Answer
1
Explanation
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the numbers 10 and 21 do not have any common factors other than 1. Therefore, the GCF of 10 and 21 is 1.
50.
What is the LCM of 12 and 7?
Correct Answer
C. 84
Explanation
The LCM (Least Common Multiple) is the smallest number that is a multiple of both 12 and 7. To find the LCM, we can list the multiples of both numbers and find the smallest common multiple. The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84... The multiples of 7 are: 7, 14, 21, 28, 35, 42, 49... The smallest number that appears in both lists is 84, so 84 is the LCM of 12 and 7.