Test Yourself: GCF/LCM, Ratios/Rates/Proportions Quiz

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

To arrange a classroom of students into equal groups, you should use the GCF (Greatest Common Factor) to figure it out. The GCF is the largest number that divides evenly into two or more numbers. In this case, the GCF will help determine the maximum number of students that can be evenly divided into equal groups. By finding the GCF of the total number of students and the desired number of groups, you can ensure that each group has an equal number of students. The LCM (Least Common Multiple) is used to find the smallest common multiple of two or more numbers, which is not applicable in this scenario.

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.

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.

The given list of numbers includes multiples of both 6 and 8. The first three common multiples of 6 and 8 are 24, 48, and 72. These numbers are multiples of both 6 and 8 because they can be divided evenly by both 6 and 8 without leaving a remainder. Therefore, these are the correct answers.

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.

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.

To find out when the basketball team and volleyball team will have to share the gym again, we need to find the least common multiple (LCM) of their practice intervals.



The basketball team meets every 9 days.

The volleyball team meets every 3 days.



To find the LCM, we identify the prime factors of each number and take the highest power of each factor that appears in any of the numbers.



Prime factorization of 9: ( 9 = 3^2 )

Prime factorization of 3: ( 3 = 3^1 )



The LCM is the product of the highest powers of all prime factors:

LCM(9, 3) = ( 3^2 = 9 )



So, the basketball team and volleyball team will have to share the gym again every 9 days. Therefore, they will have to share the gym again in 9 days from today.

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.

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.

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.

When you want to split something into equal smaller sections, you should use the Greatest Common Factor (GCF) to figure it out. The GCF is the largest number that divides evenly into the given numbers. By finding the GCF, you can determine the maximum number of equal sections that can be created. On the other hand, the Least Common Multiple (LCM) is used to find the smallest number that is divisible by all the given numbers. Therefore, in this scenario, the GCF is the appropriate choice for dividing something into equal sections.

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.

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.

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.