Math Revision on Prime Numbers and Operations

1. What is the prime factorization of 28?

2 x 2 x 7

2 x 14

4 x 7

2 x 2 x 2 x 3

To find the prime factorization of 28, we start by dividing it by the smallest prime number, which is 2. Dividing 28 by 2 gives us 14. We can divide 14 by 2 again, resulting in 7, which is also a prime number. Thus, the prime factors of 28 are 2 (occurring twice) and 7. Therefore, the prime factorization of 28 is expressed as 2 x 2 x 7.

Explanation

To find the prime factorization of 28, we start by dividing it by the smallest prime number, which is 2. Dividing 28 by 2 gives us 14. We can divide 14 by 2 again, resulting in 7, which is also a prime number. Thus, the prime factors of 28 are 2 (occurring twice) and 7. Therefore, the prime factorization of 28 is expressed as 2 x 2 x 7.

2. What is 3.5 as a fraction?

7/2

3/5

14/5

1/2

To convert the decimal 3.5 into a fraction, recognize that it can be expressed as 3.5 = 3 + 0.5. The whole number 3 can be written as 6/2, and 0.5 is equivalent to 1/2. Therefore, adding these gives 6/2 + 1/2 = 7/2. Thus, 3.5 as a fraction simplifies to 7/2.

Explanation

To convert the decimal 3.5 into a fraction, recognize that it can be expressed as 3.5 = 3 + 0.5. The whole number 3 can be written as 6/2, and 0.5 is equivalent to 1/2. Therefore, adding these gives 6/2 + 1/2 = 7/2. Thus, 3.5 as a fraction simplifies to 7/2.

3. If x = 5, what is the value of 2x + 3?

10

13

8

15

To find the value of 2x + 3 when x = 5, substitute 5 into the equation. First, calculate 2 times 5, which equals 10. Then, add 3 to this result: 10 + 3 equals 13. Thus, the value of the expression 2x + 3 when x is 5 is 13.

Explanation

To find the value of 2x + 3 when x = 5, substitute 5 into the equation. First, calculate 2 times 5, which equals 10. Then, add 3 to this result: 10 + 3 equals 13. Thus, the value of the expression 2x + 3 when x is 5 is 13.

4. What is the distance between the points (2, 3) and (5, 7)?

5

4

3

6

To find the distance between the points (2, 3) and (5, 7), we use the distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Here, \(x_1 = 2\), \(y_1 = 3\), \(x_2 = 5\), and \(y_2 = 7\). Plugging in the values, we calculate: \(d = \sqrt{(5 - 2)^2 + (7 - 3)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\). Thus, the distance between the two points is 5.

Explanation

To find the distance between the points (2, 3) and (5, 7), we use the distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Here, \(x_1 = 2\), \(y_1 = 3\), \(x_2 = 5\), and \(y_2 = 7\). Plugging in the values, we calculate: \(d = \sqrt{(5 - 2)^2 + (7 - 3)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\). Thus, the distance between the two points is 5.

5. What is the next term in the sequence 2, 4, 8, 16?

32

24

20

30

The sequence 2, 4, 8, 16 is a geometric progression where each term is obtained by multiplying the previous term by 2. Starting from 2, the sequence doubles: 2 x 2 = 4, 4 x 2 = 8, and 8 x 2 = 16. Continuing this pattern, the next term is 16 x 2, which equals 32. Thus, 32 is the next term in the sequence.

Explanation

The sequence 2, 4, 8, 16 is a geometric progression where each term is obtained by multiplying the previous term by 2. Starting from 2, the sequence doubles: 2 x 2 = 4, 4 x 2 = 8, and 8 x 2 = 16. Continuing this pattern, the next term is 16 x 2, which equals 32. Thus, 32 is the next term in the sequence.

6. If a recipe requires 2 cups of flour for every 3 cups of sugar, how much flour is needed for 9 cups of sugar?

4 cups

6 cups

5 cups

3 cups

To find the amount of flour needed for 9 cups of sugar, we can set up a ratio based on the recipe. The ratio of flour to sugar is 2 cups of flour for every 3 cups of sugar. To determine how much flour corresponds to 9 cups of sugar, we can calculate it as follows:

(2 cups flour / 3 cups sugar) = (x cups flour / 9 cups sugar).

Cross-multiplying gives us 3x = 18, leading to x = 6. Therefore, 6 cups of flour are required for 9 cups of sugar.

Explanation

To find the amount of flour needed for 9 cups of sugar, we can set up a ratio based on the recipe. The ratio of flour to sugar is 2 cups of flour for every 3 cups of sugar. To determine how much flour corresponds to 9 cups of sugar, we can calculate it as follows:

(2 cups flour / 3 cups sugar) = (x cups flour / 9 cups sugar).

Cross-multiplying gives us 3x = 18, leading to x = 6. Therefore, 6 cups of flour are required for 9 cups of sugar.

7. How many edges does a cube have?

8

12

6

10

A cube is a three-dimensional geometric shape with six square faces. Each face of the cube shares its edges with adjacent faces. Since a cube has 12 edges, each edge is counted once, connecting two vertices. To visualize, each of the six faces has four edges, but since each edge belongs to two faces, the total number of unique edges is 12. Thus, a cube has 12 edges.

Explanation

A cube is a three-dimensional geometric shape with six square faces. Each face of the cube shares its edges with adjacent faces. Since a cube has 12 edges, each edge is counted once, connecting two vertices. To visualize, each of the six faces has four edges, but since each edge belongs to two faces, the total number of unique edges is 12. Thus, a cube has 12 edges.

8. What is the probability of rolling a 3 on a fair six-sided die?

1/6

1/3

1/2

1/4

A fair six-sided die has six equally likely outcomes, numbered 1 through 6. Each number has an equal chance of being rolled. Since there is only one favorable outcome (rolling a 3) out of the six possible outcomes, the probability of rolling a 3 is calculated as the number of favorable outcomes divided by the total number of outcomes. This results in a probability of 1/6.

Explanation

A fair six-sided die has six equally likely outcomes, numbered 1 through 6. Each number has an equal chance of being rolled. Since there is only one favorable outcome (rolling a 3) out of the six possible outcomes, the probability of rolling a 3 is calculated as the number of favorable outcomes divided by the total number of outcomes. This results in a probability of 1/6.