Test Your 6th Grade Math IQ

Explanation
To find 49% of 130, we can multiply 130 by 0.49. This calculation gives us 63.7, which is the correct answer.

Explanation
The prime factorization of a number involves breaking it down into its prime factors. In this case, the number 36 can be broken down into 2 x 2 x 3 x 3. This means that 2 and 3 are the prime factors of 36, and they are repeated twice each.

Explanation
If a $100 item is first discounted by 25% and then the discounted price is raised by 25%, you can calculate the new price as follows:

1. First, calculate the discounted price after a 25% discount:
   Discounted Price = Original Price - (Discount Percentage * Original Price)
   Discounted Price = $100 - (0.25 * $100)
   Discounted Price = $100 - $25
   Discounted Price = $75

2. Now, calculate the price after raising the discounted price by 25%:
   New Price = Discounted Price + (Raise Percentage * Discounted Price)
   New Price = $75 + (0.25 * $75)
   New Price = $75 + $18.75
   New Price = $93.75

So, the new price after the 25% discount and then a 25% raise is $93.75.

Explanation
The example 3 x 1 = 3 demonstrates the Multiplicative Identity. The multiplicative identity is the number 1 in mathematics, which, when multiplied by any other number, leaves that number unchanged. In this example, when a number (3) is multiplied by 1, the result is the same number (3). This is because multiplying any number by 1 does not change the value of the number. Therefore, 3 x 1 = 3 represents the property of the Multiplicative Identity.

Explanation
The cube of a number is obtained by multiplying the number by itself twice. In this case, the cube of 12 is calculated as 12 x 12 x 12, which equals 1728.

Explanation
The measure of an angle that covers 5% of a circle can be found by multiplying the percentage (5%) by the total degrees in a circle (360 degrees) and dividing by 100. Therefore, 5% of 360 degrees is 18 degrees.

Explanation
One foot is equal to approximately 30 centimeters. This conversion is based on the fact that 1 foot is equal to 12 inches, and 1 inch is equal to 2.54 centimeters. Therefore, when we multiply 12 inches by 2.54 centimeters, we get approximately 30 centimeters.

Explanation
The prime factorization of 264 is 2 x 2 x 2 x 3 x 11. This means that 264 can be expressed as the product of these prime numbers. Prime factorization is a way to break down a number into its smallest prime components.

Explanation
To write a number in scientific notation, we move the decimal point to the right or left until there is only one non-zero digit to the left of the decimal point. In this case, 0.013 can be written as 1.3 x 10^-2 because we moved the decimal point two places to the right to get the non-zero digit 1.3. The negative exponent indicates that the decimal point was moved to the left.

Explanation
The square of a number is obtained by multiplying the number by itself. In this case, the number is 14. Therefore, to find the square of 14, we multiply 14 by 14, which equals 196.

Explanation
The perimeter of a square is the sum of all its sides. In this case, the perimeter is given as 20 centimeters. Since a square has all sides equal in length, we can divide the perimeter by 4 to find the length of each side. 20 divided by 4 is equal to 5, so each side of the square is 5 centimeters long.

Explanation
The measure of the angle that covers 81% of a circle is 291.6 degrees. This can be determined by multiplying the percentage (81%) by the total degrees in a circle (360). Therefore, 81% of 360 is equal to 291.6 degrees.

Explanation
192 is divisible by 3 because the sum of its digits (1 + 9 + 2) is equal to 12, which is divisible by 3.