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What are compatible numbers in the third grade?

When determining compatible numbers, a student must consider what numbers divide cleanly into other numbers. For example, 5 and 10 both divide evenly into any number that ends in a 0. All even numbers divide neatly into other even numbers. All of this must be considered when picking compatible numbers.\nFor example, if a student needs to divide 9 into 70, he can round the 9 up to 10 so that it will divide evenly into 70. The answer with the actual numbers is 7.778, while the answer with compatible numbers is 7. If the problem is 31 divided by 4, 31 can be rounded to 30 and 4 can be rounded to ..

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How do you calculate the perimeter of the base of a rectangular prism?

Determine the dimensions of the baseThe base of a rectangular prism has four sides. The two lengths of the base are equal and the two widths are equal as well. Measure the sides using a ruler or a tape measure.Multiply the value of each dimension by 2Multiply the length by 2. Do the same with the width.Add the productsAdd the values obtained from the previous step. The sum is the perimeter of the base of a rectangular prism.

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Is 1 a prime number?

Until the 19th century, 1 was often considered a prime number. The thinking changed, however, to accommodate the fundamental theorem of arithmetic, which mandates that each number has a unique factorization. Two is the smallest prime number, because it is larger than 1 and its only factors are 1 and itself. It is also the only even prime number, because all other even numbers have 2 as a factor. The next nine prime numbers are 3, 5, 7, 11, 13, 17, 19, 23 and 29.

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Why can the denominator of a rational expression never be equal to zero?

For example, if dividing six by zero produced a real quotient, then it would follow that multiplying that quotient by zero would give a product of six. Since any number multiplied by zero equals zero, there is no such quotient. Algebraic manipulations involving fractions with zero denominators often lead to meaningless solutions because dividing by zero is an invalid operation.

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What is 40 percent as a decimal?

Another way to determine the decimal form of a percentage is to divide the percentage by 100. Forty divided by 100 is 0.40, which is the decimal form of 40 percent. Decimals and percentages are both based on the number 100, making it easy to convert from one to the other.\nTo convert a decimal to its corresponding percentage, multiply by 100 or move the decimal point two places to the right. Using 0.40 as an example, moving the decimal point two places to the right gives a result of 40 percent.

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What is the antiderivative of e2x?

An antiderivative of a general function, f(x), is a function that can be differentiated with respect to x to give f(x). The general result for the antiderivative must contain an arbitrary constant, c, because all constants differentiate to zero. By substituting minimum and maximum values for x into the antiderivative, one can compute a definite integral from this result. It is straightforward to show that (e^(2x))/2 + c differentiates to e^(2x) by using the general rule that e^(f(x)) differentiates to f'(x)e^(f(x)), where f'(x) is the derivative of f(x) with respect to x.

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How do you use a place value table when teaching math?

Place value tables can account for whole numbers reaching into the trillions. They are designed to be read left to right, with the larger numbers coming first, and its categories — trillions, millions, thousands and ones — are broken into separate distinctions of hundreds, tens and ones. There is a blank row between the category and subcategory rows where the number in question can be written.\nWhen using a place value table to help determine the place of one digit, simply write the number in the blank row. Only one digit can fit in any block. For example, when writing the number 2,564, th..

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What are some interesting facts about the number 30?

Another math fact about the number 30 is that it is considered a pyramid number made up of the first four numbers such that 1^2 + 2^2 +3^2 + 4^2 equals 30. A pyramidal number corresponds to a set of points arranged in layers or stacks so that a square pyramid shape is formed. A pyramid number is also called a square pyramidal number.Polygons that are 30-sided are known as tricontagons. Some polyhedra that contain 30 edges are an icosahedron and dodecahedron. If n is a number equal to or greater than 2, then n^5 - n can be divided by 30. For example, letting n = 3 in the given expression result..

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How do you find the discriminant of a quadratic equation?

Put the quadratic equation in standard formIn standard form, a quadratic equation has all the coefficients and variables placed on the left side of the equal sign, with only the number 0 remaining on the right side of the equal sign. Order the terms so that the variables with the highest exponents are farthest to the left. A quadratic equation in standard form has this basic format: ax^2 + bx +c = 0.Substitute the coefficients from the equation into the formula b^2-4acOnce the quadratic equation is in standard form, the coefficients are already in the order a, b, c, so it is easy to substitute..

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What is a perpendicular bisector?

The first step in this method is to place the compass needle on one end of a horizontal line segment. The compass hinge is then adjusted so the distance between the compass needle and the tip of the writing implement is slightly more than half the length of the line segment.\nDraw an arc in the area above and below the middle of the line segment while the compass needle remains at the end of the line segment. Make sure the angle of the compass hinge remains unchanged throughout this process.\nMove the compass needle to the opposite end of the line segment without altering the hinge, and repeat..

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