How to Divide Decimals by Decimals

Students learn to divide a decimal by a decimal by first multiplying both decimals by the power of 10 that changes the second decimal to a whole number. For example, to divide 0.16 by 0.8, first multiply both decimals by 10, to get 1.6 8. Next, divide the decimal by the whole number in the same way that one would divide a whole number by a whole number (using long division). However, at the end of the problem, the decimal point is brought straight up from the decimal that is inside the division symbol to the answer that is written on top of the division symbol.

How to Find the Area of Triangles

Students learn the formula for the area of a triangle, and are asked to solve problems using this formula. Note that right triangle formulas and trigonometry are used extensively in the problems in this lesson.

Square Roots

Students learn to simplify square roots. For example, to simplify the square root of 16, since 4 squared is 16, the square root of 16 is 4. Note that 16 is a perfect square, so its square root is an integer. To simplify the square root of a number that is not a perfect square, such as 45, first find the prime factorization of the number, in this case 3 times 3 times 5. Next, since the 3's pair up, a 3 comes out of the radical, and since the 5 does not pair up, it stays inside the radical. So the square root of 45 simplifies to 3 times the square root of 5.

Geometry - Definition of Parallel Lines

Students learn the definitions of parallel lines, skew lines, parallel planes, and transversals, and are asked to identify these types of lines/planes in given figures. Students are also asked to identify alternate interior angles, same-side interior angles, and corresponding angles. Always, sometimes, and never questions are included in this lesson.

Simplifying Radicals

Students learn to simplify a square root by setting up a factor tree for the number inside the radical. If a factor pairs up in the factor tree, then it comes out of the radical. If a factor does not pair up, then it stays inside. Students also learn to simplify a cube root by setting up a factor tree for the number inside the radical. If a factor is part of a group of three factors that are the same, then it comes out of the radical. If a factor is not part of a group of three factors that are the same, then it stays inside.

Using Coordinates to Find Slope

Students are given the coordinates of two points, and are asked to find the slope of the line that passes through the points (without graphing). To solve the problems in this lesson, students use the slope formula, which states that m = (y2 -- y1) / (x2 -- x1). The slope formula can be read as "slope equals the second y coordinate minus the first y-coordinate over the second x-coordinate minus the first x-coordinate".

Divisibility of a Number

This video discusses the Rules of Identifying the Divisibility of a Number.

Order of Operations with Fractions

Students combine the order operations (PEMDAS) with adding, subtracting, multiplying, and dividing fractions. In other words, multiplication and division come before addition and subtraction, and multiplication and division are done based on order of appearance from left to right in the problem, and addition and subtraction are done based on order of appearance from left to right in the problem.

How to Multiply and Divide Fractions

Students learn to multiply two fractions by multiplying across the numerators, and multiplying across the denominators. Students learn to divide two fractions by taking the reciprocal of the second fraction, then multiplying the fractions.

How to Multiply Decimals Together

Students learn to multiply decimals in the same way that one would multiply whole numbers (vertically). However, at the end of the problem, students must determine where the decimal goes in the answer by counting the total number of digits to the right of the decimal point in the original numbers, then placing the decimal point in the answer so that the answer has this same total number of digits to the right of the decimal point. For example, after multiplying 1.05 x 7.4, since there are a total of 3 digits to the right of the decimal point in the original numbers, place the decimal point in the answer so that there are 3 digits to the right of the decimal point.

How to Find the Absolute Value of Integer

Students learn that the absolute value of a number is its distance from zero on a number line. For example, the absolute value of --8 is +8, because --8 is 8 units from zero on the number line. Note that the absolute value of any positive or negative integer is positive. Students also learn that the first step to simplifying absolute value problems is to simplify inside the absolute value, if possible.

How to Use a Graph of Line to Find Slope

In this video tutorial, learn how to determine the slope of a line.

slope = rise / run

How to Add and Subtract Using a Number Line

This video reviews the addition and subtraction of positive and negative integers using a number line, where a positive integer represents a move to the right, and a negative integer represents a move to the left. Remember that minus a negative can be thought of as plus a positive.

How to Add and Subtract Fractions

Students learn to add or subtract fractions using the least common denominator, which is the least common multiple for the denominators of the fractions. Once the fractions are given a common denominator by multiplying the numerator and denominator of each fraction by the appropriate number, then the fractions can be added or subtracted by adding or subtracting the numerators, and leaving the denominator the same.

How to Multiply and Divide Positive and Negative Numbers

Students review the multiplication and division of positive and negative integers. The rules for multiplying integers are as follows:

• positive times positive equals positive
• positive times negative equals negative
• negative times positive equals negative
• negative times negative equals positive.

The rules for dividing integers are as follows:

• positive divided by positive equals positive
• positive divided by negative equals negative
• negative divided by positive equals negative
• negative divided by negative equals positive

How to do Metric Unit Conversions

Students learn that in the metric system, all measures of length are based on meters. For example, a centimeter is 1/100 of a meter. And all measures of weight are based on grams. For example, a kilogram is 1000 grams. And all measures of volume are based on liters. For example, a milliliter is 1/1000 of a liter. Students are then asked to solve problems using conversion factors, such as 4,500 milligrams = ____ grams.

How to Convert From a Mixed Number to an Improper Fraction

In this video tutorial, learn how to convert from a mixed number to an improper fraction.

How to Ace Calculus

Written by three gifted-and funny-teachers, How to Ace Calculus provides humorous and readable explanations of the key topics of calculus without the technical details and fine print that would be found in a more formal text. Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams-all the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun.

Available at Amazon.com.