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For a complete lesson on solving quadratic equations by factoring, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve quadratic equations by the method of their choice, using the following rules. If possible, use the factoring method. If there is no coefficient on the squared term, and the middle term of the trinomial is even, use completing the square. If there is a coefficient on the squared term, and if the middle term is odd, use the quadratic formula. If the variable only appears in the squared term, get the variable by itself on one side of the equation and square root both sides.

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For a complete lesson on the discount formula, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students solve word problems using the "discount" formula, which states original price x rate of discount = discount. Students also solve word problems using the "sale price" formula, which states: original price -- discount = sale price. For example: A tennis racket marked at $110.50 is on sale at 20% off. What is the discount? What is the sale price? Students also solve word problems using the "rate of discount" formula, which is the same as the percent decrease formula: amount of change/ original number. For example: An old video game is marked down from $48 to $18. What is the rate of discount?

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For a complete lesson on converting percents to fractions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to write percents as fractions and fractions as percents. For example, to write 6% as a fraction, remember that percent means "out of 100", so 6% can be written as the fraction 6 which reduces to 3/50. So 6% can be written as the fraction 3/50. To write 7/10 as a percent, set up the proportion 7/10 = x/100, then use cross products to get (7)(100) = (10)(x), or 700 = 10x, and dividing both sides by 10, 70 = x. So 7/10 can be written as 70%.

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For a complete lesson on interest word problems, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve "interest" word problems, such as the following. Pam invested $5000. She earned 14% on part of her investment and 6% on the rest. If she earned a total of $396 in interest for the year, how much did she invest at each rate? Note that this problem requires a chart to organize the information. The chart is based on the interest formula, which states that the amount invested times the rate of interest = interest earned. The chart is then used to set up the equation.

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For a complete lesson on simplifying expressions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve problems using the distributive property as the first step, then combining like terms. Students also learn to change minus signs to plus negatives in order to avoid making common errors with signs when distributing.

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For a complete lesson on circumference of a circle, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the circumference of a circle is the distance around the circle, and the formula for the circumference of a circle is 2 times pi times the radius of the circle. Pi is the ratio of the circumference to the radius, which is approximately 22 or 3.14. So a circle with a radius of 3 feet has a circumference of 2 times pi times 3, or 6 pi feet. And since pi = 3.14, 6 pi feet can also be written as 6 times 3.14, or 18.84 feet. Finally, note that the radius of a given circle is half the diameter of the circle. So to find the circumference of a circle with a given diameter, first find the radius of the circle by dividing the diameter by 2.

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For a complete lesson on adding and subtracting radicals, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to add or subtract radicals by first breaking down the given radicals and simplifying each term, then combining terms that have the same number inside the radical. For example, 15 root 2 + 6 root 2 = 21 root 2. Students also learn that a problem in the form (7 + 4 root 5)(2 -- 3 root 5) can be simplified using the FOIL method, and a problem in the form (1 + root 3)^2 can be rewritten as (1 + root 3)(1 + root 3).

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For a complete lesson on prime factorization, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the prime factorization of a number is the given number written as the product of its prime factors. For example, to find the prime factorization of 45, use a factor tree to find that 45 is 5 x 9, and 9 is 3 x 3. So the prime factorization of 45 is 5 x 3 x 3, or 5 x 3^2. Note that the prime factorization of a prime number, such as 23, is the number itself.

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For a complete lesson on the Pythagorean Theorem, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn the Pythagorean Theorem, which states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse, or a^2 + b^2 = c^2. Students are then asked to find missing side lengths of right triangles using the Pythagorean Theorem.

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For a complete lesson on solving absolute value equations, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that when solving an absolute value equation, such as 2 + I x + 1 I = 8, the first step is to isolate the absolute value by subtracting 2 from both sides to get I x + 1 I = 6. The next step is to split the equation up into two separate equations in the following way x + 1 = 6 or x + 1 = -6. Notice that in the second equation, the 6 becomes negative. Finally, the last step is to solve each of the remaining equations to get x = 5 or x = -7.

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For a complete lesson on converting percents to decimals, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to write percents as decimals and decimals as percents. For example, to write 82% as a decimal, think of 82% as 82 and remember that dividing by 100 moves the decimal point two places to the left, to get 0.82. So 82% can be written as the decimal 0.82. Since a percent can be written as a decimal by moving the decimal point two places to the left, a decimal can be written as a percent by moving the decimal point two places to the right. For example, to write 0.4 as a percent, move the decimal point two places to the right to get 40. So 0.4 can be written as 40%.

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For a complete lesson on factoring by grouping, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to factor a polynomial that has four terms by grouping the first two terms together and the last two terms together, then factoring out the Greatest Common Factor from each group. For example, to factor ax -- ay + cx -- cy, the first step is to factor out an "a" from the first two terms, and factor out a "c" from the last two terms, to get a(x -- y) + c(x -- y). The problem can now be thought of as two terms, each with a Greatest Common Factor of (x -- y), so an (x -- y) can be factored out, to get (x -- y)(a + c).

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For a complete lesson on area of a circle, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the formula for the area of a circle is pi times radius squared, so the area of a circle that has a radius of 5 inches is pi times 5 squared, or 25 pi square inches. And since pi = 3.14, 25 pi square inches can also be written as 25 times 3.14, or 78.5 square inches. Note that the radius of a given circle is half the diameter of the circle. So to find the area of a circle with a given diameter, first find the radius of the circle by dividing the diameter by 2.

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For a complete lesson on exponents, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve problems that combine the exponent rules covered in this chapter. For example, students may use the power rule, the product rule, and the quotient rule all in the same problem. Students also learn that when a fraction is taken to a power, both the numerator and denominator of the fraction are taken to that power.

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For a complete lesson on subtraction, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to subtract numbers with two or more digits, such as 985 - 47. The first step is to line up the numbers vertically so that the units digits are in the same column. Next, subtract the units digits, the tens digits, and the hundreds digits. When subtracting the units digits, notice that it is not possible to subtract 7 ones from 5 ones, so 1 ten must be borrowed from the tens column, leaving 7 tens and 15 ones. Now, subtracting the units digits, 15 - 7 = 8, subtracting the tens digits, 7 - 4 = 3, and subtracting the hundreds digits, 9 - 0 = 9. So 985 - 47 = 938. Note that the answer to a subtraction problem is called the difference, so the difference of 985 - 47 is 938.

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For a complete lesson on addition, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to add numbers with two or more digits, such as 139 + 25. The first step is to line up the numbers vertically so that the units digits are in the same column. Next, add the units digits, the tens digits, and the hundreds digits. Adding the units digits, 9 + 5 = 14, which is the same as 1 ten and 4 ones, so put a 4 in the units column and carry a 1 to the tens column. Now, adding the tens digits, 1 + 3 + 2 = 6, and adding the hundreds digits, 1 + 0 = 1. So 139 + 25 = 164. Note that the answer to an addition problem is called the sum, so the sum of 139 + 25 is 164.

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For a complete lesson on percent increase, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to find the percent increase or percent decrease between two numbers, using the following formula amount of change/ original number. For example, to find the percent decrease if the price changes from $60 to $39, since the amount of change is $21, and the original number is $60, the percent decrease is $21/$60, which simplifies to 0.35. And remember that the answer is a percent, so move the decimal point two places to the right, to get 35%. So if the price changes from $60 to $39, the percent decrease is 35%.

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For a complete lesson on the vertical line test, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that if the x-coordinate is different in each ordered pair in a given relation, then the relation is a function. Students also learn to use mapping diagrams and the vertical line test to determine if a relation is a function.

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For a complete lesson on perimeter word problems, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve "Geometry" word problems involving perimeters of rectangles and measures of complementary and supplementary angles. Note that if two angles are complementary, they can be represented as x and 90 -- x, and if two angles are supplementary, they can be represented as x and 180 -- x.

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For a complete lesson on graphing lines using an x/y chart, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to graph a given linear equation using a chart. For example, to graph the equation y = x - 4, pick three values for x, such as -1, 0, and 1, and substitute these values into the equation to find the corresponding values of y. Next, plot the resulting points on a coordinate system and graph the line that passes through them. To graph the equation 3x + 5y = 5, first solve for y, to get y = -3 + 1. Then set up a chart, pick three values of x, such as -5, 0, and 5 (multiples of 5 so that the corresponding values of y will not be fractions), find the corresponding values of y, and graph the line.

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For a complete lesson on solving proportions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that a proportion is an equation that states that two ratios are equal. Students then learn the properties of proportion, and are asked to solve for x in given proportions, and to solve word problems involving proportions.

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For a complete lesson on converting decimals to percents, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to write percents as decimals and decimals as percents. For example, to write 82% as a decimal, think of 82% as 82 and remember that dividing by 100 moves the decimal point two places to the left, to get 0.82. So 82% can be written as the decimal 0.82. Since a percent can be written as a decimal by moving the decimal point two places to the left, a decimal can be written as a percent by moving the decimal point two places to the right. For example, to write 0.4 as a percent, move the decimal point two places to the right to get 40. So 0.4 can be written as 40%.

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For a complete lesson on combining like terms, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to add or subtract terms that involve variables by combining like terms. Like terms are terms with exactly the same variable factors. For example, 5x and 3x are like terms. However, 7x and 9y are not like terms, and neither are 8x and 8x^2. In the problem 2x + 3x + 4, only the 2x and 3x can be combined, because they are like terms, so the expression can be simplified to 5x + 4. Students also learn that the number in front of the variable is called the coefficient, and when there is no coefficient in front of the variable the coefficient is understood to be 1.

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For a complete lesson on converting fractions to mixed numbers, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that a proper fraction is a fraction whose numerator is less than or equal to its denominator. For example, 3 16/18, and 4/4 are proper fractions. And an improper fraction is a fraction whose numerator is greater than its denominator. For example, 5/2 and 10/3 are improper fractions. Note that an improper fraction can be rewritten as a mixed number. For example, 5/2 can be rewritten as 2 ½. Students are asked to write improper fractions as mixed numbers, and mixed numbers as improper fractions.

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For a complete lesson on plotting points on the coordinate system, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn how to plot points on a coordinate system. For example, the point (-1, 2) is 1 unit to the left and 2 units up on the coordinate system. Students also learn to identify the x-coordinate, the y-coordinate, the x-axis, the y-axis, quadrants I -- IV, and the origin.

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For a complete lesson on comparing fractions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to compare fractions with the same denominator, which are called like fractions, by comparing the numerators. For example, to compare 7 and 4/9, note that 7 is greater than 4, so 7/9 is greater than 4/9. Students also learn to compare fractions with the different denominators, which are called unlike fractions, by first finding a common denominator, then comparing the numerators. For example, to compare 1/2 and 1/3, first find a common denominator, or the Least Common Multiple of 2 and 3, which is 6. To get 6 in the denominator of 1/2, multiply the numerator and denominator by 3, to get 3/6. To get 6 in the denominator of 1/3, multiply the numerator and denominator by 2, to get 2/6. Next, compare 3/6 and 2/6. Note that 3 is greater than 2, so 3/6 is greater than 2/6, which means that 1/2 is greater than 1/3.

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For a complete lesson on rounding whole numbers, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to round a number to a given place using the following steps. First, find the digit in the rounding place. Next, look at the digit to the right of the rounding place. If the digit to the right of the rounding place is less than 5, round down, which means that the digit in the rounding place stays the same, and all digits to the right of the place become zero. If the digit to the right of the rounding place is 5 or greater, round up, which means add 1 to the digit in the rounding place, and all digits to the right of the rounding place become zero.

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For a complete lesson on comparing decimals, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to compare decimals by first lining up the decimals, then comparing numbers place-by-place, starting on the left. For example, to compare 17.456 and 17.501, the 1's in the tens place are the same, and the 7's in the units place are the same. However, in the tenths place,

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For a complete lesson on solving equations with fractions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve equations that involve fractions by either multiplying both sides of the equation by the reciprocal of the fraction, or multiplying both sides of the equation by the denominator of the fraction. The goal is to get rid of the fraction as soon as possible.

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For a complete lesson on addition word problems, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve addition and subtraction word problems. Note that key words for addition are altogether, total, in all. Key words for subtraction are: left, remaining, more, fewer, increase, go up, grow, decrease, go down, reduce. And key words for estimation are: estimate, approximately.

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For a complete lesson on unit rate, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that a rate is a comparison of two measurements or amounts that have different units. For example, 60 miles in 2 hours is a rate. Students learn that a unit rate is a rate in which the second rate is 1 unit. For example, 30 miles in 1 hour, or 30 miles per hour, is a unit rate. In the problems in this lesson, students are given a rate, and are asked to find the corresponding unit rate. For example, if there are 70 students in 5 classes, find the number of students per class. To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate. So in this case, divide the numerator and denominator of 70 by 5, to get 14/1, or 14 students per class, which is the unit rate.

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For a complete lesson on applications of linear functions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve word problems that involve direct variation and linear functions. Students are given table of ordered pairs, and are asked to write a rule for the linear function in slope-intercept form, graph the function, and explain the meaning of the slope and y-intercept.

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For a complete lesson on unit price, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the unit price is the cost per unit, and to find the unit price, divide the price by the number of units. For example, to find the unit price of 16 ounces of soup that costs $3.20, divide $3.20 by 16 ounces, to get $0.20 per ounce. Students are also asked to determine which of two given items is a "better buy", by finding the unit price of each item, then comparing the unit prices. The item with the smaller unit price is the "better buy".

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For a complete lesson on area of a square, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the area of a figure is the measure of how much surface is covered by the figure. The formula for the area of a rectangle is length times width, so the area of a rectangle that has a length of 7 centimeters and a width of 3 centimeters is 7 times 3, or 21 square centimeters. The formula for the area of a square is side squared, so the area of a square that has a side of length of 9 feet is 9 squared, or 81 square feet.

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For a complete lesson on estimating sums and differences, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to estimate a sum or difference by first rounding each number to the place specified in the problem. For example, to estimate 4909 + 3217 by rounding each number to the nearest thousand, first round 4909 up to 5000, and round 3217 down to 3000, then add 5000 + 3000 to get 8000.

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For a complete lesson on area of a rectangle, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the area of a figure is the measure of how much surface is covered by the figure. The formula for the area of a rectangle is length times width, so the area of a rectangle that has a length of 7 centimeters and a width of 3 centimeters is 7 times 3, or 21 square centimeters. The formula for the area of a square is side squared, so the area of a square that has a side of length of 9 feet is 9 squared, or 81 square feet.

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For a complete lesson on the power rule, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn the power rule, which states that when simplifying a power taken to another power, multiply the exponents. For example, (x^2)^3 = x^6. To simplify (6x^6)^2, square the coefficient and multiply the exponent times 2, to get 36x^12.

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For a complete lesson on expanded notation, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to use the place value chart to write numbers in a variety of ways. For example, the number 89234 can be written as the word name eighty-nine thousand, two hundred thirty-four, or in expanded notation as 8 ten thousands + 9 thousands + 2 hundreds + 3 tens + 4 units. Students also learn to find the value of a given digit in a given number. For example, the digit 5 in the number 1508346 means 5 hundred thousands.

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For a complete lesson on adding like fractions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to add like fractions by adding the numerators and keeping the denominators the same. For example, 1 + 3/8 = 4/8, and note that 4/8 must be rewritten in lowest terms, as 1/2. Students also learn to subtract like fractions by subtracting the numerators and keeping the denominators the same. For example, 16/7 -- 6/7 = 10/7, and note that 10/7 must be rewritten as the mixed number, 1 3/7.

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For a complete lesson on multiplication word problems, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve multiplication and division word problems. Note that key words for multiplication are times as many, times as much, find all if each. Key words for division are: each, per. And key words for estimation are: estimate, approximately.

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For a complete lesson on division word problems, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to solve multiplication and division word problems. Note that key words for multiplication are times as many, times as much, find all if each. Key words for division are: each, per. And key words for estimation are: estimate, approximately.

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For a complete lesson on sin cos tan, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn to find the missing side lengths and the missing angle measures in right triangles using sine, cosine, and tangent. Note that a scientific or graphing calculator is required for the problems in this lesson.

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For a complete lesson on multiplying decimals, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, 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.

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For a complete lesson on median, altitude, and perpendicular bisector, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn the definitions of a median of a triangle, an altitude of a triangle, and a perpendicular bisector. Students are then asked to identify or draw medians, altitudes, and perpendicular bisectors in given triangles.

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For a complete lesson on adding fractions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, 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.

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For a complete lesson on multiplying rational expressions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that when multiplying rational expressions, the first step is to factor each of the numerators and each of the denominators, if possible, then cancel out the factors that match up, then multiply across the numerators and across the denominators. Students also learn that when dividing rational expressions, the first step is to change the division to multiplication and flip the second fraction, then factor each of the numerators and each of the denominators, if possible, then cancel out the factors that match up, then multiply across the numerators and across the denominators.

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For a complete lesson on subtracting integers, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students review the addition and subtraction of 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. Students learn that minus a negative can be thought of as plus a positive.

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For a complete lesson on equivalent fractions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that two fractions are equivalent if the fractions are the same when they are written in lowest terms. For example, 4 and 8/14 are equivalent fractions, because they are both equal to 4/7 when written in lowest terms. Students also learn to find fractions that are equivalent to a given fraction by multiplying the numerator and denominator of the given fraction by the same number. For example, to find fractions that are equivalent to 1/8, multiply the numerator and denominator by 2, to get 2/16, multiply the numerator and denominator by 3, to get 3/24, and so on.

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