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Multiplying Integers | MathHelp.com
By MathHelp.com
This lesson covers comparing fractions. Students learn to compare fractions with the same denominator, which are called like fractions, by comparing the numerators. For example, to compare 7/9 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.
GRE Math Test Prep | MathHelp.com
By MathHelp.com
This lesson covers the product rule. Students learn the product rule, which states that when multiplying two powers that have the same base, add the exponents. For example, x^4 times x^3 = x^7. To multiply 6s^3 times 3s^6, multiply the coefficients and add the exponents, to get 18s^9. If there is no exponent on the variable, it can be given an exponent of 1. For example, x can be thought of as x^1.
6.RP.3 - Solve Word Problems Using Tape Diagrams
By MathwithMrAlmeida
In this video, Mr. Almeida shows you how to solve ratio word problems using tape diagrams. The models create equivalent ratios because you are multiplying both quantities in one ratio by the same positive number (the length of 1 unit). This meets Common Core Standard for Mathematics 6.RP.3.
Geometry Basics | MathHelp.com
By MathHelp.com
This lesson covers permutations. Students learn that a permutation is an arrangement of objects in which the order is important. For example, the permutation AB is different than the permutation BA. Students are then asked to solve word problems involving permutations. For example: Find the number of different ways 6 books can be arranged on a shelf. Note that the number of permutations can be found by multiplying the number of choices for the 1st position (6 books) times the number of choices for the second position (5 books), and so on. So the number of permutations is 6 x 5 x 4 x 3 x 2 x 1, or 720. In other words, there are 720 different ways 6 books can be arranged on a shelf.
Negative Exponents | MathHelp.com
By MathHelp.com
In this example, we’re given the functions f(x) = 3x – 2 (read as “f of x equals…”) and g(x) = root x, and we’re asked to find the composite functions f(g(9)) (read as “f of g of 9”) and g(f(9). To find f(g(9)), we first find g(9). Since g(x) = root x, we can find g(9) by substituting a 9 in for the x in the function, to get g(9) = root 9, and the square root of 9 is 3, so g(9) = 3. Now, since g(9) = 3, f(g(9)) is the same thing as f(3), so our next step is to find f(3). And remember that f(x) = 3x – 2, so to find f(3), we substitute a 3 in for the x in the function, and we have f(3) = 3 times 3 minus 2. Notice that I always use parentheses when substituting a value into a function, in this case 3. Finally, 3 times 3 minus 2 simplifies to 9 minus 2, or 7, so f(3) = 7. Therefore, f(g(9)) = 7. Next, to find g(f(9), we first find f(9). Since f(x) = 3x - 2, we find f(9) by substituting a 9 in for the x in the function, to get f(9) = 3 times 9 minus 2, which simplifies to 27 – 2, or 25, so f(9) = 25. Now, since f(9) = 25, g(f(9)) is the same thing as g(25), so our next step is to find g(25). And remember that g(x) = root x, so to find g(25), we substitute a 25 in for the x in the function, to get g(25) = root 25. Finally, the square root of 25 is 5, so g(25) = 5. Therefore, g(f(9)) = 5. It’s important to recognize that
Transitioning from counting to multiplying to find area | 3rd grade | Khan Academy
By Khan Academy
finds the area of a rectangle both by counting unit squares and multiplying side lengths
More involved multiplying decimals example
By Khan Academy
Sometimes multiplying really small decimals (with all those zeros!) can be a little intimidating. Watch as we show you a handy trick to simplify these problems and solve them.
Multiplying decimals 3
By Khan Academy
Sometimes multiplying really small decimals (with all those zeros!) can be a little intimidating. Watch as we show you a handy trick to simplify these problems and solve them.
Multiplying decimals 3
By Khan Academy
Multiplying decimals? Try multiplying without the decimals first, them add them back in. We'll show you.
Evaluating Logarithms | MathHelp.com
By MathHelp.com
In this example, notice that we have a polynomial divided by a binomial, and our binomial is in the form of an x term minus a constant term, or x – c. In this situation, instead of having to use long division, like we did in the previous lesson, we can divide the polynomials using synthetic division, which is a much more efficient method. Here’s how it works. We start by finding the value of c. Since –c = -3, we know that c = 3. Next, we put the value of c inside a box, so we put the 3 inside a box. It’s very important to understand that the number that goes inside the box always uses the opposite sign as the constant term in the binomial. In other words, since the constant term in the binomial is -3, the number that goes inside the box, is positive 3. Next, we write the coefficients of the dividend, which are 2, -7, 4, and 5. Be very careful with your signs. Now, we’re ready to start our synthetic division. First, we bring down the 2. Next, we multiply the 3 in the box times 2 to get 6, and we put the 6 under the -7. Next, we add -7 + 6 to get -1. Next, we multiply the 3 in the box times -1 to get -3, and we put the -3 under the 4. Next, we add 4 + -3 to get 1. Next, we multiply the 3 in the box times 1 to get 3, and we put the 3 under the 5. Finally, we add 5 + 3 to get 8. Now, notice that we have a 2, -1, 1, and 8 in the bottom row of our synthetic division. These values will give us our answer: the first 3 numbers represent the coefficients of the quotient, and the last number is the remainder. And it’s important to understand that our answer will be one degree less than the dividend. In other words, since our dividend starts with x cubed, and we’re dividing by x, our answer will start with x squared. So our answer is 2x squared – 1x + 1 + 8 over x – 3. Notice that we always use descending order of powers in our quotient. In this case x squared, x, and the constant. Finally, remember that we add the remainder over the divisor, just like we did in the previous lesson on long division, and we have our answer. It’s important to understand that we’ll get the same answer whether we use synthetic division or long division. However, synthetic division is much faster.
Multiplying and Dividing Decimals | 7.NS.A.2c | 7th Grade Math
By ParksMath | Todd Parks
ParksMath explains how to multiply and divide decimals numbers without the use of a calculator. Understanding how to change a decimal number so that it is an integer, makes multiplying and dividing decimals much easier. This quick tutorial will give you thee tools that you need to find the product or quotient of any decimal number.
Understand & Calculate Equivalent Fractions - [11]
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
[3.OA.5-1.0] Multiplication Properties - Common Core Standard
By Front Row
Discover more Common Core Math at https://www.frontrowed.comApply properties of operations as strategies to multiply.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 2) = (8 × 5) (8 × 2) = 40 16 = 56. (Distributive property.)Front Row is a free, adaptive, Common Core aligned math program for teachers and students in kindergarten through eighth grade. Front Row allows students to practice math at their own pace - learning advanced concepts when they 're ready and receiving remediation when they struggle. Front Row provides teachers with access to a detailed data dashboard and weekly email reports that show which standards are causing students difficulty, what small groups can be formed for interventions, and how their students are progressing in math.Discover more Common Core Math at https://www.frontrowed.com