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Algebra Math Presentation

Transcript: List of variables with: no equals sign - expression equaks sign - equation inequality sign ( greater than or less than) - inequality # Expression Description 1 a ± b A number (b) added to or subtracted from another number (a) 2 (a ± b) ± c Expression #1 plus or minus another number (c) 3 (a ± b)^c Expression #1 multiplied by itself (c) amount of times 4 ab A number multiplied by another number 5 (ab)^c Expression #4 multiplied by itself (c) amount of times 6 ab ± c Expression #4 plus or minus another number (c) 7 ab/c Expression #4 divided by another number (c) 8 (a ± b)/c Expression #1 divided by another number (c) 9 a/b A number (a) divided by another number (b) 10 a^b/c A number (a) multiplied by itself (b) amount of times then divided by another number (c) 11 √ a The square root of a number (a) Equations that involve fractions To solve you need Lowest Common Denominator Distributive Law Equations which have a range instead of an equal sign Solved the same as a linear equation Graphed For example: “A farmer has c chickens, e eggs, 2 roosters, and n nests. The number of eggs is 2 times the number of hens, the number of hens is 3 more than the number of nests, and the number of nests is 10 times the number of roosters. How many eggs are there?” You would rewrite it as: e = 2h, h = n + 3, n = 10 x 2. n = 20, so e = 2 x (20 + 3) e = 46 Some Formulae to remember (a + b)^2 = a^2 + 2ab + b^2 (a – b)^2 = a^2 – 2ab + b^2 (a + b)(a – b) = a^2 – b^2 (x + a)(x + b) = x^2 + (a + b)x + ab “(a+b)^c” has the coefficient pattern of Pascals Triangle where to the 0 is 1 and the exponent pattern of a^c, c-1, c-2, etc until 0 and b^0, 0+1, 0+2, etc until c. Uses the balance method Does the same thing to both sides but reverses the sign (positive to negative) Also known as exponent laws They explain how to simplify exponents in an equation Replacing a variable with a number Often occurs when some numbers and one variable are in a question You rewrite the question in terms of the variable and solve Or you can check your work by going through and replacing the variable with your answer Simplifying For example: a > 2 is graphed as a < 2 is graphed the same but facing the other direction a >= 2 is the same line but the circle is coloured in Problem Solving For example: (2 + x)(7 + y) = (2)(7) + (2)(y) + (x)(7) + (x)(y) = 14 + 2y + 7x + xy = xy + 7x + 2y + 14 For example: a + a + b + b you could simplify it as 2a + 2b because if you count it up there are 2 “a”s written and 2 “b”s. Whereas a x a = a^2, a x a x a = a^3, etc. Mixture Problems For example: 3^a = 27 we need to have 27 as a power of 3. We know that it is 3^3 so we know that 3^a = 3^3 so a = 3. a^0 = 1 but only if a != 0 a^-b = 1/a^b 1/a^-b = a^b a^-1 = 1/a a^b/c = c√a^b Exponential Equations a^b x a^c = a^(b+c) a^b / a^c = a^(b-c) (a^b)^c = a^bc (ab)^c = a^c b^c (a/b)^c = a^c/b^c For example: “How much water(a) must be added to 1L of 5% cordial to make a 4% cordial mixture?” a + 95% x 1 = 96% x (a + 1), a/1 x 100/100 + 95/100 = 96/100 x a + 95/100, 100a + 95 = 96a + 96, 100a – 96a = 96 – 95, 4a = 1, a = 1/4L For example: 5x + 7 = 32 5x +7 – 7 = 32 – 7 5x = 25 5x/5 = 25/5 X = 5 Notation Linear Equations Index Laws Algebra When the variable is in the exponent Solved the same as linear equations Rational Equations Substitution Gathering like terms Values are only sepatated by addition or subtraction signs Any multiplication or division can be simplified. Upon completion order answer form greatest to lowest Incorporates rewriting equations in terms of a variable Involve using one equation to solve another Taking a word problem and turning it into an equation then solving it This is done by: determining the variable(s) determining the operations writing it out solving it For example: In 5 years, I will be twice as old as I am today. How old am I? Unknown: age = x Operation: +, x Written out: x + 5 = 2x Solve: x + 5 – 5 = 2x – 5 x = 2x – 5 x = 5 Problem solving tool that uses letters to represent unknown values called variables For example: 5^1/2 = 2√5 (the square root of 5 to the 1) Equations Linear Inequations Expanding brackets One acronym is FOIL: First, Outside, Inside, Last Meaning you multiply the values in that order

Algebra math

Transcript: Fractions By:Spyros Fractions origin! Fractions originated in Egypt where they used the fraction as a number system which could be written. They used hieroglyphics to write them out on walls and other things! Where it was created This is an example of what the different symbols represented. Development! It was developed to divide food to different people. They created it to divide food to the people in a easier manner. With fractions it made this process a lot easier, also a lot quicker. How was it developed? How it was used! How was it used? The Egyptians used fractions as a source of division. They would divide the amount of stuff they had evenly amongst others. They also used it when they were doing hard labour like building the pyramids. They would use fractions to divide the amount of work they needed to do with all the people so, that nobody was doing more or less work than others. How it is used today! Fractions are relevant in today's world because it allows you to figure out how much of something you want, need or have. For example, if I have 12 cookies and there are 4 people each of us is going to get 3 cookies. That shows how many cookies we could have. It's used today in many different ways like baking. If your baking fractions come into play when you are measuring ingredients. Also, at a restaurant if you have 4 slices of pizza and 2 people then you would use fractions to figure out that each person gets 2 slices. How it is used today? Sources used! Sources!,Using%20Egyptian%20Fractions%20to%20Evenly%20Divide%20an%20Object%20into%20Equal,structures%20required%20massive%20labor%20work.,a%20fraction%20of%20the%20hour.

presentation math Algebra

Transcript: Director: Christopher. Information: Carson, William. Helper: Tegar, Bennett, Rhenald. ALGEBRA Group : Chris, Tegar, Rhenald William, Bennett, and Carson Mathematics History History Founded by Al-Kwarizmi In the 9th Century, India. From a book called "Kitab Al-Jabr" The use of the word "algebra" dates from the 16th century. -William Algebra Algebra Algebra consists of letter as a variable to call something and a number as the number of the letter. -Bennett Example of Algebra 6X , -Y , Z , etc Example of A Problem Example 2X x Y = , 4A x 2B= , etc The use of letter The use of letter In Algebra, letters are only used for calling something with any letter that you want. But the letters can be any number. Like x , y, a, b, etc -Carson The use of number in Algebra The use of number In Algebra, numbers are used for explaining how much the thing we are counting. if 1 x X we erase the 1 so it's only X Like 2A , 5B ,etc -Christopher Solving Algebra If 2 x X + 3 = 2X + 3 X = independant variable 2X= dependant variable 3= constant If x= 11 just change "X" to 11 2 x 11 + 3= 25 Solving Algebra -Rhenald Solving Algebra Example: 2(B x A ) = (2 x B) x (2 x A) =2B x 2A -(2 + B) = -2 -(-B) if there is any thing infront of () you multiply it inside first if there is nothing infront, it means you just multiply every thing inside the () by + Solving Algebra -Rhenald Solving Algebra Solving Algebra Like: 18 AX - 15 AY= 3A(6X - 5 Y) 14 V + 7 X= 7(2V + X)= 2V + X To simplify the algebra Question, devide the number but both number needs to be devided by the same number or letter and make a Question using () -Rhenald

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