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
Transcript: ALGEBRA ENGLISH MATH Presented by ETHEN KIM to ELC STUDENTS FRACTION How do we solve Fraction ? 1) Multiplying Fractions 2) Dividing Fractions 3) Adding and Subtracting Fractions Multiply Multiplying Fractions Multiply numerators across and denominators across Divide Dividing Fractions Change the division sign into a multiplication sign. Multiply top x top and bottom x bottom. Add/Subtraction Adding and subtracting Fractions 1. Find the lowest common denominator 2. Multiply fractions to match the lowest common denominator. 3. Add or subtracrt the two numerator. ( But NOT denominator) How do we solve order of operations? ORDER OF OPERATIONS 1) Simple Order of operations 2) Fraction Type Order of operations Simple Simple How can we use simplify? SIMPLIFY Q1 1st step Simplify algebraic expressions 2st step Combine like terms allowed to add or subtract Substitution SUBSTITUTION x = 5 y = 2x - 3 Q. Find the value of x and y y = 2(5) - 3 y = 10 - 3 y = 7 ( 5 , 7 ) Video Clip
Transcript: Math TEMPLATE how to adding fractions, First you find your common denominator. Then you line up your fractions. fin that you add JUST YOUR NUMERATORS. Finally you simplify fractions adding First you find your common denominator Then you line up your fractions
Transcript: we will solve this equation same variables x, 2x, 9x 8y, 9y, y y², 2y² y³, 4y³, 2y³ x, y, n or other alphabets is unknown number. it can be any numbers balance 5 = 5 5 - 3 = 5 - 3 if you do something ( +, - ,*, / ) you have to do the same to the other side By Hyeon Seo How to solve it #1 how to solve it #2 Math - Algebra BODMAS 3x - 4 = 7 + 2x 3x = 11 + 2x (plus 4 on each side) x = 11 ( minus 2x on each side) you get the answer! x = 11 Equation has a equal sign (=) You can get the answer for variable variables equation how to solve it #3
Transcript: 15-12=3 b-12=3 SUMMARY THANKS for looking clean your popcorn up Algrab Math is not hard.Algrab is nothing but subtracting,adding,division, and multiply ALGRAB MATH 1. look at the problems 2.try different numbers to to subtract 12 from something 10 through 20 to get 3. pictures 1.frist look at what you have before you do it 2.second it seem like it hard but its not it what you think but when you do it more its not hard. steps facts
Transcript: Build your expression on a comparison map How to find which is greater Our equation is; 5 − (2y − 4) − 2 or −y − (1 + y) + 4 2nd Step 1st Step After you flip them all into the positive region, you then remove what each side has in common. Like if both sides have a positive x, then you remove the x from each side. 5th Step For the second step you take the zero pairs out, which are a pair of numbers that cancel each other and the sum of them equal zero. You're right!!!! It is the left side! The third step is flipping the tiles onto the positive side so they aren't the opposite of the value anymore, they are the vaule 4th Step After all of that is done now you can tell which side is greater. What side is greater?? Math Algebra 3rd Step
Transcript: Math Algebra Intro Algebra what it is Introduction Algebra is when in an equation to represent an unknown number, you use a letter. equations usually include equations between numbers and letters to add extra confusion to a regular equation. What It is examples what equations are there? examples some examples are 9+k=c another is 5(10+9v) even more 5+q=16 some examples (8k-9)+9(8+ 8l) 8(7u-9)-6(6-6u) 9(9+9u)+(9-9o) Even More how to do it How examples of how Good Bye Good Bye
Transcript: Math Have you ever heard of electromagnetic radiation? Where is it used in the real world? Do Now! Do now! SWBAT... Learning intention Learning intention Concepts: Electromagnetic radiation: electromagnetic radiation refers to the waves of the electromagnetic field, propagating through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, light, ultraviolet, X-rays, and gamma rays. Introduction to - I do A model of how to solve a problem ("I do" question) Question 1 We do What is ....? Sample question Answer Answer Problem (solve it on your own!) You do Answer Answer Click to edit text Summary Close Homework and preparation for next class Read textbook and solve problems on p.1 Homework!
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