* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Family Letter 1 - Dwight Public Schools
Survey
Document related concepts
Unification (computer science) wikipedia , lookup
Equations of motion wikipedia , lookup
Van der Waals equation wikipedia , lookup
BKL singularity wikipedia , lookup
Euler equations (fluid dynamics) wikipedia , lookup
Calculus of variations wikipedia , lookup
Itô diffusion wikipedia , lookup
Equation of state wikipedia , lookup
Differential equation wikipedia , lookup
Derivation of the Navier–Stokes equations wikipedia , lookup
Exact solutions in general relativity wikipedia , lookup
Transcript
<< Back << || Print || CHAPTER 1 Family Letter Section A What We Are Learning Dear Family, Equations and Inequalities Your child will be learning about equations and inequalities. Initially, your child will be evaluating algebraic expressions that contain up to two variables. When given the values of the variables, your child will simply “substitute” those values for the intended variable and then simplify the expression. This skill will help your child check their answers when solving equations. Vocabulary These are the math words we are learning: Addition Property of Equality Add the same number to both sides of an equation, and the new equation will have the same solution. Algebraic Expression An expression with one or more variables. Algebraic Inequality An inequality that contains a variable. Another skill your child will be reviewing is writing algebraic expressions in place of word phrases. Listed below are examples of the four basic operations and some key phrases that may help your child write these algebraic expressions. Operation Key Word Phrases Addition Subtraction Coefficient The number multiplied by the variable. Constant A value that does not change. Division Property of Equality Divide both sides of the equation by the same number and the new equation will have the same solution. Equation A mathematical sentence that contains an equal sign. Equivalent Expression Expressions that have the same value for all the values of the variables. Evaluate To find the value of a numerical or algebraic expression. Inequality A statement comparing expressions that are not equal. Copyright © by Holt, Rinehart and Winston. All rights reserved. Expression a number plus 6 add 6 to a number the sum of 6 and a number 6 more than a number 6m a number minus 3 3 less than a number a number decreased by 3 the difference of a number and 3 m3 Multiplication 8 times a number the product of a number and 8 Division a number divided by 2 m 2 divided into a number m 2 or 2 the quotient of a number and 2 8m Your child needs to be very familiar with the four basic operations and how each operation works. This is a basic building block for solving equations, another concept your child will be learning in this section. To effectively solve equations, your child will learn the four equality properties: addition, subtraction, multiplication, and division. These properties are also known as inverse operations. Your child will use these properties to isolate the variable in order to solve an equation. An important element to equation solving is for students to always check the solution. As you help your child with his or her homework, make sure he or she does not forget this very important step. 1 Holt Pre-Algebra Holt Middle School Math << Back << CHAPTER 1 || Print || Family Letter Section A, continued Inverse Operation Operations that “undo” each other. Isolate the Variable Getting the variable alone on one side of the equal sign. Like Term Terms that have the same variable raised to the same power. Multiplication Property of Equality Multiply both sides of an equation by the same number and the statement will still be true. Simplify Perform all the operations possible, including combining like terms. Solution The value of the variable that makes the equation true. Solution of an Inequality A number that makes an inequality true. Solution Set The set of all solutions that make the statement true. Solve Find the value of the variable that makes the equation true. Subtraction Property of Equality Subtract the same number from both sides of the equation and the statement will still be true. This is how your child will use the properties of equality to solve a simple two-step equation. Solve 4x 3 15. 4x 3 15 3 3 4x 12 Subtract 3 from both sides using the Subtraction Property of Equality to isolate the x-term. 4x 12 4 4 Divide both sides by 4 using the Division Property of Equality in order to completely isolate the variable, x. x3 Check: ? 4x 3 15 ? 4(3) 3 15 Substitute 3 for x. ? 12 3 15 15 15 After equation solving, your child will transition to solving and graphing inequalities. The same steps will be followed to isolate a variable in an inequality as with an equation. The difference will be in the solution set. Your child will graph the solution to the inequality on a number line. Finally, your child will learn how to combine like terms in order to simplify an expression. Combining like terms is an important concept for your child to grasp. Your child will learn that just because he or she changes the way an expression looks, the value of the expression stays the same. For example: Combine like terms. 6x 8y 9x 6x 8y 9x 6x 9x 8y 15x 8y Identify like terms. Rearrange the expression. Add the coefficients of like terms. This review of algebraic concepts will give your child the confidence and skills needed to be successful in the chapters to follow. Sincerely, Term Elements of an expression that are separated by plus or minus signs. Variable A letter that represents a value that can change or vary. Copyright © by Holt, Rinehart and Winston. All rights reserved. 2 Holt Pre-Algebra Holt Middle School Math Answer Key || Print || 4 Click Here Name CHAPTER 1 Date Class Family Letter Equations and Inequalities Evaluate each expression for the given value(s) of the variable. 1. 8(x 7) for x 17 2. 6m 7n for m 12 and n 7 Write an algebraic expression for each word phrase. 3. a number decreased by 5 4. the product of a number and 9, less 4 Determine which value of the variable is a solution of the equation. 5. c 5 61; c 46, 56, or 66 6. d 37 12; d 39, 49, or 59 Solve. 7. 19 w 4 p 10. 7 9 8. 3x 42 9. 3n 2 11 11. 8 a 7 12. 16s 48 Use or to complete each inequality. 13. 3 5 10 14. (3)5 16 15. 6.1 1.5(4) Combine like terms. 16. 3x 6v 5x 3v 8 17. 4s 3s 2 5j 9s 7j Simplify. 18. 8(5 s) 2s 19. 2(4y 2) 7 Solve. 20. 5w 3w 16 21. 12x 7x 25 Answers: 1. 192 2. 23 3. n 5 4. 9n 4 5. c 56 6. d 49 7. w 23 8. x 14 9. n 3 10. p 63 11. a 15 12. s 3 13. 14. 15. 16. 8x 3v 8 17. 10s 12j 2 18. 40 6s 19. 8y 3 20. w 2 21. x 5 << Back << Copyright © by Holt, Rinehart and Winston. All rights reserved. 3 Holt Middle School Math Holt Pre-Algebra << Back << || Print || Name CHAPTER 1 Date Class Family Fun Hidden Math Terms Directions Find the hidden math terms from this section. The terms may be written backwards, forwards, or on a diagonal. For fun, make copies of the puzzle and give it to a friend or family member. Time how long it takes each person to find all of the terms. L K I S G H L E V C Q O K D C M P E Y Y I G N U F V V Q J Q I L M A G I T H I T X X V O S O V U X R S F I Z F U N U Q I I N E Q U A L I T Y E O V R T H B C L L Z Q R P P E T V Y V Y N L I K H S L F A B U S G V C Y A A E P D T U Y E G K Y U U Z E L T C O L D I F S W V T L Y V S Q A J O W T N U E L X B G S Q S I A A V E T S P H G A A N F U P N I S G U O R P N A Q E T T B N T S F I P M M F K L N N I Q U R E E Q M E S E I Z P R C V T X B C N H A C T X W X Z N D C L E W N B V U I E C T R W V L P A W O Q I T C N J V X A ALGEBRAIC EXPRESSION ALGEBRAIC INEQUALITY COEFFICIENT CONSTANT EQUATION EQUIVALENT EXPRESSIONS EVALUATE INEQUALITY Copyright © by Holt, Rinehart and Winston. All rights reserved. A Y I F Y Z L R H G L C F E Z R W I C R E Y O I B U J E B R Q W Y K N I I F V B T X N J O X D S A U H H D I F T O O Z E H C S B K R B S O P E W M L M S C V E G A L G E B R A I C E X P R E S S I O N L N I V R D W N O I T A U Q E U H A Y H A G S S H O Z T N V A R I A B L E C V S N E E B U A F J S F I Y C M N P H Y R J N E L B A I R A V E H T E T A L O S I B P INVERSE OPERATIONS ISOLATE THE VARIABLE LIKE TERMS SIMPLIFY SOLUTION SOLVE SUBSTITUTE VARIABLE 4 Holt Pre-Algebra Holt Middle School Math