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Chapter 1 Study Guide

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Chapter 1 Study Guide

1. 1. <ul>Order Of Operations </ul>PEMDAS: P lease E xcuse M y D ear A unt S ally #1 Step 4: Add or Subtract in order by reading the problem from left to right. Step 1: Parenthesis first Step 2: Exponents or powers second Step 3: Multiply or Divide in order by reading the problem from left to right. _ _ _ _ _ _
2. 2. The rules for order of operations exist so that everyone can perform the same consistent operations and achieve the same results. <ul>Order Of Operations Example </ul>Follow all the rules for order of operations. Remember PEMDAS #2
3. 3. #3 Parenthesis 1 st Exponents 2 nd Mult. / Div. left to right Add / Subt. left to right P E MD AS <ul>PEMDAS </ul>
4. 4. An expression is NOT an equation because it does not have an equal sign. There are 2 types of expressions. NUMERICAL EXPRESSION : Contains only numbers and symbols. Example: 5 3 + 4 ALGEBRAIC EXPRESSION : Contains numbers, symbols, and variables. Also known as a variable expression. Example: m + 8 A VARIABLE is a letter or symbol that represents a number. Example: x TYPES OF E X P R E S S I O N S #4
5. 5. #5 Substitute & Evaluate when x = 2 and y = 4 Evaluate Show the substitution Show your work down Circle your answer Show your work down, one step at a time, no equal signs!
6. 6. add plus sum increased by total more than added to subtract minus difference decreased by diminished by less than subtracted from less multiply times product … of... divide quotient Key Words #6 twice
7. 7. WORD PHRASES A word phrase is a sentence that can be translated into a variable expression or equation. A word phrase is like a verbal phrase. It is made up of only words. Example: The difference of 8 and a number. Algebraic Expression: 8 - n #7
8. 8. Write an Algebraic Expression for the Word Phrases. 5.8 more than 4 times a 5.8 + 4a or 4a + 5.8 The difference of 3a and 2 3a - 2 6 less than the number 58t 58t - 6 <ul>Writing Algebraic Expressions </ul># 8
9. 9. Integers Integers - are the set of numbers including positive whole numbers, negative whole numbers and zero. Negative Numbers Positive Numbers * Negative integers are less than zero *Positive integers are greater than zero * The integer zero is neither positive or negative #9 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
10. 10. Opposites Pairs of integers that are the same distance from zero on a number line are opposites . Example: 3 and -3 are opposites because each integer is 3 units away from zero Other Examples: 2 and –2 5 and -5 #10
11. 11. Absolute Value Absolute value of an integer is the distance the number is from zero on a number line. Examples: |-2| = 2 |1| = 1 The absolute value of -5 is 5 spaces from zero . #11 Two vertical bars around the number means find the absolute value . 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
12. 12. Steps To Add Integers 1) Put in the 1 st number of + or – 2) Add the 2 nd number of + or – 3) Balance out what you have 5) The leftovers are the final answer Virtual Manipulative: Color Chips - Addition #12 4) One + balances out one – When a + and – cancel each other out it is called a NEUTRAL FIELD or ZERO BANK
13. 13. Integer Addition Rules If the signs are the same Add the numbers. The sign stays the same. 4 + 3 = -4 + -3 = + + + + + + + 7 _ _ _ _ _ _ _ -7 If the signs are different Subtract the numbers. The “larger number” determines the sign of the answer. -9 + 5 = 9 - 5 = 4 Subtract the numbers - 4 #13 _ _ _ _ _ + + + + + _ _ _ _ Answer -4 because you started with more negatives
14. 14. 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Ground Floor -5 + 2 = -3 -5 + 2 Positive = Up Negative = Down Add Integers With a Number Line #14
15. 15. <ul>A Model to Subtract Integers </ul>1) Put in the 1 st number of + or – 2) Subtract , or remove, the 2 nd number of + or – Show that you remove them by circling them & attaching an arrow to them. 3) IF YOU CANNOT REMOVE THE 2 nd NUMBER ADD ENOUGH ZERO PAIRS SO YOU CAN. 4) Count your remaining tiles. (one + balances out one - ) 5) Record your answer (the leftovers) #15
16. 16. <ul>Subtract Integers Example 1 </ul>3 - 2 1) Put in 3 2) Take away 2 3) You are left with 1 = 1 3 - -2 1) Put in 3 2) You can’t take away –2 so add 2 zeros 3) Take away -2 4) You are left with + 5 = 5 + + + + + - - + + + #16
17. 17. <ul>Subtract Integers Example 2 </ul>-3 - -2 1) Put in -3 2) Take away -2 3) You are left with -1 = -1 -3 - 2 1) Put in -3 2) You can’t take away 2 so add 2 zeros 3) Take away +2 4) You are left with -5 = -5 http://www.matti.usu.edu/nlvm/nav/frames_asid_162_g_2_t_1.html _ _ _ _ _ + + _ _ _ #17
18. 18.  Subtracting Integer Rules Keep the first number and add the opposite . 5 – 6 5 – 6 Is the same as = -1 4 – ( – 2 ) Is the same as 4 – ( – 2 ) = 6 -3 – 1 Is the same as -3 – ( 1 ) = -4 #18 * SUBTRACT = PLUS CHANGE!
19. 19. 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 Integer Elevator Ground Floor -4 - 2 = -6 -4 - 2 1)Start at 0. Move to the 1 st number. 2) Then look at the 2 nd number. 3) Subtract a Positive = Down 4) Subtract a Negative=Up Subtract Integers With a Number Line #19
20. 20. To Remember Multiply & Divide Integers #20 When good things, happen to good people, that’s good! + • + = + When bad things, happen to bad people, that’s good! – • – = + When good things, happen to bad people, that’s bad! + • – = – When bad things, happen to good people, that’s bad! – • + = – +  + = + –  – = + +  – = – –  + = –
21. 21. RULES FOR DIVIDING INTEGERS When determining the sign, the rules of multiplying integers are the same for dividing integers. If the signs are the same , the answer is positive . - 64  - 8 = 8 If the signs are different , the answer is negative . - 8  4 = -2 #21
22. 22. 0 8 = 8 0 = 0 undefined 22 Dividing with Zero A calculator might display “ ERROR ” when you divide by 0. No ZERO in the denominator!
23. 23. Equations An equation is a mathematical statement that shows 2 quantities are equal . An equation contains an equal sign. #23 12 – 3 = 9 Numerical 3a = 30 Algebraic To solve any equation use inverse operations . Your goal is to get the variable all by itself.
24. 24. To solve an addition equation m + 8 = 12 Get the variable alone. – 8 –8 Subtract 8 from both sides. m = 4 +8 and -8 cancel each other out. 4 + 8 = 12 Show your check. Subtract the same number from both sides #24 12 = 12 Finish your check!
25. 25. To solve a subtraction equation a – 15 = 22 Get the variable alone. +15 +15 Add 15 to both sides . a = 37 +15 and -15 cancel out 37 - 15 = 22 Show your check! Add the same number to both sides #25 22 = 22 Finish your check!
26. 26. To Solve a Multiplication Equation 5x = 40 Get the variable alone. 5 5 Divide 5 into both sides. x = 8 5 divided by 5 cancels out to 1. 5 8 = 40 Show your check! Divide the same number into both sides #26 40 = 40 Finish your check!
27. 27. To Solve a Division Equation = 20 Get the variable alone. 2 = 2 20 Multiply both sides by 2. x = 40 2 divided by 2 cancels out to 1. Show your check! x 2 x 2 Multiply the same number to both sides #27 20 = 20 Finish your check!