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Pre algebra help


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Pre algebra help

  1. 1. Pre-Algebra Help From the Beginning: An over view of every lesson I’ve learned (so far)
  2. 2. The Border Problem <ul><li>Algebra-a generalization of arithmetic </li></ul><ul><li>Method 1: </li></ul><ul><li>9  4=36 </li></ul><ul><li>(10-1)  4=36 </li></ul><ul><li>(N-1)  4=b </li></ul><ul><li>N represents the number of squares on one side </li></ul><ul><li>B represents the number of squares on the border </li></ul>
  3. 3. Border Problem (cont.) <ul><li>Method 2: </li></ul><ul><li>10  4-4=36 </li></ul><ul><li>N  4-4=b </li></ul><ul><li>4N-4=b </li></ul><ul><li>Method 3: </li></ul><ul><li>10  10-8  8=36 </li></ul><ul><li>n  n-(n-2)(n-2) </li></ul><ul><li>n  n-(n-2) </li></ul>
  4. 4. Border Problem (cont) <ul><li>Method 4: </li></ul><ul><li>8  4=32+4=36 </li></ul><ul><li>4(n-2)+4=b </li></ul><ul><li>Method 5: </li></ul><ul><li>10+10+8+8=36 </li></ul><ul><li>n+n+(n-2)+(n-2)=b </li></ul><ul><li>Method 6: </li></ul><ul><li>10+9+9+8=36 </li></ul><ul><li>N+(n-1)+(n-1)+(n-2)=b </li></ul>
  5. 5. Order of Operations <ul><li>Parentheses </li></ul><ul><li>Exponents </li></ul><ul><li>Multiplication/Division </li></ul><ul><li>Addition/Subtraction </li></ul><ul><li>PEMDAS must be used within parentheses </li></ul><ul><li>If there are () within () then use PEMDAS on the inner most () first </li></ul><ul><li>If there is a fraction in the problem you must use PEMDAS to find the numerator/denominator before evaluating the fraction </li></ul>
  6. 6. Variables and Expressions <ul><li>Variable: a letter that takes the place of a number </li></ul><ul><li>Algebraic expression: an expression that contains sums and/or products of variables and numbers </li></ul><ul><li>Substitution Property of Equality: states that if two quantities are equal then one can replace the other </li></ul><ul><li>Example: if x=2 and 2x=4 the 2  2=4 if h=8 then 5h is 5  8 </li></ul>
  7. 7. Word Sort Addition Sum Plus More than In all total Subtraction Less Subtract Less than Minus difference Multiplication Times Multiplied Factors Of Product each Division Divided Quotient Separate Ratio Rate In,an,per
  8. 8. Properties <ul><li>Deductive Reasoning: using facts, properties, and rules to justify reasoning for a correct answer </li></ul><ul><li>Counter Example: an example that shows a statement (conjecture) is not true </li></ul><ul><li>The Properties Include: </li></ul><ul><li>Distributive </li></ul><ul><li>Associative </li></ul><ul><li>Communitive </li></ul><ul><li>Symmetric Property of Equality </li></ul><ul><li>Transitive Property of Equality </li></ul><ul><li>Additive Identity </li></ul><ul><li>Multiplicative Identity Property </li></ul><ul><li>Multiplicative property of Zero </li></ul>
  9. 9. Number Line and Absolute Value <ul><li>Number Line: </li></ul>0 -1 1 2 2 Negative Integers Positive Integers Opposites
  10. 10. Number Line and Absolute Value (cont) <ul><li>Integers are positive whole numbers, negative whole numbers, and zero which is neutral. </li></ul><ul><li>The arrows indicate the number line goes on forever in both directions. </li></ul><ul><li>When traveling in the number line from left to right the numbers are always getting larger . </li></ul>
  11. 11. Number Line and Absolute Value (cont) <ul><li>Absolute Value: of a number is the distance the number is away from zero on the number line. </li></ul><ul><li>Since distance can’t be negative absolute value can’t be negative. </li></ul><ul><li>l l is the symbol for absolute value </li></ul><ul><li>Example: l 4 l=4 and l -4 l= 4 </li></ul>
  12. 12. Adding and Subtracting Integers <ul><li>Use number line: </li></ul><ul><li>To add positive numbers move to the right because the sum must be larger then its addend. </li></ul><ul><li>To subtract positive numbers move to the left because we have less then we started with. </li></ul><ul><li>Examples: </li></ul><ul><li>-3+5=2 </li></ul><ul><li>10-15=-5 </li></ul><ul><li>-5+11=6 </li></ul>
  13. 13. Using Counters to Add <ul><li>-4+-3= -7 </li></ul>+ = Red=negative Yellow=positive
  14. 14. Using Counters (cont) <ul><li>3+-5=-2 </li></ul>+ = When one positive tile is paired with a negative tile the result is called a zero pair.
  15. 15. Rules for Adding Integers <ul><li>Adding Integers with the same sign: </li></ul><ul><li>Find the absolute value of each number </li></ul><ul><li>Add then together </li></ul><ul><li>Keep the sign </li></ul><ul><li>Adding Integers with different signs: </li></ul><ul><li>Find the absolute value of each number </li></ul><ul><li>Subtract them </li></ul><ul><li>Keep the sign of the number with the karger absolute value </li></ul>
  16. 16. Additive Inverse Property <ul><li>Adding a number and its opposite is equal to zero. </li></ul><ul><li>-254+254=0 </li></ul><ul><li>-1.5+1.5=0 </li></ul><ul><li>-1,375+1,375=0 </li></ul><ul><li>a+(-a)=0 </li></ul>
  17. 17. Using Counters to Subtract <ul><li>Example: </li></ul><ul><li>6-3=6+(-3)=3 </li></ul>+ + These both are equal to positive 3.
  18. 18. Distributive Property <ul><li>Calculate the area of the entire rectangle. </li></ul>7 + 3 4 Area as Product 4(7+3) 4  10=40 7 4 3 4 Area as Sum 7  4=28 3  4=12 28+12=40