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Pre-Algebra Final Review
The document provides a comprehensive overview of integers, including definitions, operations (addition, subtraction, multiplication, division), and rules for working with fractions. It includes practice problems and emphasizes the importance of sign rules and the relationships between positive and negative numbers. Key concepts such as variables, coefficients, and simplifying expressions are also explained.
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Pre-Algebra Final Review
- 1. -Step one: Cleanout your file in the back! -Look for any notes handed in! -Also, look for any vocabulary! -Grab all your old tests!
- 2. • Integer: Apositive or negative whole number including zero. • Whole Number: Any number over one. • Number Line: A line where all negative numbers are on the left, zero is in the middle, and positive numbers are on the right. • Positive Number: Any number on the right side of the number line. • Negative Number: Any number on the left side of the number line. • Increasing Order: Smallest to biggest.
- 3. • When Signsare the same, add the numbers! EX: -5 - 1 = 5 + 1 • Answer gets the sign of the larger number. 5 is the largest number it’s sign is a (-). Answer is -6.
- 4. • When Signsare the different subtract the numbers. EX: -5 + 1 = 5 - 1 • Answer gets the sign of the larger number. 5 is the largest number it’s sign is a (-). Answer is -4.
- 5. Let’s Practice 1) 5- 6 = 2) -3 + 2 = 3) 6 + 5 = 4) -8 + 7 = 5) 9 - 9 = Remember: If signs are the same add the numbers, if signs are different subtract the numbers. Then give the answer the sign of the largest number! -1 -1 +11 -1 0
- 6. Rules for Integers •When Parenthesis ( ) are involved we get to doodle! • This is where you need to draw some faces. (Bet you didn’t know you’d be doing Art in Math!)
- 7. Rules for Adding& Subtracting Integers Continued • When you multiply a (+ x -) you get a (-). • When you multiply a (- x -) you get a (+). • When you multiply a (+ x +) you get a (+). 5 + (-1) = 4 5 – (-1) = 6 5 + (+5) = 10 - + +
- 8. Let’s Practice 1) 4– (-5) = 2) 9 + (-7) = 3) 6 – (+2) = 4) 8 – (-7) = 5) 9 + (+3) = Remember: DRAW the faces first! If signs are the same add the numbers, if signs are different subtract the numbers. Then give the answer the sign of the largest number! 9 2 4 15 12 + - + - +
- 9. Let’s Practice Cont. 1)5 + (-2) = 2) 3 – (-4) = 3) 1 – (+2) = 4) 5 – (-3) = 5) 7 – (-6) = Remember: DRAW the faces first! If signs are the same add the numbers, if signs are different subtract the numbers. Then give the answer the sign of the largest number! - + + - + 3 7 -1 8 13
- 10. • Reciprocal: Flippingof a fraction. • Rational Number: All real numbers… - 3, -2, -1, 0, 1, 2, 3… • Absolute Value: Two lines on either side of a number asking how far away from zero. • Product: To multiply • Quotient: To divide
- 11. Rules for Multiplying Integers(x) • The product of two integers with the same signs is POSITIVE. • The product of two integers with different signs is NEGATIVE.
- 12. Rules Summary for Multiplication •Positive x Positive = Positive • Negative x Negative = Positive • Positive x Negative= Negative • Negative x Positive = Negative
- 13. Let’s Practice “Multiplication” 1)6 x (-3) = 2) 3 x 3 = 3) -4 x 5 = 4) -6 x (-2) = 5) -7 x (-8) = -18 9 -20 12 56 Remember: Positive x Positive = Positive Negative x Negative = Positive Positive x Negative= Negative Negative x Positive = Negative
- 14. Did you knowthat the rules for multiplication and division are the same?
- 15. Rules for Dividing Integers(÷) • The quotient of two integers with the same signs is POSITIVE. • The quotient of two integers with different signs is NEGATIVE.
- 16. Rules Summary for Division •Positive ÷ Positive = Positive • Negative ÷ Negative = Positive • Positive ÷ Negative= Negative • Negative ÷ Positive = Negative
- 17. Let’s Practice “Division” 1)18 ÷ (-2) = 2) -48 ÷ (-6) = 3) -27 ÷ 9 = 4) 64 ÷ 8 = 5) 30 ÷ (-5) = -9 +8 -3 +8 -6 Remember: Positive ÷ Positive = Positive Negative ÷ Negative = Positive Positive ÷ Negative= Negative Negative ÷ Positive = Negative
- 18. • Denominator: Bottomnumber of a fractions. • Numerator: Top number of a fraction. • Whole Number: Any number over one. • Bar: The line between two numbers creating a fraction.
- 19. 1. Count bythe bottom number. 2. Circle the match. 3. Count over to the match. 4. Multiply by the old top number. 5. Add/Subtract • Play with the top-leave the bottom alone. • Remember to borrow if you need to. 6. Divide if top number is bigger 7. Reduce if you need to. New Bottom Number New Top Number
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- 25. • Improper Fraction:When the numerator is larger than the denominator. • Proper Fraction: When a fraction has been simplified and reduced fully. • Reduce: To divide the top and bottom number of a fraction by the same number. • Simplify: To make an improper fraction proper.
- 26. Reduce if youcan: You can’t reduce side to side! Multiply straight across. Divide if top number is bigger.
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- 28. Flip the SECONDfraction = Change the sign Reduce if you can: You can’t reduce side to side! Multiply straight across. Divide if top number is bigger.
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- 30. • Inverse Operation:Addition & Subtraction or Multiplication & Division. • Fulcrum: Equal sign. • Additive Inverse Strategy: Moves opposite of the whole term to the other side. • Multiplicative Inverse Strategy: Moves part of the term to the other side.
- 31. Solve the followingequation for x: x – 4 = 9 + 4 +4 x = 13 We are able to get the x by itself by ADDING 4 to each side!
- 32. Solve the followingequation for p: p + 7 = 21 - 7 - 7 p = 14 We are able to get the p by itself by SUBTRACTING 7 from each side!
- 33. Solve the followingequation for m 3 m = 18 • Divide both sides by 3 and simplify -- your work should look like this : 3 m = 18 3 3 m = 6
- 34. Solve the followingequation for n: 2n = 3 5 7 • Multiply each side by the inverse of 2 5 : 5 • 2n = 3 • 5 2 5 7 2 n = 15 14 = 1 1 14
- 35. • Variable: Aletter or symbol that stands for an unknown number. • Terms: Parts of an algebraic expression of an equation separated by operations. • Coefficient: The number in front of a variable. • Like Terms: Terms that have the same variable. • Constant: A number not attached to a variable. • Combining Like Terms: Putting together terms that have the same variable.
- 36. Rule 1: Eachaction should get the letter (variable) closer to being alone. Rule2: Additive inverse strategy moves the opposite of the whole term to the other side. >change signs - cancel – keep or put with a like term Rule 3: Multiplicative inverse strategy moves part of a term to the other side. >if a number is next to variable – divide >if a number is below variable - multiply Rule 4: Combining like terms put terms with same ending together that are on the same side of the equal sign.
- 37. 14m + 2– 10m – 11 4m -9 22p + 6 – 32p +14 -10p + 20
- 38. 4n2 – 3n+ 6n – 5n2 -1n2 +3n 4x(x-4) + 3(-x-5) 4x2 – 16x – 3x – 15 4x2 - 19x - 15