Name _________________________ SLHS Summer Assignment for Algebra 1 (No Calculator) Use the instructional links to help you solve each problem. We encourage you to complete this assignment prior to the first day of class- it will help prepare you to be successful in Algebra 1! Topic 1 – Number Sense (Adding, Subtracting, Multiplying, and Dividing Integers) A. Adding and Subtracting https://www.khanacademy.org/math/arithmetic/addition-subtraction/basic_addition/v/basic-addition https://www.khanacademy.org/math/arithmetic/addition-subtraction/basic_addition/v/basic-subtraction https://www.khanacademy.org/math/arithmetic/addition-subtraction/two_dig_add_sub/v/subtraction-2 When adding or subtracting numbers, think of a number line! When adding, move to the right, and when subtracting, move to the left. 1. −15 + 4 = 2. 10 − 5 = 3. 4 − 8 = 4. −7 − 3 = 5. 1 − 0 = 6. −10 + 13 = 7. −11 + (−2) = 8. −2 − (−4) = 9. 3 + (−5) = B. Multiplying and Dividing https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-concept/v/multiplication-intro https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-concept/v/more-on-the-concept-of-multiplication https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-concept/v/the-idea-of-division Remember: (−) ∙ (−) = + (+) ∙ (+) = + (−) ∙ (+) = − (+) ∙ (−) = − Example: Example: Example: Example: −5 ∙ −2 = 10 3∙2=6 −4 ∙ 1 = −4 7 ∙ −1 = −7 When multiplying or dividing, it’s extremely important to know the multiplication table up to 12! Bottom line: memorize it! It will make your life easier 56 = 10. −12 ∙ 3 = 11. 72 ÷ 9 = 12. 13. 3 ∙ 11 = 14. −7 ∙ −4 = 15. 12 ÷ 6 = −8 Topic 2 – Fractions (Adding, Subtracting, Multiplying, Dividing) A. Adding and Subtracting https://www.khanacademy.org/math/arithmetic/fractions/Adding_and_subtracting_fractions/v/adding-fractions-with-likedenominators https://www.khanacademy.org/math/arithmetic/fractions/Adding_and_subtracting_fractions/v/subtracting--fractions https://www.khanacademy.org/math/arithmetic/fractions/fractions-unlike-denom/v/adding-and-subtracting-fractions When adding or subtracting fractions, they must have common denominators! 16. 4 + = 19. 4 + = 3 7 1 17. 1 − = 8 20. 5 − = 23. 5 + = 3 22. 4 + 7 9 2 = 2 2 2 3 18. 1 21. 1 24. 2 4 4 3 + 3 + = 10 10 4 3 5 10 6 2 6 − = 5 = B. Multiplying and Dividing https://www.khanacademy.org/math/arithmetic/fractions/multiplying_fractions/v/multiplying-a-fraction-by-a-fraction https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/v/conceptual-understanding-of-dividing-fractions-byfractions When multiplying fractions, multiply straight across. Always reduce fractions in the final answer. Example: 1 3 ∙ = 2 5 1∙3 2∙5 = 3 10 When dividing fractions, keep the first fraction the same, change the sign to multiplication, and take the reciprocal of the second. Then multiply. In other words: keep, change, flip! 2 Example: 3 𝟏𝟏 2 𝟒𝟒 ÷ = ∙ = 𝟒𝟒 3 𝟏𝟏 8 3 25. 2 3 28. 10 6 29. 31. 2 32. ∙ = 5 1 3 5 ∙ = 2 3 ÷ = 1 26. 1 7 ∙ = 5 4 4 3 − ∙ = 9 7 2 5 ÷ 4 −10 = 27. 12 −2 30. 2 33. 2 9 ∙ 3 = 2 ÷ = 4 3 − ÷ 2 10 7 = Topic 3 – Order of Operations https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/v/introduction-to-order-of-operations Remember the acronym PEMDAS when simplifying expressions or solving equations because it tells the order in which to simplify. P (Parentheses) E (Exponents) M D (Multiplication/Division-whichever comes first) A S (Adding/Subtraction—whichever comes first) Simplify. 34. 3(2 + 4) 35. 9 − 32 ÷ 4 36. 40 ÷ 4 − (5 − 3) 37. (5 + 16) ÷ 7 − 2 38. 4 − 32 − 1 39. 4 + (−3)2 − 1 Topic 4 – Solving Equations http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/adding-and-subtracting-thesame-thing-from-both-sides When solving equations, you need to isolate the variable by performing the inverse operation. The nice thing about solving equations is you can always check your answer by evaluating the equation with your answer. Example 1: 𝑥𝑥 + 7 = 4 −7 −7 𝑥𝑥 = −3 Example 2: 7𝑥𝑥 = 14 ÷7 Example 3: 𝑥𝑥 6 ÷7 𝑥𝑥 = 2 𝑥𝑥 =4 6∙6 = 4∙6 𝑥𝑥 = 24 Inverse operation of addition is subtraction Subtract 7 from both sides You solved for 𝑥𝑥! Inverse operation of multiplication is division Divide both sides by 7 You solved for 𝑥𝑥! Inverse operation of division is multiplication Multiply both sides by 6 You solved for 𝑥𝑥! Solve for the indicated variable. 40. 𝑥𝑥 + 6 = 10 43. 𝑥𝑥 5 =3 46. 32 = −4𝑥𝑥 41. −4 + 𝑘𝑘 = 9 42. 10𝑡𝑡 = 60 44. 𝑦𝑦 − 18 = 2 45. −12 = 4𝑝𝑝 47. 𝑤𝑤 + 17 = 27 48. 𝑥𝑥 −7 = 11