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6th Grade Math Final Study Guide – Part 2: Expressions Define the following terms. Base: The number that gets multiplied by an exponent. Exponent: The number that tells us how many times to multiply the base. Powers: Numbers expressed using exponents. Numerical expression: A combination of numbers and operations. Orders of operation: Standard method for solving expressions. Variable: A symbol or letter that represents an unknown value. Equivalent expression: Two expression that are equal. Answer the following questions. What does the distributive property allow us to do? Write a mathematical expression as an example. Multiply a number across a sum of two numbers, i. e. a x (b + c) = a x b + a x c What does the commutative property allow us to do? Write a mathematical expression as an example. Change the order that numbers are multiplied or added, i. e. a + b = b + a What does the associative property allow us to do? Write a mathematical expression as an example. Change the grouping of numbers that are multiplied or added, i. e. (a + b) + c = a + (b + c). What does the identity property allow us to do? Write a mathematical expression as an example. Add a number to 0 or multiply a number by 1 to get the same number, i. e. a + 0 = a and a x 1 = a. What are the four levels of the order of operations? L1 – Parenthesis; L2 – Exponents; L3 – Multiply/Divide (L to R); L4 – Add/Subtract (L to R) What is an inverse operation? For each math operation, give its inverse operation. An operation that undoes or reverses an operation. Addition: Subtract Subtraction: Add Multiplication: Divide Division: Multiply Calculate the following expressions. 1. 43 + 15 = 64 + 15 = 79 2. (2 + 4) ∗ 15 = 6 × 15 = 90 3. 4 − 2 + 6 − 5 + 35 = 2 + 6 − 5 + 35 = 8 − 5 + 35 = 3 + 35 = 38 4. 5 ∗ 3 ∗ 2 ÷ 2 ∗ 34 = 15 ∗ 2 ÷ 2 ∗ 34 = 30 ÷ 2 ∗ 34 = 15 ∗ 34 = 510 5. 3 + 4 ∗ 5 + 6 − 6 ÷ 3 = 3 + 20 + 6 − 2 = 23 + 6 − 2 = 29 − 2 = 27 6. (1 + 2)2 + 5 ∗ 2 = 32 + 5 ∗ 2 = 9 + 10 = 19 7. 1000 − (2 + 4) ∗ 152 = 1000 − 6 ∗ 152 = 1000 − 6 ∗ 225 = 1000 − 1350 = −350 8. 18 ÷ (1 + 2)2 + 5 ∗ 2 − 20 = 18 ÷ 32 + 5 ∗ 2 − 20 = 18 ÷ 9 + 5 ∗ 2 − 20 = 2 + 10 − 20 = 12 − 20 = −8 Solve the following equations. 1. 𝑥 − 25 = 350 Add 25 to both sides. X = 375 2. 𝑥 + 25 = 75 Subtract 25 from both sides. X = 50 3. 34𝑥 = 3400 Divide both sides by 34. X = 100 4. 𝑥 ÷ 17 = 289 Multiply both sides by 17. X = 4913 5. 𝑥 − 4 = 24 Add 4 to both sides. X = 28 6. 𝑥 − 35.1 = 18.35 Add 35.1 to both sides. X = 53.45 7. 𝑥 + 3.6 = 25.3 Subtract 3.6 from both sides. X = 21.7 1 3 8. 𝑥 − 2 4 = 5 5 3 2 9. 𝑥 ÷ 5 = 7 3 3 3 Add 2 ¼ to both sides. X = 7 17/20 Multiply both sides by 3/5. X = 4 3/5 10. 7 𝑥 = 7 Divide both sides by 3/7. X = 1 11. 3.5𝑥 = 25.7 Divide both sides by 3.5. x = 7.34286 12. 𝑥 8 13. 𝑥 3.5 =7 = 7.3 14. 𝑥 + 19 = 81 Multiply both sides by 8. X = 56 Multiply both sides by 3.5. x = 25.55 Subtract 19 from both sides. X = 62 15. 𝑥 + 95 = 1,356 16. 𝑥 13 = 350 Subtract 95 from both sides. X = 1261 Multiply both sides by 13. X = 4550 17. Luis bought 6 new tennis balls. If he now has a total of 18 tennis balls, how many did he start with? x + 6 = 18 Subtract 6 from both sides. X = 12