Download 6th Grade Math Final Study Guide – Part 2: Expressions Define the

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