1.1 Variables and Expressions How can a verbal expression be translated to an algebraic expression? Recall: Variable: Algebraic Expression: Examples of Algebraic Expressions: Different ways to show multiplication: Product Factors Powers Power: Base: Exponent: Symbols Words Meaning 3 1 3 to the first power 3 2 3 to the second power 3 3 3∙3∙3 3 4 3∙3∙3∙3 2 6 x to the nth power Evaluate: Examples: 1. Evaluate 2 6 2. Evaluate 4 3
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1.1 Variables and Expressions How can a verbal … Variables and Expressions How can a verbal expression be translated to an algebraic expression? Recall: Variable: Algebraic Expression:
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1.1 Variables and Expressions
How can a verbal expression be translated to an algebraic
expression? Recall:
Variable:
Algebraic Expression:
Examples of Algebraic Expressions:
Different ways to show multiplication:
Product Factors
Powers
Power:
Base:
Exponent:
Symbols Words Meaning 31 3 to the first power 32 3 to the second power 33 3 ∙ 3 ∙ 3
34 3 ∙ 3 ∙ 3 ∙ 3
2𝑏6 𝑥𝑛 x to the nth power
Evaluate:
Examples:
1. Evaluate 26
2. Evaluate 43
You Try:
3. Evaluate 35
4. Evaluate 24
Translating Expressions:
You will often need to translate between verbal expressions and algebraic expressions. What is
the difference between a verbal expression and an algebraic expression?
Writing Algebraic Expressions
**The phrase that always gives the most problems is “less than”
Which expression means three less than seven?
7 – 3 or 3 - 7
This often gets confused with three less seven, which means…
Examples:
Write an algebraic expression for each verbal expression.
1. Eight more than a number
2. 7 less the product of 4 and a number x
3. One third of the original area a
4. The product of 7 and m to the fifth power
You Try:
Write an algebraic expression for each verbal expression.
5. 5 less than a number
6. 9 plus the product of 2 and the number d
7. Two thirds of the original volume V
8. The product of 3 and a to the seventh power
Writing Verbal Expressions
**There are many ways to write verbal expressions that all mean the same thing
Examples:
Write a verbal expression for each algebraic expression.
1. 4𝑚3
2. 𝑐2 + 21𝑑
3. 𝑥4 −𝑦
9
You Try:
Write a verbal expression for each algebraic expression.
4. 7𝑥3 + 1
5. 𝑦5 − 16𝑦
6. 8𝑥2
5
Practice Problems Evaluate each expression
1. 92 2. 44 3. 82 4. 106 5. 35 6. 153
Write an algebraic expression for each verbal expression.
7. The sum of a number and 14
8. 6 less than a number t
9. 24 less than 3 times a number
10. 1 minus the quotient of r and 7
11. Two-fifths of a number j squared
12. n cubed increased by 5
13. X more than 7
14. A number less 35
15. One-third of a number
16. F divided by 10
17. The quotient of 45 and r
18. 49 increased by twice a number
19. 18 decreased by 3 times d
20. K squared minus 11
21. 20 divided by t to the fifth power
22. The area of a circle is the number 𝜋 times the square of the radius. Write an
expression that represents the area of a circle with radius r.
Write a verbal expression for each algebraic expression.
23. 1
8𝑦
24. 𝑤 − 24
25. 3𝑥2
26. 𝑟4
9
27. 2𝑎 + 6
28. 𝑛3 ∙ 𝑝5
29. 1
2𝑛3
30. 𝑎2 − 18𝑏
31. 17 − 4𝑚5
32. 12𝑧2
5
1.2 Order of Operations
How do you evaluate numerical and algebraic expressions using the
Order of Operations? Order of Operations
Step 1:
Step 2:
Step 3:
Step 4:
Evaluate Numerical Expressions
Evaluate each expression using the order of operations.
Examples:
1. 15 ÷ 3 ∙ 6 − 42
2. 8 − 6 ∙ 4 ÷ 3
You Try:
3. 32 + 72 − 5 ∙ 2
4. 48 ÷ 23 ∙ 3 + 5
Evaluate Numerical Expressions with Grouping Symbols
Examples of Grouping Symbols:
Examples:
Evaluate each expression.
1. 2(5) + 3(4 + 3)
2. 2[5 + (30 ÷ 6)2]
3. 6+4
32∙4
4. (8 − 3) ∙ 3(3 + 2)
You Try:
Evaluate each expression.
5. (15 − 9) + 3 ∙ 6
6. 45 + [(1 + 1)3 ÷ 4]
7. 62−8
4(3+7)
8. 4[12 ÷ (6 − 2)]2
9. 25−6∙2
33−5∙3−2
Evaluate Algebraic Expressions
To evaluate an algebraic expression, replace the variables with their values. Then use the order