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• order of operations
• Evaluate numerical expressions by using the order of operations.
• Evaluate algebraic expressions by using the order of operations.
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A.3 The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. (A) Use symbols to represent unknowns and variables.
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Evaluate Expressions
Evaluate 48 ÷ 23 ● 3 + 5.
48 ÷ 23 ● 3 + 5 = 48 ÷ 8 ● 3 + 5 Evaluate powers.
= 6 ● 3 + 5 Divide 48 by 8.
= 18 + 5 Multiply 6 and 3.
= 23 Add 18 and 5.
Answer: 23
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A. A
B. B
C. C
D. D
0% 0%0%0%
A. 7
B. –39
C. –33
D. 1
Evaluate the expression 3 + 62 ÷ 4 – 5.
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Grouping Symbols
A. Evaluate (8 – 3) ● 3(3 + 2).
(8 – 3) ● 3(3 + 2) = 5 ● 3(5)Evaluate inside group symbols.
= 15(5) Multiply.
= 75 Multiply.
Answer: 75
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Grouping Symbols
B. Evaluate 4[12 ÷ (6 – 2)]2.
4[12 ÷ (6 – 2)]2 = 4(12 ÷ 4)2 Evaluate innermost expression first.
= 4(3)2 Evaluate expression in grouping symbol.
= 4(9) Evaluate power.
= 36 Multiply.
Answer: 36
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Grouping Symbols
Evaluate the power in the numerator.
C.
Multiply 6 and 2 in the numerator.
Subtract 32 and 12 in the numerator.
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Grouping Symbols
Evaluate the power in the denominator.
Multiply 5 and 3 in the denominator.
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1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. –60
B. 66
C. 88
D. 68
A. Evaluate the expression 2(4 + 7) ● (9 – 5).
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1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 9
B. 18
C. 108
D. 3
B. Evaluate the expression 3[5 – 2 ● 2]2.
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Evaluate an Algebraic Expression
Evaluate 2(x2 – y) + z2 if x = 4, y = 3, and z = 2.
2(x2 – y) +z2 = 2(42 – 3) + 22 Replace x with 4, y with 3 and z with 2.
= 2(16 – 3) + 22 Evaluate 42.
= 2(13) + 22 Subtract 3 from 16.
= 2(13) + 4 Evaluate 22.
= 26 + 4 Multiply 2 and 13.
= 30 Add.
Answer: 30
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1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 6
B. 28
C. 36
D. 10
Evaluate x3 – y2 + z, if x = 3, y = 2, and z = 5.
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ARCHITECTURE Each of the four sides of the Great Pyramid at Giza, Egypt, is a triangle. The base of each triangle originally measured 230 meters. The height of each triangle originally measured 187 meters. The area of a triangle is one-half the product of the length of the base b and the height h.
A. Write an expression that represents the area of one side of the Great Pyramid.
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Words one half of the product of length of base and height
Variables b = base; h = height
Equation × b ● h
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B. Find the area of one side of the Great Pyramid.
Replace b with 230 and h with 187.
Multiply 230 by 187.
Multiply by 43,010.
Divide 43,010 by 2.
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A. A
B. B
C. C
D. D
0% 0%0%0%
A. 3813 ft2
B. 7626 ft2
C. 15,252 ft2
D. 32 ft2
Find the area of a triangle with a base of 123 feet and a height of 62 feet.