• order of operations

• Evaluate numerical expressions by using the order of operations.

• Evaluate algebraic expressions by using the order of operations.

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.

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

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.

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

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

Grouping Symbols

Evaluate the power in the numerator.

C.

Multiply 6 and 2 in the numerator.

Subtract 32 and 12 in the numerator.

Grouping Symbols

Evaluate the power in the denominator.

Multiply 5 and 3 in the denominator.

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).

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.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

C.

A. 1

B.

C. 4

D.

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

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.

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.

Words one half of the product of length of base and height

Variables b = base; h = height

Equation × b ● h

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.

Answer: The area of one side of the Great Pyramid is 21,505 m2.

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.