Question

Directions: Write the symbolic form of the written expressions given below. First write them in written expression, and then with the appropriate order of operations, evaluate the expression and simplify or solve.

1. Three less than the product of thirteen squared and four.
2. The product of eight minus six and x.
3. The square root of thirty-six plus the sum of eight and four squared.
4. Nineteen less than the product of seven and four minus the quotient of sixteen and four.
5. X to the fourth power plus the product of six and the square root of nine.
6. Fifteen plus eight cubed minus the sum of fourteen and six squared.
7. The product of three and fifteen minus nine plus the quotient of fifteen and three.
8. The product of seventeen and y, plus the square root of eighty-one minus the product of six and x minus four.

Part B

Directions: Write the written form of the following expressions given in the symbolic form.

9. 4(3x + 2) – 9
10. √144 – (62 –x)

11. (28 ÷ 4) – (x + 7)

12. x3 – 4y - (6 + 2)
13. (64 ÷ 8) – (x • 6)
14. 72 (4 - 15x)

15. 4(√144 + 93)–y
16. 54 + 7y – (8 + 9x)

Part C

Directions: Write the symbolic form from each of the word problems below. Use the character’s names as the variables. No need to simplify your answers.

17. If Jamond has three more books than the sum of Mason and Adam, then how many books does he have?
18. If Nancy answered five more word problems than the quotient of Samantha and Trisha’s answers, then how many word problems did Nancy answer?
19. Jolie was trying to learn a new word every day. She started keeping track of how many new words she had learned. If she learned 6 more new words than four to the 6th power, then how many new words did Jolie learn?
20. Ricky and Sam were practicing their writing in school. If Ricky’s practice contained six fewer letters than the product of Sam’s answers and 10, how many letters did Ricky write?

Answer 1

1. Symbolic form: 13^2 * 4 - 3
Evaluation: (13^2 * 4) - 3 = 676 * 4 - 3 = 2704 - 3 = 2701

2. Symbolic form: (8 - 6) * x
Evaluation: (8 - 6) * x = 2 * x = 2x

3. Symbolic form: sqrt(36) + (8 + 4^2)
Evaluation: sqrt(36) + (8 + 4^2) = 6 + (8 + 16) = 6 + 24 = 30

4. Symbolic form: 7 * 4 - 16 / 4 - 19
Evaluation: 28 - 4 - 19 = 9

5. Symbolic form: x^4 + 6 * sqrt(9)
Evaluation: x^4 + 6 * 3 = x^4 + 18

6. Symbolic form: 15 + 8^3 - (14 + 6^2)
Evaluation: 15 + 512 - (14 + 36) = 15 + 512 - 50 = 477

7. Symbolic form: 3 * 15 - 9 + 15 / 3
Evaluation: 45 - 9 + 5 = 41

8. Symbolic form: 17y + sqrt(81) - 6x * 4 - 4
Evaluation: 17y + 9 - 24x - 4

Part B

9. Symbolic form: 4(3x + 2) - 9
Written form: Four times the quantity of three times x plus 2, minus 9.

10. Symbolic form: sqrt(144) - (62 - x)
Written form: The square root of 144 minus the quantity of 62 minus x.

11. Symbolic form: (28 / 4) - (x + 7)
Written form: Twenty-eight divided by 4, minus the quantity of x plus 7.

12. Symbolic form: x^3 - 4y - (6 + 2)
Written form: x cubed minus 4y minus the quantity of 6 plus 2.

13. Symbolic form: (64 / 8) - (x * 6)
Written form: Sixty-four divided by 8, minus the quantity of x times 6.

14. Symbolic form: 72 * (4 - 15x)
Written form: Seventy-two times the quantity of 4 minus 15x.

15. Symbolic form: 4(sqrt(144) + 93) - y
Written form: Four times the quantity of the square root of 144 plus 93, minus y.

16. Symbolic form: 54 + 7y - (8 + 9x)
Written form: Fifty-four plus 7y minus the quantity of 8 plus 9x.

Part C

17. Symbolic form: Jamond = Mason + Adam + 3

18. Symbolic form: Nancy = Samantha / Trisha + 5

19. Symbolic form: Jolie = 4^6 + 6

20. Symbolic form: Ricky = Sam * 10 - 6

Answer 2

Part A

1. Written Expression: "Three less than the product of thirteen squared and four."

Symbolic Form: 4 * (13^2) - 3

Evaluation: 4 * 169 - 3 = 676 - 3 = 673

2. Written Expression: "The product of eight minus six and x."

Symbolic Form: (8 - 6) * x

Evaluation: 2 * x = 2x

3. Written Expression: "The square root of thirty-six plus the sum of eight and four squared."

Symbolic Form: sqrt(36) + (8 + 4^2)

Evaluation: 6 + (8 + 16) = 6 + 24 = 30

4. Written Expression: "Nineteen less than the product of seven and four minus the quotient of sixteen and four."

Symbolic Form: (7 * 4 - 16 / 4) - 19

Evaluation: (28 - 4) - 19 = 24 - 19 = 5

5. Written Expression: "X to the fourth power plus the product of six and the square root of nine."

Symbolic Form: x^4 + 6 * sqrt(9)

Evaluation: x^4 + 6 * 3 = x^4 + 18

6. Written Expression: "Fifteen plus eight cubed minus the sum of fourteen and six squared."

Symbolic Form: 15 + 8^3 - (14 + 6^2)

Evaluation: 15 + 512 - (14 + 36) = 15 + 512 - 50 = 527 - 50 = 477

7. Written Expression: "The product of three and fifteen minus nine plus the quotient of fifteen and three."

Symbolic Form: 3 * 15 - 9 + 15 / 3

Evaluation: 45 - 9 + 5 = 36 + 5 = 41

8. Written Expression: "The product of seventeen and y, plus the square root of eighty-one minus the product of six and x minus four."

Symbolic Form: 17*y + sqrt(81) - (6*x - 4)

Evaluation: 17y + 9 - (6x - 4) = 17y + 9 - 6x + 4 = 17y + 13 - 6x

Part B

9. Written Expression: "Four times the sum of three times x and two, minus nine."

10. Written Expression: "The square root of one hundred forty-four minus the difference of sixty-two and x."

11. Written Expression: "The quotient of twenty-eight and four minus the sum of x and seven."

12. Written Expression: "X cubed minus four times y minus the sum of six and two."

13. Written Expression: "The quotient of sixty-four and eight minus the product of x and six."

14. Written Expression: "Seventy-two times the difference of four and fifteen times x."

15. Written Expression: "Four times the sum of the square root of one hundred forty-four and ninety-three, minus y."

16. Written Expression: "Fifty-four plus seven times y minus the sum of eight and nine times x."

Part C

17. If Jamond has three more books than the sum of Mason and Adam, then how many books does he have?

Symbolic Form: J = M + A + 3

18. If Nancy answered five more word problems than the quotient of

Samantha and Trisha’s answers, then how many word problems did Nancy answer?

Symbolic Form: N = (S / T) + 5

19. Jolie was trying to learn a new word every day. She started keeping track of how many new words she had learned. If she learned 6 more new words than four to the 6th power, then how many new words did Jolie learn?

Symbolic Form: J = 4^6 + 6

20. Ricky and Sam were practicing their writing in school. If Ricky’s practice contained six fewer letters than the product of Sam’s answers and 10, how many letters did Ricky write?

Symbolic Form: R = 10 * S - 6