Chapter 1

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. A number decreased by 7

Explain how the associative and commutative properties can help simplify \([(25)(97)](-4)\).

Simplify each numerical expression. $$-\frac{2}{3}\left(\frac{1}{4}\right)+\left(-\frac{1}{3}\right)\left(\frac{5}{4}\right)$$

Simplify each of the numerical expressions. $$12+5[3(7-4)]$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Five less than a number

Your friend keeps getting an answer of 64 when simplifying \(-2^{6}\). What mistake is he making, and how would you help him?

Simplify each numerical expression. $$(-6)(-9)+(-7)(4)$$

Simplify each of the numerical expressions. $$[3+2(4 \cdot 1-2)][18-(2 \cdot 4-7 \cdot 1)]$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. A number subtracted from 75

Write a sentence explaining in your own words how to evaluate the expression \((-8)^{2}\). Also write a sentence explaining how to evaluate \(-8^{2}\).

Simplify each numerical expression. $$(-7)(-7)-(-6)(4)$$

Simplify each of the numerical expressions. $$3[4(6+7)]+2[3(4-2)]$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. The product of a number and 50

For what natural numbers \(n\) does \((-1)^{n}=-1\) ? For what natural numbers \(n\) does \((-1)^{n}=1\) ? Explain your answers.

Simplify each numerical expression. $$3(5-9)-3(-6)$$

Simplify each of the numerical expressions. $$14+4\left(\frac{8-2}{12-9}\right)-2\left(\frac{9-1}{19-15}\right)$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. One-third of a number

Is the set \(\\{0,1\\}\) closed with respect to addition? Is the set \(\\{0,1\\}\) closed with respect to multiplication? Explain your answers.

Simplify each numerical expression. $$7(8-9)+(-6)(4)$$

Simplify each of the numerical expressions. $$12+2\left(\frac{12-2}{7-2}\right)-3\left(\frac{12-9}{17-14}\right)$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Four less than one-half of a number

Simplify each numerical expression. $$(6-11)(4-9)$$

Simplify each of the numerical expressions. $$[7+2 \cdot 3 \cdot 5-5] \div 8$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Seven more than three times a number

Simplify each numerical expression. $$(7-12)(-3-2)$$

Simplify each of the numerical expressions. $$[27-(4 \cdot 2+5 \cdot 2)][(5 \cdot 6-4)-20]$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. The quotient of a number and 8

Simplify each numerical expression. $$-6(-3-9-1)$$

Simplify each of the numerical expressions. $$\frac{3 \cdot 8-4 \cdot 3}{5 \cdot 7-34}+19$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. The quotient of 50 and a number

Simplify each numerical expression. $$-8(-3-4-6)$$

Simplify each of the numerical expressions. $$\frac{4 \cdot 9-3 \cdot 5-3}{18-12}$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Nine less than twice a number

Simplify each numerical expression. $$56 \div(-8)-(-6) \div(-2)$$

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Six more than one-third of a number

Simplify each numerical expression. $$-65 \div 5-(-13)(-2)+(-36) \div 12$$

Explain in your own words the difference between the reflexive property of equality and the symmetric property of equality.

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Ten times the difference of a number and 6

Simplify each numerical expression. $$-3[5-(-2)]-2(-4-9)$$

Your friend keeps getting an answer of 30 when simplifying \(7+8(2)\). What mistake is he making and how would you help him?

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Twelve times the sum of a number and 7

Simplify each numerical expression. $$-2(-7+13)+6(-3-2)$$

Do you think \(3 \sqrt{2}\) is a rational or an irrational number? Defend your answer.

Answer the question with an algebraic expression. Brian is \(n\) years old. How old will he be in 20 years?

Simplify each numerical expression. $$\frac{-6+24}{-3}+\frac{-7}{-6-1}$$

Explain why every integer is a rational number but not every rational number is an integer.

Answer the question with an algebraic expression. Crystal is \(n\) years old. How old was she 5 years ago?

Simplify each numerical expression. $$\frac{-12+20}{-4}+\frac{-7-11}{-9}$$

Answer the question with an algebraic expression. Pam is \(t\) years old, and her mother is 3 less than twice as old as Pam. What is the age of Pam's mother?

Simplify each numerical expression. $$14.1-(17.2-13.6)$$