Grocery shopping Hot dogs are sold in packages of ten, but hot dog buns come in packs of eight. What is the smallest number of hot dogs and buns that can be purchased if you want to have the same number of hot dogs and buns? (Hint: it is the LCM!)

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2.5 Exercise 75

Translate from algebra to English.

$3 \cdot 8$

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2.5 Exercise 77

Translate from algebra to English.

$24 \div 6$

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2.5 Exercise 79

Translate from algebra to English.

$50 \geq 47$

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2.5 Exercise 81

Translate from algebra to English.

$n + 4 = 13$

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2.5 Exercise 83

Determine if each is an expression or equation.

$5 + u = 84$

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2.5 Exercise 85

Determine if each is an expression or equation.

$4 y - 11$

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2.5 Exercise 87

Write in exponential form.

$2 \cdot 2 \cdot 2$

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2.5 Exercise 89

Write in exponential form.

$x \cdot x \cdot x \cdot x \cdot x \cdot x$

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2.5 Exercise 91

Write in expanded form.

$8^{4}$

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2.5 Exercise 93

Write in expanded form.

$y^{5}$

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2.5 Exercise 95

Simplify each expression.

$3^{4}$

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2.5 Exercise 97

Simplify each expression.

$2^{7}$

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2.5 Exercise 99

Simplify.

$10 + 2 \cdot 5$

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2.5 Exercise 101

Simplify.

$\left(30 + 6\right) \div 2$

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2.5 Exercise 103

Simplify.

$7^{2} + 5^{2}$

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2.5 Exercise 105

Simplify.

$4 + 3 \left(10 - 1\right)$

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2.5 Exercise 107

Evaluate the following expressions.

$9 x - 5 \text{when} x = 7$

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2.5 Exercise 109

Evaluate the following expressions.

$3 a - 4 b \text{when} a = 10 , b = 1$

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2.5 Exercise 111

Identify the terms in each expression.

$12 n^{2} + 3 n + 1$

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2.5 Exercise 113

Identify the coefficient of each term.

$6 y$

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2.5 Exercise 115

Identify the like terms.

$5 x^{2} , 3 , 5 y^{2} , 3 x , x , 4$

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2.5 Exercise 117

Simplify the following expressions by combining like terms.

$15 a + 9 a$

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2.5 Exercise 119

Simplify the following expressions by combining like terms.

$4 x + 7 x + 3 x$

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2.5 Exercise 121

Simplify the following expressions by combining like terms.

$8 n + 2 + 4 n + 9$

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2.5 Exercise 123

Simplify the following expressions by combining like terms.

$7 y^{2} + 2 y + 11 + 3 y^{2} - 8$

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2.5 Exercise 125

Translate the following phrases into algebraic expressions.

the difference of $x$ and $6$

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2.5 Exercise 127

Translate the following phrases into algebraic expressions.

the product of $3 n$ and $9$

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2.5 Exercise 129

Translate the following phrases into algebraic expressions.

$5$ times the sum of $y$ and $1$

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2.5 Exercise 131

Translate the following phrases into algebraic expressions.

Jack bought a sandwich and a coffee. The cost of the sandwich was $\$\text{3}$ more than the cost of the coffee. Call the cost of the coffee $c .$ Write an expression for the cost of the sandwich.

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2.5 Exercise 133

Determine whether each number is a solution to the equation.

$y + 16 = 40$

ⓐ $24$
ⓑ $56$

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2.5 Exercise 135

Determine whether each number is a solution to the equation.

$4 n + 12 = 36$

ⓐ $6$
ⓑ $12$

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2.5 Exercise 137

Determine whether each number is a solution to the equation.

$15 x - 5 = 10 x + 45$

ⓐ $2$
ⓑ $10$

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2.5 Exercise 141

Solve each equation using the subtraction property of equality.

$c + 8 = 14$

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2.5 Exercise 143

Solve each equation using the subtraction property of equality.

$23 = x + 12$

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2.5 Exercise 145

Solve each equation using the addition property of equality.

$y - 7 = 16$

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2.5 Exercise 147

Solve each equation using the addition property of equality.

$19 = p - 15$

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2.5 Exercise 149

Translate each English sentence into an algebraic equation.

The sum of $7$ and $33$ is equal to $40 .$

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2.5 Exercise 151

Translate each English sentence into an algebraic equation.

The product of $4$ and $8$ is equal to $32 .$

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2.5 Exercise 153

Translate each English sentence into an algebraic equation.

Twice the difference of $n$ and $3$ gives $76 .$

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2.5 Exercise 155

Translate each English sentence into an algebraic equation and then solve it.

Eight more than $x$ is equal to $35 .$

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2.5 Exercise 157

Translate each English sentence into an algebraic equation and then solve it.

The difference of $q$ and $18$ is $57 .$

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2.5 Exercise 159

Solve each equation.

$h - 15 = 27$

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2.5 Exercise 161

Solve each equation.

$z + 52 = 85$

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2.5 Exercise 163

Solve each equation.

$27 = q + 19$

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2.5 Exercise 165

Solve each equation.

$31 = v - 25$

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2.5 Exercise 167

List all the multiples less than $50$ for each of the following.

$3$

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2.5 Exercise 169

List all the multiples less than $50$ for each of the following.

$8$

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2.5 Exercise 171

Using the divisibility tests, determine whether each number is divisible by $2 , \text{by} 3 , \text{by} 5 , \text{by} 6 , \text{and by} 10 .$

$96$

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2.5 Exercise 173

Using the divisibility tests, determine whether each number is divisible by $2 , \text{by} 3 , \text{by} 5 , \text{by} 6 , \text{and by} 10 .$

$420$

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2.5 Exercise 175

Find all the factors of each number.

$30$

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2.5 Exercise 177

Find all the factors of each number.

$180$

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2.5 Exercise 179

Identify each number as prime or composite.

$19$

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2.5 Exercise 181

Identify each number as prime or composite.

$121$

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2.5 Exercise 183

Find the prime factorization of each number.

$84$

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2.5 Exercise 185

Find the prime factorization of each number.

$350$

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2.5 Exercise 187

Find the least common multiple of each pair of numbers.

$9 , 15$

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2.5 Exercise 189

Find the least common multiple of each pair of numbers.

$25 , 35$

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2.5 Exercise 191

Describe how you have used two topics from The Language of Algebra chapter in your life outside of your math class during the past month.

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2.5 Exercise 193

Translate from an algebraic equation to English phrases.

$15 - x$

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2.5 Exercise 195

Identify each as an expression or equation.

$x + 6 = 9$

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2.5 Exercise 197

Identify each as an expression or equation.

ⓐ Write $n \cdot n \cdot n \cdot n \cdot n \cdot n$ in exponential form.
ⓑ Write $3^{5}$ in expanded form and then simplify.

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2.5 Exercise 199

Simplify, using the order of operations.

$\left(8 + 1\right) \cdot 4$

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2.5 Exercise 201

Simplify, using the order of operations.

$\left(8 + 4\right) \div 3 + 1$

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2.5 Exercise 203

Simplify, using the order of operations.

$5 \left[2 + 7 \left(9 - 8\right)\right]$

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2.5 Exercise 205

Evaluate each expression.

$y^{3} \text{when} y = 5$

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2.5 Exercise 207

Evaluate each expression.

$h w \text{when} h = 12 , w = 3$

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2.5 Exercise 209

Translate each phrase into an algebraic expression.

$5$ more than $x$

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2.5 Exercise 211

Translate each phrase into an algebraic expression.

three times the difference of $a \text{and} b$

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2.5 Exercise 213

Solve each equation.

$n - 6 = 25$

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2.5 Exercise 215

Translate each English sentence into an algebraic equation and then solve it.

$15$ less than $y$ is $32 .$

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2.5 Exercise 217

Translate each English sentence into an algebraic equation and then solve it.

List all the multiples of $4$ that are less than $50 .$

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2.5 Exercise 219

Translate each English sentence into an algebraic equation and then solve it.

Find the prime factorization of $1080 .$

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