Chapter 2: The Language of AlgebraContent check — Prealgebra, Chapter 2: The Language of Algebra

$\text{Add:}43+69.$
If you missed this problem, review Example 1.19.

$\text{Multiply:}(896)201.$
If you missed this problem, review Example 1.48.

$\text{Divide:}\mathrm{7,263}÷9.$
If you missed this problem, review Example 1.64.

Translate from algebra to words.

ⓐ $18+11$

ⓑ $(27)(9)$

ⓒ $84÷7$

ⓓ $p-q$

Translate from algebra to words.

ⓐ $47-19$

ⓑ $72÷9$

ⓒ $m+n$

ⓓ $(13)(7)$

Translate from algebra to words.

ⓐ $14\le 27$

ⓑ $19-2\ne 8$

ⓒ $12>4÷2$

ⓓ $x-7<1$

Translate from algebra to words.

ⓐ $19\ge 15$

ⓑ $7=12-5$

ⓒ $15÷3<8$

ⓓ $y-3>6$

Use Figure 2.2 to fill in the appropriate $\text{symbol},$ $\text{=},$ $\text{<},$ $\text{or}\text{>}.$

ⓐ MPG of Prius_____MPG of Versa

ⓑ MPG of Mini Cooper_____ MPG of Corolla

Use Figure 2.2 to fill in the appropriate $\text{symbol},$ $\text{=},$ $\text{<},$ $\text{or}\text{>}.$

ⓐ MPG of Fit_____ MPG of Prius

ⓑ MPG of Corolla _____ MPG of Fit

Determine if each is an expression or an equation:

ⓐ $23+6=29$

ⓑ $7·3-7$

Determine if each is an expression or an equation:

ⓐ $y÷14$

ⓑ $x-6=21$

Write each expression in exponential form:

$41·41·41·41·41$

Write each expression in exponential form:

$7·7·7·7·7·7·7·7·7$

Write each exponential expression in expanded form:

ⓐ $4^8$

ⓑ $a^7$

Write each exponential expression in expanded form:

ⓐ $8^8$

ⓑ $b^6$

Simplify:

ⓐ $5^3$

ⓑ $1^7$

Simplify:

ⓐ $7^2$

ⓑ $0^5$

Simplify the expressions:

ⓐ $12-5·2$

ⓑ $(12-5)·2$

Simplify the expressions:

ⓐ $8+3·9$

ⓑ $(8+3)·9$

Simplify:

$42÷7·3$

Simplify:

$12·3÷4$

Simplify:

$30÷5+$ $10(3-2)$

Simplify:

$70÷10+$ $4(6-2)$

Simplify:

$9+$ $5^3-$ $[4(9+3)]$

Simplify:

$7^2-$ $2[4(5+1)]$

Simplify:

$3^2+2^4÷2+4^3$

Simplify:

$6^2-5^3÷5+8^2$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$16-9$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$5·6$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$28÷4$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$x+8$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$(2)(7)$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$14<21$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$36\ge 19$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$3n=24$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$y-1>6$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$2\le 18÷6$

Use Variables and Algebraic Symbols

In the following exercises, translate from algebraic notation to words.

$a\ne 7·4$

Identify Expressions and Equations

In the following exercises, determine if each is an expression or an equation.

$9·6=54$

Identify Expressions and Equations

In the following exercises, determine if each is an expression or an equation.

$5·4+3$

Identify Expressions and Equations

In the following exercises, determine if each is an expression or an equation.

$x+7$

Identify Expressions and Equations

In the following exercises, determine if each is an expression or an equation.

$y-5=25$

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

$3·3·3·3·3·3·3$

Simplify Expressions with Exponents

In the following exercises, write in exponential form.

$x·x·x·x·x$

In the following exercises, write in expanded form.

$5^3$

In the following exercises, write in expanded form.

$2^8$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

ⓐ $3+8·5$

ⓑ $\text{(3+8)}·5$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$2^3-12÷(9-5)$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$3·8+5·2$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$2+8(6+1)$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$4·12/8$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$6+10/2+2$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$(6+10)÷(2+2)$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$20÷4+6·5$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$20÷(4+6)·5$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$4^2+5^2$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

${(4+5)}^2$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$3(1+9·6)-4^2$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$2[1+3(10-2)]$

Is $n÷5$ an expression or an equation?
If you missed this problem, review Example 2.4.

Simplify $4^5.$
If you missed this problem, review Example 2.7.

Simplify $1+8\cdot 9.$
If you missed this problem, review Example 2.8.

Evaluate:

$y+4\text{when}$

ⓐ $y=6$

ⓑ $y=15$

Evaluate:

$a-5\text{when}$

ⓐ $a=9$

ⓑ $a=17$

Evaluate:

$8x-3,\text{when}$

ⓐ $x=2$

ⓑ $x=1$

Evaluate:

$4y-4,\text{when}$

ⓐ $y=3$

ⓑ $y=5$

Evaluate:

$x^2\text{when}x=8.$

Evaluate:

$x^3\text{when}x=6.$

Evaluate:

$2^x\text{when}x=6.$

Evaluate:

$3^x\text{when}x=4.$

Evaluate:

$2x+$ $5y-$ $4\text{when}x=$ $11\text{and}y=$ $3$

Evaluate:

$5x-$ $2y-$ $9\text{when}x=$ $7\text{and}y=$ $8$

Evaluate:

$3x^2+$ $4x+$ $1\text{when}x=$ $3.$

Evaluate:

$6x^2-$ $4x-$ $7\text{when}x=$ $2.$

Identify all terms in the given expression, and their coefficients:

$4x+3b+2$

Identify all terms in the given expression, and their coefficients:

$9a+13a^2+a^3$

Identify the like terms in the list or the expression:

$9,$ $2x^3,$ $y^2,$ $8x^3,$ $15,$ $9y,$ $11y^2$

Identify the like terms in the list or the expression:

$4x^3+$ $8x^2+$ $19+$ $3x^2+$ $24+$ $6x^3$

Simplify:

$7x+9+9x+8$

Simplify:

$5y+$ $2+$ $8y+$ $4y+$ $5$

Simplify:

$3x^2+$ $9x+$ $x^2+$ $5x$

Simplify:

$11y^2+$ $8y+$ $y^2+$ $7y$

Translate the given word phrase into an algebraic expression:

ⓐ the difference of $47$ and $41$

ⓑ the quotient of $5x$ and $2$

Translate the given word phrase into an algebraic expression:

ⓐ the sum of $17$ and $19$

ⓑ the product of $7$ and $x$

Translate each word phrase into an algebraic expression:

ⓐ Eleven more than $x$

ⓑ Fourteen less than $11a$

Translate each word phrase into an algebraic expression:

ⓐ $19$ more than $j$

ⓑ $21$ less than $2x$

Translate the word phrase into an algebraic expression:

ⓐ four times the sum of $p$ and $q$

ⓑ the sum of four times $p$ and $q$

Translate the word phrase into an algebraic expression:

ⓐ the difference of two times $x\text{and 8}$

ⓑ two times the difference of $x\text{and}8$

The length of a rectangle is $5$ inches less than the width. Let $w$ represent the width of the rectangle. Write an expression for the length of the rectangle.

The width of a rectangle is $2$ meters greater than the length. Let $l$ represent the length of the rectangle. Write an expression for the width of the rectangle.

Geoffrey has dimes and quarters in his pocket. The number of dimes is seven less than six times the number of quarters. Let $q$ represent the number of quarters. Write an expression for the number of dimes.

Lauren has dimes and nickels in her purse. The number of dimes is eight more than four times the number of nickels. Let $n$ represent the number of nickels. Write an expression for the number of dimes.

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

$7x+8\text{when}x=2$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

$5x-4\text{when}x=6$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

$x^2\text{when}x=12$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

$x^5\text{when}x=2$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

$3^x\text{when}x=3$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

$x^2+$ $3x-$ $7\text{when}x=$ $4$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

$2x+$ $4y-$ $5\text{when}x=$ $7,$ $y=$ $8$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

${(x-y)}^2\text{when}x=$ $10,$ $y=$ $7$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

${(x+y)}^2\text{when}x=$ $6,$ $y=$ $9$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

$a^2+$ $b^2\text{when}a=$ $3,$ $b=$ $8$

Evaluate Algebraic Expressions

In the following exercises, evaluate the expression for the given value.

$2l+$ $2w\text{when}l=$ $15,$ $w=$ $12$

Identify Terms, Coefficients, and Like Terms

In the following exercises, list the terms in the given expression.

$15x^2+6x+2$

Identify Terms, Coefficients, and Like Terms

In the following exercises, list the terms in the given expression.

$10y^3+y+2$

In the following exercises, identify the coefficient of the given term.

$8a$

In the following exercises, identify the coefficient of the given term.

$5r^2$

In the following exercises, identify all sets of like terms.

$x^3,$ $8x,$ $14,$ $8y,$ $5,$ $8x^3$

In the following exercises, identify all sets of like terms.

$9a,$ $a^2,$ $16ab,$ $16b^2,$ $4ab,$ $9b^2$

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

$10x+3x$

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

$17a+9a$

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

$4c+2c+c$

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

$9x+3x+8$

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

$7u+2+3u+1$

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

$7p+6+5p+4$

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

$10a+$ $7+$ $5a-$ $2+$ $7a-$ $4$

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the given expression by combining like terms.

$3x^2+$ $12x+$ $11+$ $14x^2+$ $8x+$ $5$

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

The sum of 8 and 12

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

The difference of 14 and 9

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

The product of 9 and 7

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

The quotient of 36 and 9

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

The difference of $x$ and $4$

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

The product of $6$ and $y$

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

The sum of $8x$ and $3x$

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

The quotient of $y$ and $3$

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

Eight times the difference of $y$ and nine

Translate English Phrases into Algebraic Expressions

In the following exercises, translate the given word phrase into an algebraic expression.

Five times the sum of $x$ and $y$

In the following exercises, write an algebraic expression.

Adele bought a skirt and a blouse. The skirt cost $\text{\$15}$ more than the blouse. Let $b$ represent the cost of the blouse. Write an expression for the cost of the skirt.

In the following exercises, write an algebraic expression.

The number of girls in a second-grade class is $4$ less than the number of boys. Let $b$ represent the number of boys. Write an expression for the number of girls.

In the following exercises, write an algebraic expression.

Greg has nickels and pennies in his pocket. The number of pennies is seven less than twice the number of nickels. Let $n$ represent the number of nickels. Write an expression for the number of pennies.

In the following exercises, use algebraic expressions to solve the problem.

Car insurance Justin’s car insurance has a $\text{\$750}$ deductible per incident. This means that he pays $\text{\$750}$ and his insurance company will pay all costs beyond $\text{\$750.}$ If Justin files a claim for $\text{\$2,100,}$ how much will he pay, and how much will his insurance company pay?

$\text{Evaluate}x+$ $8\text{when}x=$ $11.$
If you missed this problem, review Example 2.13.

$\text{Evaluate}5x-$ $3\text{when}x=$ $9.$
If you missed this problem, review Example 2.14.

Translate into algebra: the difference of $x$ and $8.$
If you missed this problem, review Example 2.24.

$\text{Is}x=$ $3\text{a solution of}4x-$ $7=$ $16\text{?}$

$\text{Is}x=$ $2\text{a solution of}6x-$ $2=$ $10\text{?}$

$\text{Is}y=$ $3\text{a solution of}9y-$ $2=$ $8y+$ $1\text{?}$

$\text{Is}y=$ $4\text{a solution of}5y-$ $3=$ $3y+$ $5\text{?}$

Write the equation modeled by the envelopes and counters, and then solve the equation:

Write the equation modeled by the envelopes and counters, and then solve the equation:

Solve:

$x+6=19$

Solve:

$x+9=14$

Solve:

$95=y+67$

Solve:

$91=y+45$

Solve:

$x-9=13$

Solve:

$y-1=3$

Solve:

$19=a-18$

Solve:

$27=n-14$

Translate the sentence into an algebraic equation:

The sum of $7$ and $6$ gives $13.$

Translate the sentence into an algebraic equation:

The sum of $8$ and $6$ is $14.$

Translate the sentence into an algebraic equation:

The product of $6$ and $9$ is $54.$

Translate the sentence into an algebraic equation:

The product of $21$ and $3$ gives $63.$

Translate the given sentence into an algebraic equation:

Twice the difference of $x$ and $5$ gives $30.$

Translate the given sentence into an algebraic equation:

Twice the difference of $y$ and $4$ gives $16.$

Translate and solve:

Seven more than $x$ is equal to $37.$

Translate and solve:

Eleven more than $y$ is equal to $28.$

Translate and solve:

The difference of $z$ and $17$ is equal to $37.$

Translate and solve:

The difference of $x$ and $19$ is equal to $45.$

Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each given value is a solution to the equation.

$x+13=21$

ⓐ $x=8$

ⓑ $x=34$

Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each given value is a solution to the equation.

$m-4=13$

ⓐ $m=9$

ⓑ $m=17$

Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each given value is a solution to the equation.

$3p+6=15$

ⓐ $p=3$

ⓑ $p=7$

Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each given value is a solution to the equation.

$18d-9=27$

ⓐ $d=1$

ⓑ $d=2$

Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each given value is a solution to the equation.

$8u-4=4u+40$

ⓐ $u=3$

ⓑ $u=11$

Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each given value is a solution to the equation.

$20h-$ $5=$ $15h+$ $35$

ⓐ $h=6$

ⓑ $h=8$

Model the Subtraction Property of Equality

In the following exercises, write the equation modeled by the envelopes and counters and then solve using the subtraction property of equality.

Model the Subtraction Property of Equality

In the following exercises, write the equation modeled by the envelopes and counters and then solve using the subtraction property of equality.

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

$a+2=18$

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

$p+18=23$

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

$r+76=100$

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

$16=x+9$

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

$93=p+24$

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

$465=d+398$

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

$y-3=19$

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

$u-6=24$

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

$f-55=123$

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

$19=n-13$

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

$10=p-38$

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

$268=y-199$

Translate Word Phrase to Algebraic Equations

In the following exercises, translate the given sentence into an algebraic equation.

The sum of $8$ and $9$ is equal to $17.$

Translate Word Phrase to Algebraic Equations

In the following exercises, translate the given sentence into an algebraic equation.

The difference of $23$ and $19$ is equal to $4.$

Translate Word Phrase to Algebraic Equations

In the following exercises, translate the given sentence into an algebraic equation.

The product of $3$ and $9$ is equal to $27.$

Translate Word Phrase to Algebraic Equations

In the following exercises, translate the given sentence into an algebraic equation.

The quotient of $54$ and $6$ is equal to $9.$

Translate Word Phrase to Algebraic Equations

In the following exercises, translate the given sentence into an algebraic equation.

Twice the difference of $n$ and $10$ gives $52.$

Translate Word Phrase to Algebraic Equations

In the following exercises, translate the given sentence into an algebraic equation.

The sum of three times $y$ and $10$ is $100.$

Translate to an Equation and Solve

In the following exercises, translate the given sentence into an algebraic equation and then solve it.

Five more than $p$ is equal to $21.$

Translate to an Equation and Solve

In the following exercises, translate the given sentence into an algebraic equation and then solve it.

The sum of $r$ and $18$ is $73.$

Translate to an Equation and Solve

In the following exercises, translate the given sentence into an algebraic equation and then solve it.

The difference of $d$ and $30$ is equal to $52.$

Translate to an Equation and Solve

In the following exercises, translate the given sentence into an algebraic equation and then solve it.

$12$ less than $u$ is $89.$

Translate to an Equation and Solve

In the following exercises, translate the given sentence into an algebraic equation and then solve it.

$325$ less than $c$ gives $799.$

Translate to an Equation and Solve

In the following exercises, translate the given sentence into an algebraic equation and then solve it.

Insurance Vince’s car insurance has a $\text{\$500}$ deductible. Find the amount the insurance company will pay, $p,$ for an $\text{\$1800}$ claim by solving the equation $500+p=1800.$

Translate to an Equation and Solve

In the following exercises, translate the given sentence into an algebraic equation and then solve it.

Sale purchase Arthur bought a suit that was on sale for $\text{\$120}$ off. He paid $\text{\$340}$ for the suit. Find the original price, $p,$ of the suit by solving the equation $p-120=340.$

Which of the following numbers are counting numbers (natural numbers)?
$0,4,215$
If you missed this problem, review Example 1.1.

Find the sum of $3,5,$ and $7.$
If you missed the problem, review Example 2.1.

Determine whether each number is a multiple of $2\text{:}$

ⓐ $678$

ⓑ $\mathrm{21,493}$

Determine whether each number is a multiple of $2\text{:}$

ⓐ $979$

ⓑ $\mathrm{17,780}$

Determine whether each number is a multiple of $5.$

ⓐ $675$

ⓑ $\mathrm{1,578}$

Determine whether each number is a multiple of $5.$

ⓐ $421$

ⓑ $\mathrm{2,690}$

Determine whether each number is a multiple of $10\text{:}$

ⓐ $179$

ⓑ $\mathrm{3,540}$

Determine whether each number is a multiple of $10\text{:}$

ⓐ $110$

ⓑ $\mathrm{7,595}$

Determine whether each number is a multiple of $3\text{:}$

ⓐ $954$

ⓑ $\mathrm{3,742}$

Determine whether each number is a multiple of $3\text{:}$

ⓐ $643$

ⓑ $\mathrm{8,379}$

Determine whether the given number is divisible by $2,$ $3,$ $5,$ $\text{and}10.$

$6240$

Determine whether the given number is divisible by $2,$ $3,$ $5,$ $\text{and}10.$

$7248$

Determine whether the given number is divisible $\text{by}2,$ $3,$ $5,$ $\text{and}10.$

$4962$

Determine whether the given number is divisible $\text{by}2,$ $3,$ $5,$ $\text{and}10.$

$3765$

Find all the factors of the given number:

$96$

Find all the factors of the given number:

$80$

Identify the number as prime or composite:

$91$

Identify the number as prime or composite:

$137$

Identify Multiples of Numbers

In the following exercises, list all the multiples less than $50$ for the given number.

$2$

Identify Multiples of Numbers

In the following exercises, list all the multiples less than $50$ for the given number.

$4$

Identify Multiples of Numbers

In the following exercises, list all the multiples less than $50$ for the given number.

$6$

Identify Multiples of Numbers

In the following exercises, list all the multiples less than $50$ for the given number.

$8$

Identify Multiples of Numbers

In the following exercises, list all the multiples less than $50$ for the given number.

$10$

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,$ $3,$ $4,$ $5,$ $6,$ $\text{and}10.$

$84$

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,$ $3,$ $4,$ $5,$ $6,$ $\text{and}10.$

$75$

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,$ $3,$ $4,$ $5,$ $6,$ $\text{and}10.$

$168$

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,$ $3,$ $4,$ $5,$ $6,$ $\text{and}10.$

$900$

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,$ $3,$ $4,$ $5,$ $6,$ $\text{and}10.$

$896$

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,$ $3,$ $4,$ $5,$ $6,$ $\text{and}10.$

$375$

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,$ $3,$ $4,$ $5,$ $6,$ $\text{and}10.$

$350$

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,$ $3,$ $4,$ $5,$ $6,$ $\text{and}10.$

$1430$

Use Common Divisibility Tests

In the following exercises, use the divisibility tests to determine whether each number is divisible by $2,$ $3,$ $4,$ $5,$ $6,$ $\text{and}10.$

$\mathrm{22,335}$

Find All the Factors of a Number

In the following exercises, find all the factors of the given number.

$36$

Find All the Factors of a Number

In the following exercises, find all the factors of the given number.

$60$

Find All the Factors of a Number

In the following exercises, find all the factors of the given number.

$144$

Find All the Factors of a Number

In the following exercises, find all the factors of the given number.

$588$

Identify Prime and Composite Numbers

In the following exercises, determine if the given number is prime or composite.

$43$

Identify Prime and Composite Numbers

In the following exercises, determine if the given number is prime or composite.

$39$

Identify Prime and Composite Numbers

In the following exercises, determine if the given number is prime or composite.

$71$

Identify Prime and Composite Numbers

In the following exercises, determine if the given number is prime or composite.

$481$

Identify Prime and Composite Numbers

In the following exercises, determine if the given number is prime or composite.

$209$

Identify Prime and Composite Numbers

In the following exercises, determine if the given number is prime or composite.

$667$

Identify Prime and Composite Numbers

In the following exercises, determine if the given number is prime or composite.

Banking Frank’s grandmother gave him $\text{\$100}$ at his high school graduation. Instead of spending it, Frank opened a bank account. Every week, he added $\text{\$15}$ to the account. The table shows how much money Frank had put in the account by the end of each week. Complete the table by filling in the blanks.

Weeks after graduation	Total number of dollars Frank put in the account	Simplified Total
$0$	$100$	$100$
$1$	$100+15$	$115$
$2$	$100+15\cdot 2$	$130$
$3$	$100+15\cdot 3$
$4$	$100+15\cdot \left[\right]$
$5$	$100+\left[\right]$
$6$
$20$
$x$