Integer Expressions and Equations Quiz

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Questions and Answers

The temperature on Sunday is 35 °F. On Monday, the temperature is 20°F warmer. Write an expression for the temperature on Monday.

35 + 20

A balloon ride is flying 70 meters high from the ground. It drops 10 meters. Write an expression for the balloon's new height.

70 - 10

Simplify the expression -2+(-8)

-10

Rose has 5 candies. Daisy has 5 more candies than Rose. How many candies does Daisy have?

<p>10</p> Signup and view all the answers

Simplify the expression (3 - 2)²

<p>1</p> Signup and view all the answers

Simplify the expression 7(4 + 5)

<p>63</p> Signup and view all the answers

Simplify the expression 8+12 / 5

<p>10.4</p> Signup and view all the answers

Simplify the expression (7-9)4+5

<p>-7</p> Signup and view all the answers

Simplify the expression 7+24-9

<p>22</p> Signup and view all the answers

For the expression 4-5/2, describe this expression using math vocabulary and use at least five words.

<p>The expression is a difference, involving the subtraction of 5 divided by 2 from 4. The expression also has a quotient, which is a result of dividing 5 by 2.</p> Signup and view all the answers

Describe the expression -4-3(7-9)²/12 using math vocabulary and use at least six words.

<p>The expression is a difference, involving the subtraction of a product from a negative integer. The product consists of a base of 3 and an exponent of 2. The base is multiplied by the difference between 7 and 9. The entire expression is a quotient with a power in the denominator.</p> Signup and view all the answers

Write an expression that is a sum of three terms. The first term is a positive integer, the second term is a group, and the third term is a power with an exponent of 3.

<p>2 + (3 + 4) - 5³</p> Signup and view all the answers

Write an expression that is a quotient with a product in the numerator. The first factor is a negative integer and the second factor is a group. The denominator is a power.

<p>-4(2+3)/5²</p> Signup and view all the answers

Plot and label Point A (4, -3) and Point B (-3.5, -5) on the coordinate plane below

<p>Point A and Point B are plotted.</p> Signup and view all the answers

Write a variable expression for "4 less than twice n".

<p>2n - 4</p> Signup and view all the answers

Write a variable expression for "three times the difference of m and 4".

<p>3(m - 4)</p> Signup and view all the answers

Write a variable expression for "the sum of x¹⁰, all divided by 5".

<p>(x¹⁰) / 5</p> Signup and view all the answers

Write a variable expression for "x increased by one-half of k".

<p>x + k/2</p> Signup and view all the answers

In the expression 40h + 20/5, what does 40 represent?

<p>The hourly rate for renting the boat.</p> Signup and view all the answers

In the expression 40h + 20/5, what does 40h + 20 represent?

<p>The total cost of renting the boat and life jackets.</p> Signup and view all the answers

In the expression 40h + 20/5, what does the entire expression represent?

<p>The cost per person for renting the boat and life jackets.</p> Signup and view all the answers

What expression represents the total cost to bowl, if it costs $4 to rent bowling shoes and $2 per game to bowl, where g represents the number of games?

<p>4 + 2g</p> Signup and view all the answers

Solve the equation p - 10 = -15. Show all steps.

<p>p - 10 = -15 Given equation p - 10 + 10 = -15 + 10 Addition Property of Equality p = -5 Simplify</p> Signup and view all the answers

Solve the equation -4 = -n + 4. Show all steps.

<p>-4=-n+4 Given equation -4+n=-n+4+n Addition Property of Equality -4+n=4 Simplify -4+n+4=4+4 Addition Property of Equality n=8 Simplify</p> Signup and view all the answers

Solve the equation -15=h/5. Show all steps.

<p>-15=h/5 Given equation -15 * 5 = h/5 * 5 Multiplication Property of Equality -75 = h Simplify</p> Signup and view all the answers

Solve the equation 5m = -65. Show all steps.

<p>5m=-65 Given equation 5m / 5 = -65 / 5 Division Property of Equality m = -13 Simplify</p> Signup and view all the answers

Examine the student work below. Check their solution to determine if there is an error. Explain what is correct and incorrect in each step of their work. Solve the equation on your work and check the new solution. The equation is -5 + x = 10

<p>The student added 5 to both sides in the first step. This is correct. The student correctly simplified the expression on the left side. The student's answer is correct.</p> Signup and view all the answers

Examine the student work below. Check their solution to determine if there is an error. Explain what is correct and incorrect in each step of their work. Solve the equation on your work and check the new solution. The equation is -7d = 70.

<p>The student added 7 to both sides of the equation. This is incorrect. The student should have divided both sides by -7 to solve for d. The student's answer is incorrect.</p> Signup and view all the answers

Is p = 5 a solution to the equation 1 + p/3 = 2?

<p>True (A)</p> Signup and view all the answers

Is n = 14 a solution to the equation -1 + n/2 = 6?

<p>True (A)</p> Signup and view all the answers

Is m = 8 a solution to the equation 58 = 2 + 7m?

<p>True (A)</p> Signup and view all the answers

Is x = 7 a solution to the equation -56 = 7(-1 + x)?

<p>True (A)</p> Signup and view all the answers

Is k = 3 a solution to the equation -3 - 8k = -27?

<p>True (A)</p> Signup and view all the answers

Is x = 16 a solution to the equation 8x - 8 = -64?

<p>True (A)</p> Signup and view all the answers

Is h = 11 a solution to the equation -18 = - h - 7?

<p>True (A)</p> Signup and view all the answers

Is f = 22 a solution to the equation -3 = -4 + 4/6f?

<p>True (A)</p> Signup and view all the answers

Solve the equation 8 = 3x - 5 - 4. Show all your steps.

<p>8 = 3x - 5 - 4 Given equation 8 = 3x - 9 Simplify 8 + 9 = 3x - 9 + 9 Addition Property of Equality 17 = 3x Simplify 17 / 3 = 3x / 3 Division Property of Equality 17 / 3 = x Simplify</p> Signup and view all the answers

Solve the equation 6m + 2 - 4m = 10. Show all your steps.

<p>6m + 2 - 4m = 10 Given equation 2m + 2 = 10 Combine Like Terms 2m + 2 - 2 = 10 - 2 Subtraction Property of Equality 2m = 8 Simplify 2m / 2 = 8 / 2 Division Property of Equality m = 4 Simplify</p> Signup and view all the answers

Solve the equation 8 = 6k - 2(k + 4). Show all steps.

<p>8 = 6k - 2(k + 4) Given equation 8 = 6k - 2k - 8 Distributive Property 8 = 4k - 8 Simplify 8 + 8 = 4k - 8 + 8 Addition Property of Equality 16 = 4k Simplify 16 / 4 = 4k / 4 Division Property of Equality 4 = k Simplify</p> Signup and view all the answers

Solve the equation 210 - 2(h) = -20. Show all steps.

<p>210 - 2h = -20 Given equation 210 - 2h - 210 = -20 - 210 Subtraction Property of Equality -2h = -230 Simplify -2h / -2 = -230 / -2 Division Property of Equality h = 115 Simplify</p> Signup and view all the answers

A triangle has side lengths 12 feet, x + 2 feet, and 2x + 2 feet. The perimeter of the triangle is 46 feet. Write and solve an equation to find the value of x. Show your work.

<p>12 + (x + 2) + (2x + 2) = 46 Given equation 12 + x + 2 + 2x + 2 = 46 Simplify 3x + 16 = 46 Combine Like Terms 3x + 16 - 16 = 46 - 16 Subtraction Property of Equality 3x = 30 Simplify 3x / 3 = 30 / 3 Division Property of Equality x = 10 Simplify</p> Signup and view all the answers

A square has a side length of 5x + 2 yards. The perimeter of the square is 44 square yards. Write and solve an equation to find the value of x. Show your work.

<p>4(5x + 2) = 44 Given equation 20x + 8 = 44 Distributive Property 20x + 8 - 8 = 44 - 8 Subtraction Property of Equality 20x = 36 Simplify 20x / 20 = 36 / 20 Division Property of Equality x = 1.8 Simplify</p> Signup and view all the answers

Flashcards

Sum

An expression that combines two or more numbers through addition. The result is called the sum.

Difference

An expression that combines two or more numbers through subtraction. The result is called the difference.

Product

An expression where two or more numbers are multiplied together. The result is called the product.

Quotient

An expression where one number is divided by another. The result is called the quotient.

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Power

An expression that involves a base number multiplied by itself a certain number of times. The number of times the base is multiplied is called the exponent.

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Expression

A way of expressing a quantity using numbers and symbols, such as +,-, x, ÷.

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Variable

A value that can change or vary. Often represented by a letter.

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Constant

A symbol that represents a specific number. It cannot change.

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Terms

The combination of numbers and variables in an expression, separated by mathematical operations.

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Exponent

A number that tells us how many times a base is multiplied by itself.

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Base

The number that is multiplied by itself in an expression with an exponent.

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Combine Like Terms

Combining terms in an expression that have the same variable and exponent. For example, 2x + 3x = 5x.

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Distributive Property

A rule that states that the product of a number and a sum equals the sum of the products of the number with each term inside the parentheses. For example, 3(x+2) = 3x + 6.

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Simplify

The process of simplifying an expression by performing operations according to the order of operations (PEMDAS/BODMAS).

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Equation

A mathematical statement that two expressions are equal. It contains an equals sign (=).

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Solution

A value that makes an equation true when substituted for the variable.

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Addition Property of Equality (APOE)

The property that allows us to add the same value to both sides of an equation without changing its truth.

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Subtraction Property of Equality (SPOE)

The property that allows us to subtract the same value from both sides of an equation without changing its truth.

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Multiplication Property of Equality (MPOE)

The property that allows us to multiply both sides of an equation by the same non-zero value without changing its truth.

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Division Property of Equality (DPOE)

The property that allows us to divide both sides of an equation by the same non-zero value without changing its truth.

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Coordinate Plane

A visual representation of data on a plane using two axes, usually labelled as x-axis (horizontal) and y-axis (vertical). Each point is represented by an ordered pair (x, y).

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Ordered Pair

A pair of numbers that represent a specific location on a coordinate plane. The first number represents the x-coordinate (horizontal position) and the second number represents the y-coordinate (vertical position).

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Perimeter of a triangle

The perimeter of a triangle is the total distance around its three sides. It is calculated by adding the lengths of all three sides

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Perimeter of a square

The perimeter of a square is the total distance around its four sides. It is calculated by adding the lengths of all four sides, or by multiplying the length of one side by 4.

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Area of a square

The area of a square is the amount of space it covers. It is calculated by multiplying the length of one side by itself.

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One-step equation

A one-step equation is an equation that can be solved in one step using the properties of equality.

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Inverse Operation

A mathematical operation that reverses the effect of another operation. For example, addition is the inverse of subtraction, multiplication is the inverse of division, and vice versa.

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Checking the solution

The process of checking if a solution makes the equation true by substituting the solution value for the variable. If both sides of the equation are equal, the solution is correct.

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Finding and fixing errors

The act of identifying and correcting errors in mathematical work, either in one's own work or the work of others.

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Real-world problem

A mathematical problem that can be translated into an equation.

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Total cost of renting a boat

The total cost of renting a boat for a certain number of hours, calculated by adding the hourly rate and the one-time fee for life jackets.

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Number of games played

The number of games played.

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Cost per person for renting a boat

The total cost of renting a boat for a certain number of hours, taking into account the hourly rate, the one-time fee, and the number of people sharing the cost.

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Study Notes

Integer Expressions and Equations

  • Classify integer expressions as sum, difference, product, quotient, or power.
  • Simplify integer expressions. Ex: Simplify -5 + (-2) = -7
  • Translate real-world problems into integer expressions. Ex: Temperature on Sunday: 35°F. On Monday it is 20°F warmer: 35 + 20= 55°F.

Simplify Integer Expressions

  • Combine like terms to simplify expressions and then solve the equations.
  • Apply the distributive property to simplify integer expressions.
  • Solve one-step equations and justify each step. Ex: Solve p-10=-15. p = -15 +10 = -5.
  • Verify solutions by substituting the solution into the original equation.

Classifying Variable Expressions

  • Classify variable expressions as a sum, difference, product, quotient, or power.
  • Evaluate variable expressions when given different values of the variable.

Solving One-Step Equations

  • Solve equations using the Properties of Equality. Ex: -7d = 70. d= -10.
  • Justify each step when solving equations. Ex: -7d = 70. / -7 d= -10. (Divide both sides by -7).
  • Check solutions for accuracy.

Creating Expressions

  • Create variable expressions that match given criteria.
  • Create variable expressions for real-world problems.

Graphing Points

  • Label points on a coordinate plane (x, y).
  • Plot points from given coordinates.

Variable Expressions and Real-World Problems

  • Create expressions to represent real-world scenarios. Ex: Cost to bowl = 4 + 2g where g is the number of games played.
  • Analyze variable expressions in context.

Solving Equations and Checking Solutions

  • Use the correct order of operations when evaluating or solving.

Solving Multi-Step Equations

  • Distribute and solve: Ex: Solve 6m+2 – 4m = 10
  • Identify and combine like terms: Ex: 2m + 2= 10
  • Solve for the variable: 2m =8, m=4

Determine if a Given Value is a Solution

  • Determine if the given value satisfies the equation

Geometry Problems

  • Find the perimeter of a triangle from given side lengths, and solve for unknowns.
  • Find the area and perimeter of a rectangle with given variables.

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