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Questions and Answers
Which of the following lists the numbers $-1.75$, $2$, $1.25$, $-2$, and $0$ in ascending order?
Which of the following lists the numbers $-1.75$, $2$, $1.25$, $-2$, and $0$ in ascending order?
- $-2, -1.75, 0, 1.25, 2$ (correct)
- $-1.75, -2, 0, 1.25, 2$
- $2, 1.25, 0, -1.75, -2$
- $0, -1.75, 1.25, -2, 2$
Given runners Sean, Lacy, Maura, and Amos with time changes (in minutes) of $-3.2$, $1.25$, $1.43$, and $-2.2$ respectively, who had the second fastest time change?
Given runners Sean, Lacy, Maura, and Amos with time changes (in minutes) of $-3.2$, $1.25$, $1.43$, and $-2.2$ respectively, who had the second fastest time change?
- Lacy
- Sean
- Amos (correct)
- Maura
If a point has coordinates $\left(-\frac{3}{2}, -2\frac{1}{4}\right)$, in which quadrant is it located?
If a point has coordinates $\left(-\frac{3}{2}, -2\frac{1}{4}\right)$, in which quadrant is it located?
- Quadrant II
- Quadrant I
- Quadrant IV
- Quadrant III (correct)
In which quadrant is the point $\left(4\frac{3}{5}, -6\frac{1}{5}\right)$ located?
In which quadrant is the point $\left(4\frac{3}{5}, -6\frac{1}{5}\right)$ located?
A pizza costs $p$. Which expression represents '$2.50 more than one-fourth the cost of a pizza'?
A pizza costs $p$. Which expression represents '$2.50 more than one-fourth the cost of a pizza'?
A point is located at $\left(-\frac{4}{5}, 3\frac{1}{4}\right)$. Which quadrant does this point lie in?
A point is located at $\left(-\frac{4}{5}, 3\frac{1}{4}\right)$. Which quadrant does this point lie in?
Without plotting, which of the following points is furthest from the origin?
Without plotting, which of the following points is furthest from the origin?
A plumber charges $50 for a house visit plus $40 per hour of work. If $h$ represents the number of hours worked, which expression represents the total cost?
A plumber charges $50 for a house visit plus $40 per hour of work. If $h$ represents the number of hours worked, which expression represents the total cost?
Which point is closest to the x-axis?
Which point is closest to the x-axis?
A gymnastics studio charges an annual fee of $35 plus $20 per class. If $c$ represents the number of classes taken, which expression represents the total cost?
A gymnastics studio charges an annual fee of $35 plus $20 per class. If $c$ represents the number of classes taken, which expression represents the total cost?
A rectangle has a length that is half its width. If $w$ represents the width, which expression represents the perimeter of the rectangle?
A rectangle has a length that is half its width. If $w$ represents the width, which expression represents the perimeter of the rectangle?
Consider a rectangle in the coordinate plane. Two of its vertices are at $(-2, 3)$ and $(5, 3)$. Which of the following points could be another vertex of the rectangle?
Consider a rectangle in the coordinate plane. Two of its vertices are at $(-2, 3)$ and $(5, 3)$. Which of the following points could be another vertex of the rectangle?
In a triangle, two sides have the same length, and the third side is 1.5 times longer than the other two. If $x$ represents the length of the two equal sides, which expression represents the perimeter of the triangle?
In a triangle, two sides have the same length, and the third side is 1.5 times longer than the other two. If $x$ represents the length of the two equal sides, which expression represents the perimeter of the triangle?
Evaluate the expression $8x$ when $x = \frac{3}{4}$
Evaluate the expression $8x$ when $x = \frac{3}{4}$
Evaluate the expression $y^2$ when $y = 2.5$
Evaluate the expression $y^2$ when $y = 2.5$
Evaluate the expression $\frac{10}{3}$ when $x = \frac{3}{4}$
Evaluate the expression $\frac{10}{3}$ when $x = \frac{3}{4}$
Which statement correctly compares $-4\frac{7}{15}$ and $-4.25$?
Which statement correctly compares $-4\frac{7}{15}$ and $-4.25$?
Arrange the numbers $-1.55$, $-1\frac{11}{100}$, and $-1\frac{23}{25}$ from least to greatest.
Arrange the numbers $-1.55$, $-1\frac{11}{100}$, and $-1\frac{23}{25}$ from least to greatest.
Consider the set of numbers: $-5.52$, $-5\frac{1}{5}$, and $-5$. Which of the following statements accurately describes their order?
Consider the set of numbers: $-5.52$, $-5\frac{1}{5}$, and $-5$. Which of the following statements accurately describes their order?
A runner's goal change was $-2\frac{3}{4}$ seconds, and their actual time change was -2.8 seconds. Which change was smaller (worse)?
A runner's goal change was $-2\frac{3}{4}$ seconds, and their actual time change was -2.8 seconds. Which change was smaller (worse)?
If three numbers are ordered from least to greatest as $-3.15, -3\frac{1}{8}, -3\frac{1}{10}$, which of the following statements is true?
If three numbers are ordered from least to greatest as $-3.15, -3\frac{1}{8}, -3\frac{1}{10}$, which of the following statements is true?
Monique has 20 daisies and 25 roses. Without mixing flowers, what is the greatest number of flowers she can put in each vase?
Monique has 20 daisies and 25 roses. Without mixing flowers, what is the greatest number of flowers she can put in each vase?
Using the distributive property, what is the expanded form of the expression $3(x + 8)$?
Using the distributive property, what is the expanded form of the expression $3(x + 8)$?
Simplify the following expression: $12 \cdot \frac{3}{4}$
Simplify the following expression: $12 \cdot \frac{3}{4}$
Factor the following expression using the GCF: $16 + 48$
Factor the following expression using the GCF: $16 + 48$
Which expression is equivalent to $5(x + 24)$ based on the distributive property?
Which expression is equivalent to $5(x + 24)$ based on the distributive property?
Which of the following expressions is equivalent to $(x + 10) + x + 9$?
Which of the following expressions is equivalent to $(x + 10) + x + 9$?
Which of the following expressions is equivalent to $0.5x + 1$?
Which of the following expressions is equivalent to $0.5x + 1$?
If $x = 2$, which expression is equivalent to $3x + 2x + x$?
If $x = 2$, which expression is equivalent to $3x + 2x + x$?
Simplify the expression: $3x + 4 + 5x - 1$.
Simplify the expression: $3x + 4 + 5x - 1$.
Simplify: $\frac{1}{2}x^2 + x + \frac{1}{2} + 2x + \frac{1}{2}x^2$.
Simplify: $\frac{1}{2}x^2 + x + \frac{1}{2} + 2x + \frac{1}{2}x^2$.
After simplifying, what is the constant term in the expression $4x^2 + 6x + 8 + x + 2$?
After simplifying, what is the constant term in the expression $4x^2 + 6x + 8 + x + 2$?
Which expression is equivalent to $10 + 7x - 5 + 4x$?
Which expression is equivalent to $10 + 7x - 5 + 4x$?
Flashcards
Rational Numbers
Rational Numbers
Numbers that can be expressed as a fraction of two integers.
Ordering Numbers
Ordering Numbers
Arranging numbers from least to greatest or vice versa.
Least to Greatest
Least to Greatest
The process of arranging numbers starting from the smallest to the largest.
Negative Numbers
Negative Numbers
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Fraction Comparison
Fraction Comparison
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Plumber's Charges
Plumber's Charges
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Gymnastics Studio Charges
Gymnastics Studio Charges
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Rectangle Perimeter
Rectangle Perimeter
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Width and Length Relation
Width and Length Relation
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Triangle Side Lengths
Triangle Side Lengths
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Algebraic Expression for Triangle Perimeter
Algebraic Expression for Triangle Perimeter
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Expression Evaluation
Expression Evaluation
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Variable Definition
Variable Definition
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Greatest Common Factor (GCF)
Greatest Common Factor (GCF)
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Distributive Property
Distributive Property
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Factor
Factor
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Expanding an expression
Expanding an expression
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Simplifying an expression
Simplifying an expression
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Algebraic Expression
Algebraic Expression
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Numerical Expression
Numerical Expression
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Quadrants
Quadrants
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Coordinates
Coordinates
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Point in Quadrant I
Point in Quadrant I
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Point in Quadrant II
Point in Quadrant II
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Point in Quadrant III
Point in Quadrant III
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Point in Quadrant IV
Point in Quadrant IV
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Negative Rational Numbers
Negative Rational Numbers
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One-Step Subtraction Equation
One-Step Subtraction Equation
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Solving for x
Solving for x
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Equation Example: 24 = x - 5
Equation Example: 24 = x - 5
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Variable in Equations
Variable in Equations
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Subtraction Check
Subtraction Check
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Cost Calculation Example
Cost Calculation Example
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Walking Speed Concept
Walking Speed Concept
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Finding Miles Biked
Finding Miles Biked
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Expand an expression
Expand an expression
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Equivalent expressions
Equivalent expressions
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Simplifying expressions
Simplifying expressions
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Substitution in expressions
Substitution in expressions
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Combining like terms
Combining like terms
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Example of expression simplification
Example of expression simplification
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Evaluation of expressions
Evaluation of expressions
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Study Notes
Integers and Number Lines
- Integers are whole numbers and their opposites (positive and negative).
- Zero is the midpoint on a number line, representing neither positive nor negative.
- Integers can be graphed on a number line, with positive numbers to the right and negative numbers to the left of zero.
Opposites and Absolute Value
- The opposite of a number is its value with the opposite sign.
- The absolute value of a number represents its distance from zero, and is always positive.
Comparing Integers
- Numbers to the left on a number line are less than numbers to the right.
- Positive numbers are greater than negative numbers.
Graphing Rational Numbers
- Rational numbers include fractions, decimals, and integers.
- They can be represented and ordered on a number line.
Coordinate Plane
- The coordinate plane is a two-dimensional grid formed by the x-axis (horizontal) and y-axis (vertical).
- Points on the coordinate plane are identified by ordered pairs (x, y).
- Ordered pairs indicate the horizontal (x-coordinate) and vertical (y-coordinate) position of a point.
- Points are located in four quadrants (I, II, III, IV) based on the signs of their coordinates.
Reflections in the Coordinate Plane
- Reflections across the x-axis: change the sign of the y-coordinate.
- Reflections across the y-axis: change the sign of the x-coordinate.
Distance Between Points on a Coordinate Plane
- The distance between two points with the same x-coordinate is the absolute value of the difference in their y-coordinates.
- The distance between two points with the same y-coordinate is the absolute value of the difference in their x-coordinates.
- The distance between two points can be calculated using the distance formula, derived from the Pythagorean theorem.
Exponents and Powers
- An exponent indicates repeated multiplication.
- Evaluating powers involves calculating the repeated multiplication.
Evaluating Expressions
- Expressions contain variables, constants, and operation symbols.
- Evaluating expressions involves substituting values for variables, performing the indicated operations.
Distributive Property
- The Distributive Property allows you to multiply a number by an expression by multiplying the number by each term inside the expression.
- For example: a * (b + c) = ab + ac
Combining Like Terms
- Combining like terms involves adding or subtracting terms that contain the exact same variables raised to the same exponents.
Solving Equations
- Equations have an equals sign (=) to show two expressions are equal.
- Solving equations means finding the value of the unknown variable.
- There are different methods to solve equations.
Properties of Operations
- Operations like addition, subtraction, multiplication, and division follow specific properties.
- These properties aid in simplifying expressions and equations.
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Description
Explore integers, rational numbers, and the coordinate plane. Learn about number lines, opposites, absolute values, and graphing. Understand how to compare integers and represent rational numbers on a number line.
