Questions and Answers
What is an expression?
What is a variable?
A symbol that represents a number that we do not know yet
What does a coefficient represent?
A number that is multiplied by a variable
What is a constant in an expression?
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What is a term?
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What is an equation?
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What does the equation 3x - 2 = 5 say about coefficients and constants?
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In the equation 4 + 9 + 5 + x = 2x, how many terms are on the left side?
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The constant on the left side of the equation 3x - 3 = 5 is 3.
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What does the term 'similar' mean in geometry?
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What is distortion in terms of shapes?
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A _______ compares how much of something there is compared to another.
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What is 14/5 known as?
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Convert 3 3/5 into an improper fraction and you will get _____.
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To ______________ an expression means to find the numerical value of.
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__________________ expressions have the same value.
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It's a great day to be a _______________.
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What is the result of evaluating 4x - 9 for x = 3?
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What is the result of evaluating 3x - 2 for x = -3?
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Write an expression for Chris and Sam combining baseball cards and selling 5 cards.
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Write an algebraic expression that represents the sum of 14 and m.
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Write an algebraic expression that represents '13 less than x'.
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What is the solution to the equation 3x + 4 = 28?
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What is the solution for r in the equation 32 = r/2?
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Simplify: 2 2/3 + 9 4/5 = _______________________________
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If trapezoid ABCD was reduced and side length DC = 15" and HG = 3", what scale factor was used?
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If I have nickels, dimes, and quarters in the ratio 2 : 3 : 7 and I have 63 quarters, how many nickels and dimes do I have?
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Are the expressions 3x + 2 and x + x + x + 2 equivalent?
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Are the expressions y * y * y - 3 and y + y + y - 3 equivalent?
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What number should replace the 'x' in the ratio table shown to successfully complete the table?
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What fraction of the new shade of purple paint made of 3 parts red and 1 part blue is blue?
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What is the simplified ratio of the smaller perimeter to the larger perimeter when comparing two squares with sides of 5" and 15"?
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What is the ratio of the smaller area to the larger area before it is simplified when comparing two squares with sides of 5" and 15"?
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In a class where the ratio of boys to girls is 17 : 15, how many boys are there if there are 60 girls?
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If Peyton Frontino hit 2 doubles and 1 triple in a game, how many doubles and triples did he hit total for the season if he hit 34 doubles?
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Anytime you multiply a number by 1, the _____________________________ stays the same size.
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Anytime you multiply a number by a value greater than 1, the _______________________ will get larger.
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Anytime you multiply a number by a value less than 1, the _______________________ will get smaller.
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Study Notes
Mathematical Expressions and Terms
- Expression: A collection of numbers, variables, and operation signs without an equation sign.
- Variable: A letter or symbol representing an unknown number.
- Coefficient: A numerical value that multiplies a variable within an expression.
- Constant: A standalone number in an expression, without any variables.
- Term: A single number, variable, or combination of both multiplied together, separated by addition or subtraction signs.
Equations and Their Properties
- Equation: A statement consisting of two expressions set equal to each other, marked with an '=' sign.
- Example: In the equation
3x - 2 = 5, the coefficient is 3 and the constant is -2. - Example: In
4 + 9 + 5 + x = 2x, there are 4 terms on the left side.
Ratios and Distortion
- Ratios: A comparative measure highlighting the relationship between two quantities, expressed as a fraction, or in various formats such as a:b or a to b.
- Distortion: Occurs when a shape is modified without a consistent scale factor, affecting its proportions.
Improper Fractions and Evaluation
-
Improper Fraction: A fraction where the numerator is greater than the denominator, e.g.
14/5which simplifies to2 4/5. - Evaluating Expressions: Involves replacing variables with numbers and calculating the result, based on the order of operations.
Algebraic Expressions
- Writing expressions for scenarios:
- Combining Chris's and Sam's baseball cards:
c + s - 5 - Sum of 14 and a variable m:
14 + m - Thirteen less than x:
x - 13
- Combining Chris's and Sam's baseball cards:
Solving Equations
- Example solution for
3x + 4 = 28yieldsx = 8. - To solve
32 = r/2, the solution isr = 64.
Simplification
- The result of
2 2/3 + 9 4/5simplifies to12 7/15.
Scale Factors and Area Ratio
- A trapezoid reduction from 15" to 3" reflects a scale factor of
1/5. - The smaller area ratio to the larger area for squares with side lengths 5" and 15" calculates as
25:225.
Ratios in Practice
- In a class where the boy-to-girl ratio is 17:15, with 60 girls, the resulting number of boys is 68.
- Peyton Frontino maintained a consistent ratio, resulting in a total of 51 doubles for the season.
Characteristics of Shape Modifications
- Scaling with a factor of 1 maintains the original size.
- A scale factor greater than 1 enlarges the shape or number.
- A scale factor less than 1 reduces the size.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of key mathematical terms with these flashcards from C.P.M. Chapter 4. This quiz covers essential concepts such as expressions, variables, coefficients, and constants. Perfect for students looking to reinforce their knowledge in algebra.
