Algebra Concepts and Applications

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Questions and Answers

What does the LCM of 4 and 6 equal?

  • 12 (correct)
  • 24
  • 18
  • 2

Which of the following expressions correctly applies the distributive property to $3(4 + 5)$?

  • $3(9)$
  • $12 + 15$ (correct)
  • $3(4) + $5$
  • $3 + 4 + 5$

When simplifying the fraction $\frac{6}{8}$, which step is correct?

  • $\frac{2}{3}$
  • $\frac{6}{16}$
  • $\frac{3}{4}$ (correct)
  • $\frac{1}{2}$

What is the correct outcome when using the order of operations to evaluate the expression $4 + 3 \times 2$?

<p>10 (D)</p> Signup and view all the answers

In coordinate geometry, how many quadrants divide the coordinate plane?

<p>Four (C)</p> Signup and view all the answers

What is the value of $\frac{15}{20}$ when simplified?

<p>$\frac{3}{4}$ (A)</p> Signup and view all the answers

Using the associative law, which equation demonstrates its principle?

<p>$(2 + 3) + 5 = 2 + (3 + 5)$ (A)</p> Signup and view all the answers

What is the result of simplifying the expression $2(x + 3) - 4$?

<p>$2x + 6 - 4$ (A)</p> Signup and view all the answers

What is the primary purpose of using decimals in mathematics?

<p>To separate whole numbers from fractional parts (A)</p> Signup and view all the answers

Which of the following statements about LCM is true?

<p>LCM is the smallest positive integer that is a multiple of two or more integers. (B)</p> Signup and view all the answers

Which arithmetic law allows for changing the order of addition?

<p>Commutative Law (D)</p> Signup and view all the answers

What is the greatest common integer that divides both 12 and 18 without leaving a remainder?

<p>6 (D)</p> Signup and view all the answers

If the expression $5(x + 2)$ is simplified using the distributive law, what will it become?

<p>$5x + 10$ (D)</p> Signup and view all the answers

Which of the following is an example of a situation where the associative law applies?

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

When converting the decimal 0.75 to a fraction, what is the resulting fraction?

<p>$\frac{3}{4}$ (C)</p> Signup and view all the answers

How can you find the LCM of two numbers, such as 8 and 12?

<p>By using prime factorization (A)</p> Signup and view all the answers

Which arithmetic law is demonstrated in the equation $2 + (3 + 4) = (2 + 3) + 4$?

<p>Associative Law (D)</p> Signup and view all the answers

What represents the smallest number that is a multiple of both 4 and 6?

<p>12 (B)</p> Signup and view all the answers

Which set of numbers is represented as integers?

<p>-3, -2, -1, 0, 1 (D)</p> Signup and view all the answers

What is the result of adding the integers -7 and 3?

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

Which of the following expressions represents the result of subtracting 5 from -2?

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

What is the result of multiplying the integers -4 and 6?

<p>-24 (D)</p> Signup and view all the answers

If the integer -5 is divided by the integer -1, what is the result?

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

Which statement correctly describes the absolute value of an integer?

<p>It represents the integer's distance from zero on the number line. (C)</p> Signup and view all the answers

What is the result when -3 is divided by 1?

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

If you multiply -2, -3, and 4 together, what is the resulting integer?

<p>24 (C)</p> Signup and view all the answers

What would be the product of -100 and 0?

<p>0 (B)</p> Signup and view all the answers

What is the result of the expression 8 - 10?

<p>-2 (D)</p> Signup and view all the answers

Flashcards

Combine Like Terms

Adding or subtracting terms with the same variables and exponents.

Distributive Property

Multiplying a number by a sum is equal to multiplying the number by each term in the sum.

Roman Numerals

A system of numerical notation using letters (I, V, X, L, C, D, M).

Integer

A whole number, including zero, positive numbers, and negative numbers.

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Fraction

A part of a whole, represented by a numerator and denominator.

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Order of Operations

Rules for evaluating mathematical expressions (PEMDAS/BODMAS).

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Coordinate Geometry

Locating points on a plane using coordinates.

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Decimal

Number with a decimal point separating the whole and fractional parts.

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LCM

Least Common Multiple - the smallest common multiple of two or more numbers.

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HCF

Highest Common Factor - the largest factor common to two or more numbers.

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Associative Law

Changing the grouping of numbers in addition or multiplication doesn't change the result.

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Commutative Law

Changing the order of numbers in addition or multiplication doesn't change the result.

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Distributive Law

Multiplying a number by a sum is the same as multiplying the number by each term and then adding.

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Decimal Representation

A way to express numbers with a decimal point separating the whole number part and the fractional part.

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LCM

The smallest positive integer that's a multiple of two or more numbers.

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HCF

The greatest common divisor of two or more numbers.

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Commutative Law (addition)

Changing the order of numbers in addition doesn't change the result.

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Commutative Law (multiplication)

Changing the order of numbers in multiplication doesn't change the result.

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Associative Law (addition)

Changing the grouping of numbers in addition doesn't change the result.

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Associative Law (multiplication)

Changing the grouping of numbers in multiplication doesn't change the result.

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Distributive Law

Multiplying a number by the sum of two numbers equals multiplying the number by each of the numbers in the sum, and then adding the results.

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Algebraic Expressions

Variables and constants combined with math operations

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Like Terms

Terms with same variables and exponents

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Simplify an Expression

Combine like terms

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Distributive Property

Distribute a number to everything within the parenthesis

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Roman Numerals

Number system using letters

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Integer

Whole numbers (positive, negative, and 0)

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Fraction

Part of a whole

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Order of Operations

Rules for solving math problems

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Line

Straight, endless in two directions

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Angle

Figure formed by two rays meeting at a point

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Coordinate Geometry

Geometry using a grid to locate points

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Study Notes

Simplifying Algebraic Expressions

  • Combine like terms by adding or subtracting coefficients.
  • Use the distributive property to remove parentheses.
  • Rearrange terms to group like terms together.

Roman Numerals

  • A system of numerical notation using letters.
  • I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000.

Integers

  • Whole numbers and their opposites, including zero.
  • Positive integers are greater than zero, negative integers are less than zero.

Fractions

  • Numbers that represent parts of a whole.
  • Consist of a numerator (top) and a denominator (bottom).
  • Fractions can be simplified by finding common factors of the numerator and denominator.

Order of Operations

  • PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).
  • Follow the order to evaluate expressions correctly.

Drawing Lines and Angles

  • A line is straight path that extends infinitely in both directions.
  • An angle is formed by two rays that share a common endpoint.
  • Types of angles: acute, obtuse, right, straight and reflex.

Coordinate Geometry

  • A system that uses coordinates (ordered pairs) to locate points on a plane.
  • The plane is divided into four quadrants.

Decimals

  • Numbers with a decimal point separating the whole number part from the fractional part.
  • Decimals can be converted to fractions and vice-versa.

LCM and HCF

  • LCM (Least Common Multiple) is the smallest number that is a multiple of two or more numbers.
  • HCF (Highest Common Factor) is the largest number that is a factor of two or more numbers.

Arithmetic Laws (Associative, Commutative, Distributive)

  • Associative Law: Changing the grouping of numbers in an addition or multiplication problem does not change the result.
  • Commutative Law: Changing the order of numbers in an addition or multiplication problem does not change the result.
  • Distributive Law: Multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the products.

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