Algebra Class Quiz - Expressions and Operations

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

<p>Finding solutions to equations (B)</p> Signup and view all the answers

<p>$rac{-(x+2)(x-4)}{(x-2)(x+2)}$ (C)</p> Signup and view all the answers

<p>Factoring $2a^3 - 3a^2$ into $a^2(2a - 3)$ (D)</p> Signup and view all the answers

<p>A proper fraction with no further simplification possible (C)</p> Signup and view all the answers

<p>A polynomial of degree 5 (D)</p> Signup and view all the answers

<p>It should always equal zero for proper simplification. (D)</p> Signup and view all the answers

<p>$4(x-3)$ (B)</p> Signup and view all the answers

<p>54 (D)</p> Signup and view all the answers

<p>36 (C)</p> Signup and view all the answers

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

<p>Finding a common denominator before combining fractions (D)</p> Signup and view all the answers

<p>$\frac{(2y - x)}{(2y - x)(2y + x)}$ (D)</p> Signup and view all the answers

<p>$x - 3$ (A)</p> Signup and view all the answers

<p>$\frac{(2p - 7)^{3}}{(2p - 7)^{4}}$ (A)</p> Signup and view all the answers

<p>$\frac{35(y - 2)}{9y - 21}$ (B)</p> Signup and view all the answers

<p>$\frac{1}{(r + s) \cdot (r - s)}$ (A)</p> Signup and view all the answers

<p>$rac{8}{25}$ (A)</p> Signup and view all the answers

<p>$rac{3a^{3}}{2y}$ (B)</p> Signup and view all the answers

<p>$rac{21m^{2}}{m^{2}-9}$ (D)</p> Signup and view all the answers

<p>$rac{3}{1}$ (D)</p> Signup and view all the answers

<p>$rac{5}{1}$ (B)</p> Signup and view all the answers

<p>18 (A)</p> Signup and view all the answers

<p>10(2a-b) (B)</p> Signup and view all the answers

<p>60 IF Q=INT(Q) THEN (D)</p> Signup and view all the answers

<p>Identify the prime factors of each denominator to find the highest powers. (C)</p> Signup and view all the answers

<p>$\frac{7}{4}$ (D)</p> Signup and view all the answers

<p>$\frac{16}{25}$ (D)</p> Signup and view all the answers

<p>$\frac{32}{63}x^3$ (D)</p> Signup and view all the answers

<p>$\frac{1}{2} \cdot \frac{3}{4} \cdot \frac{8}{9} x^2$ (D)</p> Signup and view all the answers

<p>$\frac{64n^3}{125}$ (D)</p> Signup and view all the answers

<p>$\frac{4yd}{12}$ (D)</p> Signup and view all the answers

<p>$\frac{16}{x^2y}$ (B)</p> Signup and view all the answers

<p>$\frac{5x^2}{3(x - 2)}$ (C)</p> Signup and view all the answers

The process of breaking down a polynomial expression into simpler factors, often by finding common factors or using special factoring patterns.

Simplifying an algebraic expression by dividing both the numerator and denominator by their greatest common factor.

The result of multiplying two binomials (two-term expressions). It often involves combining like terms.

Finding the values of a variable that make a polynomial expression equal to zero.

The process of combining like terms and performing arithmetic operations within an algebraic expression.

Multiplying fractions involves multiplying the numerators and the denominators. Simplify the result to the simplest form by dividing both the numerator and the denominator by their greatest common factor.

Raising a fraction to a power means multiplying the fraction by itself the number of times indicated by the exponent. Remember to apply the exponent to both the numerator and the denominator.

A power with a negative base raised to an even exponent results in a positive value. A power with a negative base raised to an odd exponent results in a negative value.

To simplify expressions involving variables and fractions, multiply the coefficients and combine the variables using the rules of exponents. Remember that a variable raised to a power means multiplying the variable by itself that many times.

The area of a square is found by multiplying the side length by itself. The volume of a cube is found by multiplying the edge length by itself three times.

The area of a triangle is calculated by multiplying the base by the height and dividing by 2. Remember to convert units to the same measurement before calculating.

To find the distance traveled, multiply the speed (rate) by the time. Ensure units are consistent before multiplying.

To simplify expressions involving fractions and variables, factor out common factors in the numerators and denominators. Remember to follow the rules of arithmetic and algebra.

A combination of numbers, variables, and operations (like addition, subtraction, multiplication, division, and exponentiation) that represent a mathematical value.

A symbol that represents an unknown or changing value. It can be any letter, such as x, y, a, or b.

The process of breaking down a mathematical expression into smaller parts that are multiplied together.

Simplifying an expression means rewriting it in a simpler form without changing its value. This involves performing operations like combining like terms or simplifying fractions.

The process of solving for the value of an unknown variable in an equation by using algebraic operations to isolate the variable.

A mathematical statement that involves dividing two polynomials.

A variable raised to a power indicates repeated multiplication of the variable by itself.

The order of operations (PEMDAS) defines the precedence of mathematical operations in a complex expression: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right).

Fractions are represented as a division of two numbers or expressions.

Dividing fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator. For example, the reciprocal of 5/3 is 3/5.

When dividing a fraction by another fraction, the first fraction remains the same, and the division operation is replaced by multiplication with the reciprocal of the second fraction. For example, a/b ÷ c/d = a/b x d/c.

Dividing by a fraction is the same as multiplying by the reciprocal of that fraction. The reciprocal of a fraction is found by switching the numerator and denominator. For example, 3/4 ÷ 2/5 is equivalent to 3/4 x 5/2.

Dividing a fraction by a fraction is the same as multiplying the first fraction by the reciprocal of the second fraction. To find the reciprocal, simply flip the numerator and denominator.

The smallest common multiple of the denominators of two or more fractions.

A way of representing the product of consecutive integers starting from 1. For example, 5! means 5 * 4 * 3 * 2 * 1.

Rewriting fractions to have the same denominator, which allows for easier addition or subtraction of fractions.

A program that uses a loop to find the smallest number that is divisible by both given integers. This number represents the least common denominator of those integers.

The program calculates the LCD by multiplying the second integer by consecutive multiples of 1 until it finds a multiple that is divisible by the first integer. This multiple represents the LCD.

A set of fractions are given, and the least common denominator (LCD) is the smallest number that all the denominators divide into. This is useful for adding or subtracting fractions with different denominators.

To simplify expressions involving fractions and variables, factor out common factors in the numerators and denominators. Then, simplify the expression by canceling out common factors. Remember to follow the rules of arithmetic and algebra.

An equation that contains variables and fractions is called a fractional equation. To solve it, you need to find the value of the variable that makes the equation true. This can be done by multiplying the entire equation by the least common denominator (LCD) to eliminate the fractions, then solve for the variable.

To simplify expressions involving multiple fractions, use the order of operations. Simplify the operations within parentheses or brackets first, then solve the exponent terms. Next, multiply and divide from left to right. Finally, add and subtract from left to right.

When solving an equation involving fractions, you need to know whether the equation has a valid solution. A valid solution is a value that does not make the equation undefined. If the solution results in a denominator of zero, the solution is not valid. To check for validity, always check if the solution makes the denominator of any fraction zero.