Understanding Rational Expressions and Fractions

The video tutorial covers rational and radical expressions, explaining their definitions and operations. It discusses how to perform addition, subtraction, multiplication, and division with fractions, and explores the relationship between rational exponents and radicals. The tutorial also provides a guide on using the Desmos calculator to simplify expressions, with practical examples and exercises to reinforce learning.

What is a rational expression?

• An expression involving only addition

• An expression involving only subtraction

• An expression involving fractions

• An expression involving whole numbers only

What must be true for adding fractions?

• They must have the same numerator

• They must be whole numbers

• They must be improper fractions

• They must have a common denominator

How do you multiply fractions?

• Multiply the numerators and denominators

• Divide the numerators and denominators

• Subtract the numerators and denominators

• Add the numerators and denominators

What is the relationship between a rational exponent and a radical?

• There is no relationship

• The denominator of the exponent becomes the index of the radical

• The numerator of the exponent becomes the index of the radical

• The exponent becomes the base of the radical

What are like radicals?

• Radicals with the same base

• Radicals with different indices

• Radicals with the same index and radicand

• Radicals with different radicands

Which letters should not be used in Desmos to avoid graphing?

• p, q, r

• m, n, o

• x, y, e

• a, b, c

In Example 1, what is the purpose of using sliders in Desmos?

• To delete the expression

• To change the color of the graph

• To adjust the values of variables

• To add more variables

What is a complex fraction?

• A fraction with only one term

• A fraction with no variables

• A fraction with a whole number

• A fraction with another fraction in its numerator or denominator

How do you find a cube root using Desmos?

• By using the division function

• By using the addition function

• By using the nth root function

• By using the subtraction function