Solving Decimal Equations and Expressions

Lesson 27 covers the distributive property and simplifying decimal equations. It begins with an introduction to the lesson's topics, followed by two examples demonstrating the use of the distributive property to expand and simplify algebraic expressions. The lesson concludes with a section on simplifying equations involving decimals by converting them into whole numbers for easier computation.

What is the main focus of lesson 27?

• Understanding fractions

• The distributive property and simplifying decimal equations

• Solving quadratic equations

• Graphing linear equations

How do you apply the distributive property to the expression XY(Y^2 - X^2Z)?

• Add XY to Y^2 and subtract X^2Z

• Multiply XY by X^2Z and add Y^2

• Multiply XY by Y^2 and subtract XY by X^2Z

• Multiply XY by Y^2 and add XY by X^2Z

What is the simplified form of XY * Y^2?

• X^3Y

• XY^3

• X^2Y

• XY^2

In the expression 2X^2Y * (Y - 4Y^5), what is the result of 2X^2Y * Y?

• 2X^2Y^3

• 2X^2Y^5

• 2X^2Y^2

• 2X^3Y

Why can't the terms 2X^2Y^2 and 8X^2Y^6 be subtracted?

• They are like terms

• They have different coefficients

• They are not like terms

• They have the same exponents

What is the first step in solving a decimal equation like 0.002K + 0.02 = 4.02?

• Divide by 1000

• Subtract 1000 from each term

• Multiply each term by 1000

• Add 1000 to each term

What is the result of multiplying 0.002 by 1000?

• 200

• 20

• 2

• 0.2

After eliminating decimals, what is the equation to solve for K in 2K + 20 = 4020?

• K = 4000

• 2K = 4020

• K = 2000

• 2K = 4000

What is the value of K after solving the equation 2K = 4000?

• 1000

• 2000

• 3000

• 4000

Why is it easier to solve decimal equations by converting them to whole numbers?

• It avoids working with fractions

• It eliminates the need for division

• It reduces the number of steps

• It simplifies calculations