Lesson 4

Practice Solving Equations and Representing Situations with Equations

Let's solve equations by doing the same to each side.

Problem 1

Select all the equations that describe each situation and then find the solution.

  1. Kiran’s backpack weighs 3 pounds less than Clare’s backpack. Clare’s backpack weighs 14 pounds. How much does Kiran’s backpack weigh?

    • \(x+3=14\)

    • \(3x=14\)

    • \(x = 14 -3\)

    • \(x = 14 \div 3\)

  2. Each notebook contains 60 sheets of paper. Andre has 5 notebooks. How many sheets of paper do Andre’s notebooks contain?

    • \(y = 60 \div 5\)

    • \( y = 5 \boldcdot 60\)

    • \(\frac{y}{5} = 60\)

    • \(5y = 60\)

Problem 2

Solve each equation.

  1. \(2x = 5\)
  2. \(y + 1.8 = 14.7\)
  3. \(6 = \frac{1}{2} z\)
  4. \(3\frac{1}{4} = \frac{1}{2} + w\)
  5. \(2.5t = 10\)

Problem 3

For each equation, draw a tape diagram that represents the equation.

  1. \(3\boldcdot x = 18\)
  2. \(3+x=18\)
  3. \(17 - 6 = x\)
(From Unit 6, Lesson 1.)

Problem 4

Find each product.

\((21.2)\boldcdot (0.02)\)

\((2.05)\boldcdot (0.004)\)

 

(From Unit 5, Lesson 8.)

Problem 5

For a science experiment, students need to find 25% of 60 grams.

  • Jada says, “I can find this by calculating \(\frac{1}{4}\) of 60.”
  • Andre says, “25% of 60 means \(\frac{25}{100} \boldcdot 60\).”

Do you agree with either of them? Explain your reasoning.

(From Unit 3, Lesson 13.)