Grade 6 | Unit 6 | Lesson 8: Equal and Equivalent | Practice Problems

Draw a diagram of \(x + 3\) and a diagram of \(2x\) when \(x\) is 1. Draw a diagram of \(x+3\) and of \(2x\) when \(x\) is 2. Draw a diagram of \(x+3\) and of \(2x\) when \(x\) is 3. Draw a diagram of \(x+3\) and of \(2x\) when \(x\) is 4. When are \(x+3\) and \(2x\) equal? When are they not equal? Use your diagrams to explain.

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Do \(4x\) and \(15+x\) have the same value when \(x\) is 5? Are \(4x\) and \(15+x\) equivalent expressions? Explain your reasoning.

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Check that \(2b + b\) and \(3b\) have the same value when \(b\) is 1, 2, and 3. Do \(2b +b\) and \(3b\) have the same value for all values of \(b\)? Explain your reasoning. Are \(2b+b\) and \(3b\) equivalent expressions?

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80% of \(x\) is equal to 100. Write an equation that shows the relationship of 80%, \(x\), and 100. Use your equation to find \(x\).

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Find these products. \((2.3) \cdot (1.4)\) \((1.72) \cdot (2.6)\) \((18.2) \cdot (0.2)\) \(15 \cdot (1.2)\)

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Calculate \(141.75 \div 2.5\) using a method of your choice. Show or explain your reasoning.

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