Expression Properties

Grade 6 · algebra · 100 practice problems · read aloud

🔊 Listen to this explanation

What Are Expression Properties? 🤔

Expression properties are special math rules that let us rewrite expressions in different ways without changing their value. Think of it like rearranging the furniture in your room—the room is the same, it just looks different! This is super useful for simplifying problems and making mental math easier.

How to Use Expression Properties

  1. Identify the numbers and operations in the expression.
  2. Choose a property that can help (see examples below).
  3. Rewrite the expression using the property.
  4. Calculate to check that the value stays the same.

Visual Examples

Example 1: Commutative Property

This property says you can swap the order of numbers when adding or multiplying.

Problem: 7 + 5 + 3

Step 1: Notice 7 + 3 is a friendly pair that makes 10.

Step 2: Use the commutative property: 7 + 3 + 5

Step 3: Solve: (7 + 3) + 5 = 10 + 5 = 15

Example 2: Distributive Property

This property lets you "distribute" a number to everything inside parentheses.

Problem: 4 × (25 + 3)

Step 1: Distribute the 4: (4 × 25) + (4 × 3)

Step 2: Calculate: 100 + 12

Step 3: Solve: 112

Common Mistakes to Avoid 🚫

Mixing up properties: The commutative property ONLY works for addition and multiplication, NOT subtraction or division. For example, 10 - 4 is NOT the same as 4 - 10.

Forgetting parentheses: When using the distributive property, you MUST multiply both terms inside the parentheses. For 5 × (2 + 8), it's (5×2) + (5×8), not 5×2 + 8.

Tips & Tricks

Look for "Friendly Numbers": Always scan for number pairs that make 10, 100, or other easy-to-work-with numbers.

Memory Aid: "Any order, same total" for commutative property. "Pass it out to all about" for distributive property.

Check Your Work: Calculate the original expression and your new one. If the answers match, you used the properties correctly!

How to Practice

  • Create your own expressions and try to rewrite them 2-3 different ways.
  • Use online math games that focus on properties of operations.
  • Explain the properties to a family member—teaching is a great way to learn!
  • Solve mental math problems by looking for number pairs that make calculations easier.

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 15% of 240 = ?

Hint: Remember that percentage means 'per hundred.' Think about how to convert a percentage to a decimal to find a portion of a whole number.

Show the answer

Answer: 36

  1. Understand that "percent" means "per hundred". So 15% means 15 per hundred, which can be written as 15/100.
  2. "Of" in mathematics usually means multiplication. So 15% of 240 means (15/100) × 240.
  3. Write the multiplication: (15/100) × 240
  4. Simplify the calculation. We can multiply 15 × 240 first, then divide by 100. 15 × 240 = 15 × (200 + 40) = (15 × 200) + (15 × 40) = 3000 + 600 = 3600
  5. Now divide by 100: 3600 / 100 = 36
  6. Alternatively, you could simplify before multiplying: (15/100) × 240 = 15 × (240/100) = 15 × (24/10) = 15 × 2.4 = 30 + 6 = 36 Both methods give the same result. ANSWER: 36

We are asked to find 15% of 240.

2 (-3)² + 2 × (-5) = ?

Hint: Remember to follow the order of operations and pay attention to negative signs when squaring numbers.

Show the answer

Answer: -1

  1. Evaluate (-3)² A negative number in parentheses squared means: (-3) × (-3) = 9. So, (-3)² = 9.
  2. Evaluate 2 × (-5) Multiplying a positive number by a negative number gives a negative result: 2 × (-5) = -10.
  3. Add the results Now we have: 9 + (-10) Adding a negative is the same as subtracting: 9 - 10 = -1. Final Answer: -1

Let's solve step by step.

3 (-12) + 25 - (-8) = ?

Hint: Remember that subtracting a negative number is the same as adding its positive equivalent. Work through the operations from left to right.

Show the answer

Answer: 21

  1. Write the problem clearly. (-12) + 25 - (-8)
  2. Handle the subtraction of a negative number. Subtracting a negative is the same as adding a positive: - (-8) becomes + 8 So now the expression is: (-12) + 25 + 8
  3. Add the numbers from left to right. First: (-12) + 25 Think of it as 25 - 12 = 13. So now we have: 13 + 8
  4. Add 13 + 8. 13 + 8 = 21 Final Answer: 21

Let's solve step-by-step:

4 (-4)³ ÷ 8 + 2 × (-5) = ?

Hint: Remember to follow the order of operations and be careful with negative signs when working with exponents.

Show the answer

Answer: -18

  1. Calculate the exponent: (-4)³ = (-4) × (-4) × (-4) = 16 × (-4) = -64
  2. Perform the division: -64 ÷ 8 = -8
  3. Perform the multiplication: 2 × (-5) = -10
  4. Add the results: -8 + (-10) = -18

The answer is -18.

5 3² × (4 + 2) - 15 ÷ 3 = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction.

Show the answer

Answer: 49

  1. Parentheses first** 4 + 2 = 6 So the expression becomes: 3² × 6 - 15 ÷ 3 **
  2. Exponents** 3² = 9 So the expression becomes: 9 × 6 - 15 ÷ 3 **
  3. Multiplication and Division from left to right** First, 9 × 6 = 54 Then, 15 ÷ 3 = 5 So the expression becomes: 54 - 5 **
  4. Subtraction** 54 - 5 = 49 **Final Answer:** 49

Let's solve the problem step-by-step using the order of operations (PEMDAS/BODMAS): PEMDAS stands for Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). We have: 3² × (4 + 2) - 15 ÷ 3 **

6 (-8)² ÷ 4 + 12 × (-3) = ?

Hint: Remember the order of operations and how negative numbers behave with exponents.

Show the answer

Answer: -20

  1. Calculate the exponent first: (-8)² = 64
  2. Perform division: 64 ÷ 4 = 16
  3. Perform multiplication: 12 × (-3) = -36
  4. Add the results: 16 + (-36) = -20

The answer is -20.

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