Negative Numbers

Grade 6 · mathematics · 99 practice problems · read aloud

🔊 Listen to this explanation

Understanding Negative Numbers

Negative numbers are numbers less than zero. We use them to represent things like temperatures below freezing, debts, or depths below sea level. They help us describe the whole world of numbers, not just things we can count.

📝 How to Add and Subtract Negative Numbers

  1. Adding a Negative is like subtracting.
    Example: 5 + (-3) = 5 - 3 = 2
  2. Subtracting a Negative is like adding.
    Example: 4 - (-2) = 4 + 2 = 6
  3. If the signs are different, find the difference and keep the sign of the larger number.

🔍 Worked Examples

Example 1: 7 + (-4)

Adding a negative is subtracting. So, 7 - 4 = 3.

Example 2: -2 - (-8)

Subtracting a negative is adding. So, -2 + 8 = 6.

Example 3: -5 + 9

Signs are different. 9 - 5 = 4. Keep the sign of the larger number (9 is positive). Answer: 4.

⚠️ Common Mistakes to Avoid

Confusing the Rules: Remember that two negatives make a positive ONLY when subtracting.
Wrong: -4 - 5 = -9, but students sometimes think it's -1.

Misreading the Signs: Always look carefully at the operation. Is it 6 + (-2) or 6 - (-2)? They have different answers!

💡 Tips & Tricks

Number Line is Your Friend: Draw a number line! Move right for addition and left for subtraction. This makes it visual.

Same Signs: Add and Keep. (-6) + (-3) = -9
Different Signs: Subtract and Keep the sign of the larger number. (-6) + 9 = 3

🎯 How to Practice

  • Use online math games that involve number lines.
  • Create flashcards with problems like (-3) + 7 and 5 - (-1).
  • Explain the steps to a friend or family member. Teaching someone else is a great way to learn!

Practice problems

6 of the 99, worked through step by step — try them before opening the answer.

1 -15 + 23 = ?

Hint: When adding numbers with different signs, find the difference between their absolute values and keep the sign of the number with the larger absolute value.

Show the answer

Answer: 8

  1. Identify the numbers. We have a negative number (-15) and a positive number (23).
  2. Think of this as starting at -15 on a number line. Adding a positive number means moving to the right.
  3. To find the difference between the two numbers, ignore the signs for a moment. The difference between 23 and 15 is 8.
  4. Since the positive number (23) is larger than the absolute value of the negative number (15), the final answer will be positive.
  5. Subtract the smaller absolute value from the larger absolute value: 23 - 15 = 8.
  6. The result is positive because the positive number was larger. Therefore, -15 + 23 = 8.

Step-by-step solution: We are given: -15 + 23

2 -25 + 42 = ?

Hint: Consider the difference between the two numbers and which one has a greater absolute value.

Show the answer

Answer: 17

  1. Start with -25.
  2. Adding a positive number (42) means moving to the right on the number line.
  3. The difference between 42 and 25 is 17.
  4. Since 42 is greater than 25, the result will be positive.
  5. -25 + 42 = 17.

The answer is 17.

3 -25 + (-18) = ?

Hint: When adding two negative numbers, combine their absolute values and keep the negative sign.

Show the answer

Answer: -43

  1. Identify the numbers: -25 and -18 are both negative.
  2. Add their absolute values: 25 + 18 = 43.
  3. Apply the negative sign to the result: -43.

The answer is -43.

4 -15 + 8 - (-3) = ?

Hint: Remember that subtracting a negative number is the same as adding its positive value. Consider the order of operations.

Show the answer

Answer: -4

  1. Start with the expression: -15 + 8 - (-3)
  2. Simplify the subtraction of the negative number: -(-3) becomes +3
  3. Rewrite the expression: -15 + 8 + 3
  4. Add the numbers from left to right: -15 + 8 = -7
  5. Continue adding: -7 + 3 = -4
  6. The final result is -4.

5 -4 × (3 + (-7)) = ?

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

Show the answer

Answer: 16

  1. First, solve the operation inside the parentheses: 3 + (-7) = -4
  2. Now the expression becomes: -4 × (-4)
  3. When multiplying two negative numbers, the result is positive: -4 × (-4) = 16

The answer is 16.

6 -25 + (-13) - 7 = ?

Hint: Remember that adding a negative number is like subtracting its positive value. Work from left to right with the operations.

Show the answer

Answer: -45

  1. Start with -25 + (-13)
  2. Adding a negative is the same as subtracting: -25 - 13 = -38
  3. Now subtract 7 from -38: -38 - 7 = -45
  4. The final answer is -45.
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