What Are Inequalities with Multiplication?
Inequalities show us when numbers are not equal!
When we multiply both sides of an inequality by the same positive number, the inequality stays the same.
But when we multiply by a negative number, the inequality flips! This is a super important rule to remember.
How Multiplication Affects Inequalities
1️⃣ Start with a simple inequality like 3 < 5
2️⃣ Multiply both sides by 2 (positive): 6 < 10 (still true!)
3️⃣ Multiply both sides by -1 (negative): -3 > -5 (the sign flips!)
Let's Practice Together!
Example 1: Positive Multiplication
If we know that 4 > 2, what happens when we multiply both sides by 3?
Original: 4 > 2
Multiply both sides by 3:
4 × 3 > 2 × 3 → 12 > 6
The inequality stays the same because we multiplied by a positive number!
Example 2: Negative Multiplication
If we know that 7 < 10, what happens when we multiply both sides by -2?
Original: 7 < 10
Multiply both sides by -2:
7 × (-2) > 10 × (-2) → -14 > -20
The inequality flips because we multiplied by a negative number!
Remember: When multiplying by negatives, less than becomes greater than and vice versa!
Parent Tips 🌟
- Real-life examples: Use temperature changes (positive vs. negative) to explain why inequalities flip with negative multiplication.
- Hands-on practice: Write inequalities on index cards and have your child multiply both sides with different numbers to see what happens.
- Visual aid: Draw number lines to show how multiplying by negatives reflects numbers to the opposite side of zero.