What Are Inequalities?
Inequalities help us compare numbers and expressions!
Just like a balance scale shows which side is heavier, inequalities show us which number is bigger or if they're equal. We use special symbols: < (less than), > (greater than), and = (equal to).
How Inequalities Work with Operations
1️⃣ Addition/Subtraction: Adding or subtracting the same number keeps the inequality the same
2️⃣ Multiplication/Division: Multiplying or dividing by positive numbers keeps the inequality the same
3️⃣ Special Rule: Multiplying or dividing by negative numbers flips the inequality!
Let's Explore with Examples
Example 1: The Cookie Jar Mystery
Sarah has 12 cookies and her brother has 8. After they each eat 3 cookies, who has more?
After eating 3 cookies each:
Example 2: The Lemonade Stand
Tom's lemonade costs \$2 per cup. He knows that 5 × \$2 < 4 × \$3. Is this true? What if prices double?
5 × \$2 = \$10
4 × \$3 = \$12
\$10 < \$12 is correct!
After doubling:
5 × \$4 = \$20
4 × \$6 = \$24
\$20 < \$24 is still correct! The inequality stayed the same.
Parent Tips 🌟
- Kitchen Math: Use measuring cups to show inequalities (½ cup < ¾ cup) and how operations affect them
- Allowance Comparison: Compare siblings' allowances before/after chores (addition/subtraction) or raises (multiplication)
- Game Night: Play "Inequality War" with cards - flip two cards each, create an expression, and determine which is greater