Multiplication and Division Properties for Inequalities (Positive Numbers)
Multiplication and division properties for inequalities with positive numbers is a Grade 6 algebra skill in Big Ideas Math Advanced 1, Chapter 7: Equations and Inequalities. Students learn that multiplying or dividing both sides of an inequality by the same positive number preserves the inequality direction, allowing them to solve one-step inequalities.
Key Concepts
When solving inequalities, you can multiply or divide both sides by the same positive number to get an equivalent inequality. The inequality sign stays the same when multiplying or dividing by positive numbers.
Multiplication by a positive number: If $a < b$ and $c 0$, then $ac < bc$.
Common Questions
How do you solve inequalities using multiplication or division?
Multiply or divide both sides of the inequality by the same positive number, keeping the inequality symbol unchanged. For example, 3x > 12 — divide both sides by 3 to get x > 4.
Does the inequality sign flip when multiplying by a positive number?
No. The inequality sign only flips when you multiply or divide by a negative number. With positive numbers, the direction stays the same.
What is the multiplication property of inequality?
If a > b and c is a positive number, then a x c > b x c. The inequality direction is preserved when multiplying both sides by the same positive value.
Where is this skill taught in Big Ideas Math Advanced 1?
Multiplication and division properties for inequalities are covered in Chapter 7: Equations and Inequalities of Big Ideas Math Advanced 1, the Grade 6 math textbook.