Undo a Fractional Coefficient
A coefficient can be a fraction, such as one half.
About 20 minutes, plus any extended practice
Open lesson 1Equations and Inequalities with Rational Structure
Solving means finding inputs that make a relationship true. Balanced operations preserve equality, whereas inequality direction must reverse when multiplication or division by a negative number reverses number-line order.
Before you begin
- Use fraction arithmetic; interpret equalities, strict inequalities and at-most language.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Choose an Efficient Balanced Operation
A nonzero factor multiplying an entire group can be divided out before expanding.
About 20 minutes, plus any extended practice
Open lesson 2Reverse the Direction when Dividing by a Negative
Multiplying an ordered pair of numbers by a negative reflects their positions across zero.
About 20 minutes, plus any extended practice
Open lesson 3Combine a Cost Cap with Whole-Number Counts
An at-most constraint includes its boundary and can be expressed with ≤.
About 20 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- California CCSS mathematics topic reference: topic reference — Equations and Inequalities with Rational Structure
These references informed the topic selection. They do not certify complete standards alignment.