🎓 GED · MATH

GED® Math Foundations: Integer & Rational Number Operations Mastery

A structured 24-session GED® Mathematical Reasoning foundation course on number-line meaning, opposites, absolute value, equivalent rational forms, signed integers and their operations, decimal and fraction operations, multi-step expressions, real-world positive and negative contexts, estimation, error analysis, and GED® problem-solving strategy. Each session includes 15 progressively challenging MCQs, followed by a 46-question cumulative final exam. The course strengthens the sign control students need before algebra, formulas, graphing, and word problems.

📚 24 sessions 📝 406 practice questions ⏰ Self-paced ✅ 100% Free
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Course Map

📚 Course Curriculum

24 sessions organized as a guided path, with 3 trial sessions open before enrollment.

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1. Integers, Direction, and the Number Line. Learning Targets. Interpret signs as direction from zero. Locate integers on a number line. Translate context words into …

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2. Opposites and Additive Inverses. Learning Targets. Identify the opposite of any rational number. Recognize additive inverses and zero pairs. Separate opposite from reciprocal and …

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3. Comparing and Ordering Integers. Learning Targets. Compare signed integers. Order several integers. Use \(<\), \(>\), and \(=\) accurately. Why This Matters. GED® choices often …

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4. Absolute Value as Distance. Learning Targets. Interpret absolute value as magnitude. Find distance between two values. Solve simple absolute-value statements. Why This Matters. Absolute …

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5. Rational Numbers on the Number Line. Learning Targets. Recognize integers as rational numbers. Locate signed fractions and decimals. Compare rational values using common forms. …

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6. Equivalent Fractions, Decimals, and Percents. Learning Targets. Convert rational-number forms. Use benchmark values. Preserve negative signs during conversion. Why This Matters. Equivalent forms let …

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7. Adding Integers with the Same Sign. Learning Targets. Add like-signed integers. Connect addition to movement. Predict sign and magnitude. Why This Matters. Like-sign addition …

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8. Adding Integers with Different Signs. Learning Targets. Add unlike-signed values. Use magnitude to determine sign. Recognize cancellation. Why This Matters. Unlike-sign addition appears constantly …

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9. Subtracting Signed Numbers. Learning Targets. Rewrite subtraction as addition. Subtract positive and negative values. Explain subtraction of a negative. Why This Matters. One dependable …

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10. Multi-Step Integer Addition and Subtraction. Learning Targets. Evaluate several signed changes. Group zero pairs. Distinguish final position from distance. Why This Matters. Real balances, …

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11. Multiplying Signed Numbers. Learning Targets. Determine a product's sign. Multiply signed magnitudes. Explain the sign rule. Why This Matters. Multiplication has a different sign …

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12. Dividing Signed Numbers. Learning Targets. Determine a quotient's sign. Verify division with multiplication. Apply zero restrictions. Why This Matters. Division reverses multiplication, so it …

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13. Products and Quotients with Multiple Negatives. Learning Targets. Use negative-factor parity. Evaluate chained products and quotients. Handle zero factors. Why This Matters. Long products …

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14. Negative Bases, Exponents, and Parentheses. Learning Targets. Evaluate negative bases. Distinguish \((-a)^n\) from \(-a^n\). Apply operation order. Why This Matters. Parentheses can completely change …

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15. Adding and Subtracting Signed Decimals. Learning Targets. Align place values. Apply signed addition rules. Estimate decimal results. Why This Matters. Decimal work combines place-value …

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16. Multiplying and Dividing Signed Decimals. Learning Targets. Apply sign rules to decimal products. Place decimal points. Verify scale by estimation. Why This Matters. A …

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17. Adding and Subtracting Signed Fractions. Learning Targets. Build common denominators. Combine signed numerators. Simplify and verify. Why This Matters. Fractions demand denominator work and …

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18. Multiplying Signed Fractions and Mixed Numbers. Learning Targets. Convert mixed numbers. Determine sign and cancel factors. Simplify products. Why This Matters. A fixed sequence …

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19. Dividing Signed Fractions. Learning Targets. Identify the divisor. Multiply by its reciprocal. Verify with multiplication. Why This Matters. Fraction division works when exactly the …

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20. Multi-Step Rational Expressions. Learning Targets. Apply order of operations. Track rational-number signs. Use intermediate estimates. Why This Matters. GED® expressions combine several skills instead …

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21. Money, Debt, Profit, and Loss. Learning Targets. Translate financial language. Calculate balances. Interpret negative results. Why This Matters. Financial contexts make signed arithmetic concrete …

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22. Temperature, Elevation, Rates, and Change. Learning Targets. Model values relative to a reference. Calculate change as final minus initial. Separate value, change, and distance. …

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23. Comparing, Estimating, and Error Analysis. Learning Targets. Predict sign and size. Compare signed rational values. Diagnose calculator and reasoning errors. Why This Matters. Estimation …

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24. GED® Signed-Number Strategy and Cumulative Review. Learning Targets. Select efficient mixed-problem methods. Explain and verify signs. Use an exam-ready correction routine. Why This Matters. …

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Course Guide

Course Syllabus

GED® Math Foundations: Integer & Rational Number Operations Mastery

Course Overview

This 24-session GED® Mathematical Reasoning course develops reliable control of signed integers and rational numbers. Learners move from number-line meaning and equivalent forms to fluent operations with integers, decimals, fractions, and mixed numbers. The final stage applies those skills to money, temperature, elevation, change, estimation, calculator use, and mixed GED®-style problems.

The course emphasizes meaning before memorization. Every operation connects to direction, distance, grouping, or scaling. Each session follows a repeatable cycle: interpret, represent, calculate, explain, check, and correct.

Course Information

  • Program: GED®
  • Subject: Mathematical Reasoning / Quantitative Problem Solving
  • Length: 24 sessions
  • Recommended pace: 3 sessions per week for 8 weeks
  • Study time: 45-60 minutes per session, plus correction time
  • Prerequisites: Whole-number arithmetic and basic fraction/decimal notation
  • Recommended mastery target: At least \(80\%\)
  • Calculator use: Mental prediction first; calculator verification when helpful

GED® Skill Alignment

Learners compare rational numbers, use absolute value, compute with signed integers/decimals/fractions, distinguish negative bases, evaluate multi-step expressions, translate real contexts, estimate results, and diagnose sign or calculator errors. These skills support GED® algebra, geometry, data analysis, formulas, and word problems.

Learning Routine

  1. Name the quantity. Decide what each number represents and what zero means.
  2. Attach the sign. Translate gain, loss, above, below, rise, and fall.
  3. Choose a representation. Use a number line, fraction model, decimal place value, or expression.
  4. Predict. Decide the expected sign, scale, and benchmark range.
  5. Calculate. Apply the rule and show the critical intermediate step.
  6. Verify. Estimate, reverse the operation, or substitute.
  7. Correct. Record the error type and a prevention habit.

Course Outline

SessionTopicEssential skill
1Integers, Direction, and the Number LineInterpret signs as direction from zero.
2Opposites and Additive InversesIdentify the opposite of any rational number.
3Comparing and Ordering IntegersCompare signed integers.
4Absolute Value as DistanceInterpret absolute value as magnitude.
5Rational Numbers on the Number LineRecognize integers as rational numbers.
6Equivalent Fractions, Decimals, and PercentsConvert rational-number forms.
7Adding Integers with the Same SignAdd like-signed integers.
8Adding Integers with Different SignsAdd unlike-signed values.
9Subtracting Signed NumbersRewrite subtraction as addition.
10Multi-Step Integer Addition and SubtractionEvaluate several signed changes.
11Multiplying Signed NumbersDetermine a product's sign.
12Dividing Signed NumbersDetermine a quotient's sign.
13Products and Quotients with Multiple NegativesUse negative-factor parity.
14Negative Bases, Exponents, and ParenthesesEvaluate negative bases.
15Adding and Subtracting Signed DecimalsAlign place values.
16Multiplying and Dividing Signed DecimalsApply sign rules to decimal products.
17Adding and Subtracting Signed FractionsBuild common denominators.
18Multiplying Signed Fractions and Mixed NumbersConvert mixed numbers.
19Dividing Signed FractionsIdentify the divisor.
20Multi-Step Rational ExpressionsApply order of operations.
21Money, Debt, Profit, and LossTranslate financial language.
22Temperature, Elevation, Rates, and ChangeModel values relative to a reference.
23Comparing, Estimating, and Error AnalysisPredict sign and size.
24GED® Signed-Number Strategy and Cumulative ReviewSelect efficient mixed-problem methods.

Assessment and Mastery

Every session ends with a checkpoint, and course-level multiple-choice practice provides cumulative retrieval. Progress when representative work reaches at least \(80\%\), the sign can be explained before calculation, and missed items can be corrected independently.

Classify mistakes as a meaning error, sign error, operation error, fraction/decimal error, order-of-operations error, calculator-entry error, or question-reading error. For each missed item, state the correct relationship and solve one similar problem.

Required Materials

  • Notebook or digital notes
  • Pencil and scratch paper
  • Number-line sketch space
  • Fraction/decimal reference sheet if needed
  • Scientific calculator or GED® onscreen-calculator practice
  • Course lessons and cumulative practice
Learning Results

Course Outcomes

Course Outcomes

By the end of the 24 sessions, learners will be able to:

Representation and Number Sense

  1. Interpret positive and negative values in directional and real-world contexts.
  2. Locate integers, fractions, and decimals on a number line.
  3. Identify opposites, additive inverses, and zero pairs.
  4. Compare and order signed rational numbers using \(<\), \(>\), and \(=\).
  5. Use absolute value to describe magnitude and distance.
  6. Convert common values among fraction, decimal, and percent forms.
  7. Use \(0\), \(\tfrac12\), and \(1\) as rational-number benchmarks.

Integer Operations

  1. Add like-signed and unlike-signed integers using magnitude reasoning.
  2. Rewrite subtraction as addition of the opposite.
  3. Multiply and divide signed integers.
  4. Explain zero-product and division-by-zero rules.
  5. Determine signs of products and quotients with multiple negatives.
  6. Distinguish \((-a)^n\) from \(-a^n\).
  7. Evaluate multi-step integer expressions in the correct order.

Rational-Number Operations

  1. Add and subtract signed decimals with aligned place values.
  2. Multiply and divide signed decimals and verify decimal scale.
  3. Add and subtract signed fractions using common denominators.
  4. Multiply signed fractions and mixed numbers in simplest form.
  5. Divide signed fractions using the divisor's reciprocal.
  6. Evaluate multi-step expressions containing integers, decimals, fractions, grouping, and exponents.

Application and GED® Readiness

  1. Model gains, losses, deposits, debts, temperatures, and elevations.
  2. Distinguish final value, signed change, distance, and absolute difference.
  3. Predict sign and approximate size before exact calculation.
  4. Verify answers with inverse operations, substitution, estimation, and calculator re-entry.
  5. Diagnose common sign, reciprocal, decimal, and question-reading errors.
  6. Solve mixed GED®-style rational-number problems with accurate notation and units.

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📝 Practice Questions

406 interactive questions with instant feedback and explanations.

Enroll for free to unlock the full practice bank after the trial sessions.