GED® Ratios, Proportions and Scale Factors
A focused 24-session GED® Mathematical Reasoning course on ratios, equivalent ratios, proportions, ratio tables, part-to-part and part-to-whole reasoning, scale drawings, map scales, similar figures, direct variation, percent proportions, and multi-step proportional word problems. The course strengthens one of the most common GED® quantitative reasoning patterns.
📚 Course Curriculum
A ratio compares quantities. The comparison can be part-to-part or part-to-whole, and the difference matters. If a class has 12 students studying math and 8 …
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Equivalent ratios name the same comparison. You create an equivalent ratio by multiplying or dividing both parts by the same nonzero number:. Ratio tables organize …
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A proportion is an equation that says two ratios are equivalent:. This can model recipes, maps, similar shapes, scale drawings, and percent problems. [[figure:proportion_cross_products Cross …
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A unit rate is a ratio with 1 in the denominator. It tells how much for one unit:. [[figure:rate_double_number_line A double number line shows two …
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In part-whole ratio problems, the ratio parts add to the total number of equal parts. Example: Blue and green tiles are in the ratio \(3:2\). …
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A scale drawing represents a real object at a smaller or larger size. A map is a scale drawing of distance. [[figure:map_scale_distance A map scale …
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Similar figures have the same shape but not necessarily the same size. Corresponding angles are equal, and corresponding side lengths are proportional. [[figure:similar_rectangles_scale Every corresponding …
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Lengths, areas, and volumes scale differently. If the length scale factor is \(k\), then:. corresponding lengths multiply by \(k\). areas multiply by \(k^2\). volumes multiply …
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A direct variation relationship has the form:. The number \(k\) is the constant of proportionality. It is also the unit rate:. Example: A car travels …
Open trial session →Percent means "per hundred," so many percent problems are proportions:. Example: What is 30% of 80?. Cross-multiply:. Percent increase and decrease also use part-whole thinking. …
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GED® proportional reasoning often appears in multi-step word problems. The challenge is deciding which relationship is proportional and which extra step is needed. Example: A …
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Ratios and proportions can be solved in several valid ways. Choose the strategy that makes the structure clearest. Useful strategies:. Simplify ratios when comparing. Use …
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GED® ratio questions often switch between fractions, decimals, and percents. The relationship is the same comparison written in different forms:. The safest conversion path is …
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Double number lines and tape diagrams make proportional relationships visible before you calculate. [[figure:rate_double_number_line A double number line keeps two related quantities aligned.]]. If 4 …
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A rate compares quantities with different units, such as miles per hour, dollars per pound, or gallons per minute. GED® questions often add a unit …
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Unit-price problems ask for cost per one item, ounce, pound, or unit. The best buy is usually the lower unit price, not the lower total …
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Mixture and recipe problems are ratio problems with context. The key is to preserve the relationship among ingredients. Example: A cleaner uses 2 cups concentrate …
Open trial session →Percent change is proportional reasoning with the original amount as the reference. If a price rises from \(\$80\) to \(\$92\), the change is \(\$12\). The …
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Scale drawings are proportional, but measurements can still include rounding or small error. If a map scale is 1 inch = 12 miles and a …
Open trial session →Similar triangles appear in GED® problems about shadows, ramps, indirect measurement, and maps. The triangles have equal corresponding angles and proportional corresponding sides. Example: A …
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Slope is a ratio:. If a line goes through \((2,5)\) and \((6,13)\), then:. and. So:. Slope is a unit rate when the axes have units. …
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Many GED® questions test whether a relationship is proportional before asking you to calculate. A relationship is proportional when:. the ratio \(y/x\) is constant. the …
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Harder GED® ratio questions are not harder because the arithmetic is wild. They are harder because the setup has more than one step. Use a …
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This final session brings the whole course together. GED® proportional reasoning can appear as a ratio, percent, graph, table, map, recipe, rate, similar figure, or …
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Course Syllabus
Course Outline
| Session | Focus |
|---|---|
| 1 | Ratio Language: Part-to-Part and Part-to-Whole |
| 2 | Equivalent Ratios and Ratio Tables |
| 3 | Proportions and Cross Products |
| 4 | Unit Rates as a Proportional Reasoning Tool |
| 5 | Part-Whole Ratio Problems |
| 6 | Scale Drawings and Map Scales |
| 7 | Similar Figures and Scale Factor |
| 8 | Scale Factor for Area and Volume |
| 9 | Direct Variation and Constant of Proportionality |
| 10 | Percent Proportions and Percent Models |
| 11 | Multi-Step Proportional Word Problems |
| 12 | Choosing a Strategy and Checking Reasonableness |
| 13 | Fractions, Decimals, Percents, and Ratio Fluency |
| 14 | Double Number Lines and Tape Diagrams |
| 15 | Rates with Unit Conversions |
| 16 | Unit Price, Best Buy, and Workplace Rates |
| 17 | Mixture and Recipe Scaling |
| 18 | Percent Change, Markups, Discounts, and Tax |
| 19 | Scale Drawing Precision and Measurement Error |
| 20 | Similar Triangles in Context |
| 21 | Slope as a Rate and Ratio |
| 22 | Proportional vs. Nonproportional Relationships |
| 23 | GED® Multi-Step Strategy: Read, Model, Solve, Check |
| 24 | Cumulative Ratios, Proportions, and Scale Factors Review |
The course moves from basic ratio language to GED®-style mixed problems involving tables, graphs, maps, scale drawings, similar figures, percent models, unit rates, and contextual judgment.
Course Outcomes
By the end of this 24-session course, students will be able to:
- Distinguish part-to-part and part-to-whole ratios.
- Build and interpret equivalent ratios, ratio tables, tape diagrams, and double number lines.
- Solve proportions using unit rates, scaling, and cross products.
- Apply proportional reasoning to recipes, maps, unit prices, rates, percent, and similar figures.
- Use scale factors correctly for lengths, areas, and volumes.
- Identify direct variation and explain why some linear or real-world relationships are not proportional.
- Convert units inside proportional word problems without reversing the scale.
- Check GED®-style answers for labels, magnitude, units, and contextual reasonableness.
📝 Practice Questions
360 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.