GEDStudy Topic
GED Mathematical Reasoning Foundations Study Guide
Review fractions, rates, percentages, equations, graphs, probability, and basic geometric measurement.
Topic Overview
Start with the requested quantity
Before computing, write what the answer should measure. Pay has dollar units, a travel rate has miles per hour, area has square units, and volume has cubic units. This habit helps identify the correct operation. If a car travels 336 miles using 12 gallons, dividing distance by fuel gives 28 miles per gallon.
Keep the base and total distinct
A discount amount is not the sale price: subtract the discount from the original price. A ratio of one ingredient to another is not automatically the ingredient’s fraction of the total. For a percentage increase, divide the change by the original value. With fractions, use a common denominator for addition but multiply numerators and denominators directly for multiplication.
Connect representations
A table, graph, equation, and written description may express the same relationship. A constant input-output rate appears as a line, and the zero-input value gives the intercept. Check an equation’s solution by substitution. For geometry, draw and label the figure, distinguish radius from diameter, and use a perpendicular height in a triangle’s area formula. Estimate the size of the answer before selecting an option.
- Reporting a discount instead of the final price.
- Confusing perimeter, area, and volume.
- Using the wrong base for a percentage.
- Ignoring units when selecting multiplication or division.
Checkpoint Quiz
Test your understanding of GED Mathematical Reasoning Foundations
These questions are for study practice only and are not official exam questions.
1. A worker earns $18 per hour for 7 hours. What is the total pay before deductions?
2. A room is 12 feet long and 9 feet wide. What is its floor area?
3. Solve 5x - 8 = 27.
4. The formula C = 15 + 4h gives a rental cost in dollars for h hours. What is the cost for 6 hours?
5. A family buys 2 adult tickets and 3 child tickets for $39. Adult tickets cost $12 each. What does one child ticket cost?
6. A bus travels 150 miles in 3 hours at a constant speed. How far does it travel in 5 hours at that speed?
7. A tank holds 40 gallons when full and currently contains 30 gallons. What fraction of its capacity is filled?
8. A line passes through (0, 2) and (3, 8). Which equation describes it?
9. A bag contains 6 black and 4 white buttons. One is chosen at random. What is the probability of choosing white?
10. Solve the inequality 3x + 2 <= 14.
Frequently asked questions
How do I find a unit rate?
Divide the total amount by the number of units, keeping the desired units in the quotient.
Why estimate before calculating?
An estimate helps detect decimal, unit, or operation errors in the final result.
What is the median?
The middle value after sorting, or the average of the two middle values when the count is even.
How do I check an equation solution?
Substitute the value into the original equation and verify that both sides agree.
