6.1 Integers, Fractions, Decimals, and Percent
Key Takeaways
- GED number sense questions often require converting among integers, fractions, decimals, and percents before comparing or calculating.
- A negative sign changes direction on the number line, so a larger absolute value can mean a smaller number when the value is negative.
- Fractions are best for exact part-whole relationships, while decimals and percents are often faster for money, measurement, and percent-change contexts.
- Percent problems usually use part = percent x whole, or percent change = change divided by original amount.
- Reasonableness checks catch the most common GED errors: wrong sign, wrong denominator, misplaced decimal point, and discount-tax order mistakes.
Why Number Form Matters on GED Math
GED Mathematical Reasoning does not usually ask you to show arithmetic in isolation. It asks whether you can use rational numbers to solve a realistic problem, compare quantities, or decide whether an answer is reasonable. That means integers, fractions, decimals, and percents are not separate topics. They are different ways to represent the same amount.
A strong strategy is to convert numbers to the form that makes the relationship easiest to see. Fractions show exact parts. Decimals are convenient for money and calculator work. Percents show a part of 100 and are common in tax, discounts, tips, commissions, interest, and percent increase or decrease.
Equivalent Forms You Should Know
| Form | Meaning | Common GED Use |
|---|---|---|
| 3/4 | Three parts out of four | Exact part of a group or measurement |
| 0.75 | Seventy-five hundredths | Money, measurement, calculator comparison |
| 75% | 75 out of 100 | Discounts, tax, percent change |
| -6 | Six units below zero | Temperature, debt, elevation, loss |
Memorize a few benchmarks: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, and 1/10 = 0.1 = 10%. These let you estimate quickly even when the calculator is not available.
Ordering Rational Numbers
To order mixed forms, choose one format. Decimals are often fastest for comparison.
Worked example: Order -3/4, -0.62, 2/5, and 0.08 from least to greatest.
Convert the fractions: -3/4 = -0.75 and 2/5 = 0.40. Now compare: -0.75, -0.62, 0.08, 0.40. The least value is farthest left on the number line, so the order is -3/4, -0.62, 0.08, 2/5.
Notice the negative-number trap. Since -0.75 is farther from 0 than -0.62, it is smaller, not larger.
Operating With Signs
For addition and subtraction, think of movement on a number line. For multiplication and division, track signs separately: same signs give a positive result, and different signs give a negative result.
Worked example: A freezer is at -8 degrees. It warms by 13 degrees, then cools by 5 degrees. What is the final temperature?
Start with -8. Warming means add: -8 + 13 = 5. Cooling means subtract: 5 - 5 = 0. The final temperature is 0 degrees.
When a problem has several signed changes, write each change in order before calculating. A debt payment increases your balance, a fee decreases it, a temperature rise adds, and a temperature drop subtracts. This habit is more reliable than trying to decide whether the final answer should be positive or negative at the end.
Percent Problems
Use one of two setups.
- Percent of a number: part = percent x whole.
- Percent change: percent change = change / original.
Worked example: A $60 tool is marked down 15%, then sales tax of 8% is added to the sale price. What is the final cost?
The discount is 15% of 60, or 0.15 x 60 = 9. The sale price is 60 - 9 = 51. Tax is 8% of 51, or 0.08 x 51 = 4.08. Final cost is 51 + 4.08 = $55.08.
Percent increase and decrease questions must use the original amount as the base. If a value rises from 40 to 50, the change is 10 and the original is 40, so the percent increase is 10/40 = 25%. Dividing by the new value gives a different question.
A GED-style check: a 15% discount lowers $60 to a little above $50, and 8% tax adds about $4. A final answer near $55 makes sense.
A balance starts at -$24. A payment of $50 is added, then a $17 fee is charged. What is the final balance?
A jacket costs $48. It is discounted by 25%, and then 8% sales tax is added to the sale price. What is the final cost?