📖 The Lesson
Fractions, mixed numbers, improper fractions, decimals, and negative numbers look very different from each other — but every one of them is just a location on the same number line. When the GED asks you to order numbers, drag them least-to-greatest, or figure out which value sits at a labeled point, it is really asking one thing: where does each number live on the line?
The main point: when number forms are mixed together, the fastest move is usually to think in decimals — and you rarely need exact decimals. Most of the time a quick estimate is enough to compare numbers and eliminate wrong answers.
What the GED actually asks. The questions almost always come down to comparing and ordering: drag numbers from least to greatest, drag them from greatest to least, order a mix of fractions, decimals and negatives, find the value at a letter on a number line, or pick which number belongs at a spot. You are not being asked to compute — you are being asked which is bigger.
Your most powerful tool: benchmarks
Memorize these four spots between 0 and 1. You will use them constantly to estimate almost any fraction.
The benchmark number line (0 to 1)
00
¼0.25
½0.50
¾0.75
11.00
Benchmark Estimating
Compare a fraction to ¼, ½, ¾, and 1.
23 is a little larger than ½ (about 0.67).
78 is very close to 1 (about 0.88).
310 is just above ¼ (0.30).
54 is larger than 1 because it equals 1¼ (1.25).
Benchmark reasoning is usually faster than calculating exact values.
Place value (the #1 decimal trap)
The most common decimal mistake on the GED is thinking a longer decimal is automatically larger. It is not. Compare digit by digit, and add trailing zeros so both numbers have the same length.
Compare 5.06 and 5.015.
Add a zero so they line up: 5.060 and 5.015.
Tenths: 0 = 0. Hundredths: 6 vs 1 → 6 wins.
So 5.06 > 5.015 — even though 5.015 has more digits.
The rule: line up the decimal points, add trailing zeros until both numbers have the same number of decimal places, then compare digits left to right. More digits does NOT mean bigger. Quick checks: 0.8 > 0.75, 2.1 > 2.09, 3.50 = 3.5, 4.07 > 4.007, 0.45 > 0.405.
Mixed numbers & improper fractions
GED questions mix these forms together, so you need to slide between them comfortably.
Improper → Mixed
Divide top by bottom.
114 : 4 goes into 11 two times with 3 left over.
So 114 = 234.
Mixed → Improper
(whole × bottom) + top.
234 : (2 × 4) + 3 = 11.
Keep the same bottom → 114.
Fraction-to-decimal benchmarks to know cold
½ = 0.5 · ¼ = 0.25 · ¾ = 0.75
110 = 0.1 ·
15 = 0.2 ·
25 = 0.4 ·
35 = 0.6 ·
45 = 0.8
Knowing these lets you turn most fractions into decimals instantly and eliminate answer choices without doing any division.
Ordering fractions
Same bottom number? Just compare the tops. Bigger top = bigger fraction: 38 < 58 < 78. The GED is rarely this kind, but it builds the idea.
Different bottoms? Estimate as decimals before reaching for common denominators — it's usually faster:
12 = 0.5
58 ≈ 0.625
34 = 0.75
Order: 12 < 58 < 34
Need a sharper estimate? Divide top by bottom — you usually only need one or two decimal places.
57 → 5 ÷ 7
5.000 ÷ 7 ≈ 0.714
That's enough to know it sits between 0.7 and 0.75.
Don't convert everything
Strong test-takers often order numbers with almost no calculation. Look at this set: 78, 12, 1¼.
78 is close to 1. 12 is 0.5. 1¼ is more than 1.
Without dividing anything: 12 < 78 < 1¼.
Convert only when you must. Estimation is faster, safer, and less error-prone than turning every number into an exact decimal.
Negative numbers
With negatives, the number further from zero is the smaller one. So −5 is smaller than −2, because −5 is further from zero. A common trap is thinking −5 is bigger because 5 is bigger than 2 — it's the opposite.
Further from zero on the left = smaller (−5 is less than −2)
Finding a value at a letter
When a letter sits on a number line, work out the size of one interval, then count over.
Step 1. Find two labeled values.
Step 2. Count the equal intervals between them.
Step 3. Interval size = (distance) ÷ (number of intervals).
Step 4. Count from a label to the letter.
Step 5. Match the value.
Point A sits two ticks past 0, with 4 ticks from 0 to 1 → each tick = ¼, so A = ½
Elimination strategies
If a value is between ½ and ¾, cross out any choice below 0.5 or above 0.75.
If a number is greater than 1, cross out every choice less than 1.
If a fraction is close to 1, cross out values near 0.5.
You often don't need the exact answer — just enough to delete the impossible ones until one remains.
Common mistakes to avoid:
- Negatives go the other way. −5 is further from zero than −2, so −5 is the smaller (more negative) number. Don't let "5 is bigger than 2" trick you.
- A longer decimal isn't automatically bigger. 5.015 has more digits than 5.06, but 5.06 is larger. Add zeros so both are the same length, then compare.
- Misreading a mixed number. 2 ¾ means 2 plus ¾ (about 2.75) — not 2 times ¾.
- Converting an improper fraction wrong. For 11/4, divide: 11 ÷ 4 = 2 remainder 3, so 2 ¾. Don't just guess.
- Ordering fractions by the bottom number alone. A bigger denominator does not mean a bigger fraction — ⅛ is smaller than ½.
- Ignoring benchmarks. Anchor to 0, ½, and 1 instead of crunching every value from scratch.
- Converting everything. If an estimate already tells you the order, you've wasted time doing exact long division.