On the SSAT, fractions, decimals, and percents are the same idea wearing three different costumes — and the test rewards students who can change costumes in a single step. This SSAT fractions decimals percents guide gives you the conversion rules, the equivalents chart you should memorize, and the percent-change shortcuts that make the no-calculator quantitative sections fast.
The SSAT does not test fractions, decimals, and percents as three separate topics — it tests how comfortably you can move between them. Computation problems on both Quantitative sections routinely give you a value in one form and ask you for an answer in another, and the fastest path to the answer almost always involves picking the most convenient form mid-problem. SSAT math fractions, percents, and decimals are connected skills, and treating them that way is the single biggest lever for raising your quantitative score.
The Middle and Upper Level SSAT each contain two Quantitative sections — Quantitative 1 near the start of the test after the writing sample, and Quantitative 2 near the end after the Verbal section — for a total of 50 multiple-choice math questions, each with five answer choices (A through E). Fractions, decimals, and percents appear in the Computation and Number Concepts content area, and they also show up indirectly inside algebra word problems, ratio-and-proportion questions, and statistics problems involving averages.
Calculators are not permitted on any SSAT math section. That means every conversion, every percent calculation, and every multi-step word problem has to be solved by hand or mentally. Students who can recognize that 3/8 is 0.375 (or that 25% of any number is one-quarter of it) finish problems in seconds instead of grinding through long division. Memorized fluency, not raw arithmetic speed, is the bottleneck on this test.
On the Middle and Upper Level SSAT, your raw score is the number of correct answers minus one-quarter of a point for each wrong answer. Random guessing on a five-choice question therefore has a slightly negative expected value, but eliminating even one or two answer choices flips the math in your favor. For fraction and percent problems, this is actually good news: estimating in fraction form often eliminates two or three obviously-wrong choices instantly.
| Feature | Middle Level | Upper Level |
|---|---|---|
| Number of math sections | 2 (Quant 1 + Quant 2) | 2 (Quant 1 + Quant 2) |
| Questions per section | 25 multiple choice | 25 multiple choice |
| Total math questions | 50 | 50 |
| Time per section | 30 minutes | 30 minutes |
| Answer choices per question | 5 (A–E) | 5 (A–E) |
| Calculator allowed? | No | No |
| Wrong-answer penalty | −1/4 point | −1/4 point |
| Section score range | 440–710 | 500–800 |
There are six possible directions of fraction decimal percent conversions, and each one has a single dependable rule. Once those six rules are automatic, the SSAT stops feeling like an arithmetic test and starts feeling like a translation exercise: read the problem, pick the easiest form, do one calculation, and answer.
The base method for converting a fraction to a decimal is plain long division: divide the numerator by the denominator and keep going until the decimal terminates or starts repeating. For 5/8, that is 5 ÷ 8 = 0.625. The catch on a non-calculator test is that long division eats time, so students who recognize the fraction as a memorized equivalent skip the division entirely.
Decimal to percent is the simplest rule on the test: move the decimal point two places to the right and add a percent sign. So 0.42 becomes 42%, and 1.05 becomes 105%. To go in the opposite direction — percent to decimal — move the decimal two places to the left and drop the percent sign. So 65% becomes 0.65, and 7.5% becomes 0.075. A common error here is moving the decimal in the wrong direction; if you ever feel unsure, sanity-check with a fact you know (50% should give 0.5, not 5).
To convert a fraction to a percent, treat it as two consecutive conversions: fraction to decimal first, then decimal to percent. So 3/8 → 0.375 → 37.5%. For very common fractions, the two-step process collapses into a single memorized jump (3/8 = 37.5%), which is exactly why the equivalents chart in the next section is worth memorizing in advance.
When the denominator of a fraction divides evenly into 10, 100, or 1000, you can skip long division entirely. Multiply the numerator and denominator by whatever it takes to make the denominator a power of 10, and you have your decimal (and your percent) by inspection. For 7/20, multiply both by 5 to get 35/100, which is 0.35 and 35%. This works because every percent is, by definition, a fraction with denominator 100.
| Convert From → To | Method | Example |
|---|---|---|
| Fraction → Decimal | Divide numerator by denominator (long division) | 3/4 → 3 ÷ 4 = 0.75 |
| Decimal → Fraction | Write digits over the appropriate power of 10, then simplify | 0.6 → 6/10 → 3/5 |
| Decimal → Percent | Move the decimal point two places to the right and add % | 0.42 → 42% |
| Percent → Decimal | Move the decimal point two places to the left and drop % | 65% → 0.65 |
| Fraction → Percent | Convert to a decimal first, then to a percent | 3/8 → 0.375 → 37.5% |
| Percent → Fraction | Write the percent over 100, then simplify | 40% → 40/100 → 2/5 |
Worked Example
Setup: Convert 7/20 to a percent without using a calculator.
Enter the numerator and denominator of any fraction and see the equivalent decimal and percent.
The following fraction percent equivalents come up so often on SSAT computation problems that memorizing them turns several test-day questions into instant recognition. Spend 15 minutes drilling this chart and you will save more than that on test day. Pay special attention to the eighths (often forgotten) and the thirds (often rounded incorrectly).
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.3% |
| 2/3 | 0.666… | 66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
These are the most-tested family of equivalents because every halving step is exact and easy. Start with 1/2 = 0.5 = 50%, halve it to get 1/4 = 0.25 = 25%, and halve again to get 1/8 = 0.125 = 12.5%. That single doubling pattern unlocks all of the eighths: 3/8 = 37.5%, 5/8 = 62.5%, 7/8 = 87.5%. SSAT problems involving discounts of 12.5% or 87.5% are instantly recognizable as 1/8 and 7/8 — a useful shortcut.
The trap with thirds is that 1/3 is exactly 0.333… (a repeating decimal), not 0.33. Treating 1/3 as 0.33 introduces a tiny error that grows when you multiply or compound it. On the SSAT, the cleaner move is to do thirds in fraction form whenever possible. The same caution applies to sixths: 1/6 = 0.1666…, 5/6 = 0.8333…, and so on. If a problem will produce a repeating result, work in fractions and only convert to a decimal at the very end.
Fifths follow a clean pattern: the numerator times 2 gives the digit in the tenths place. So 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8. Tenths are even simpler — the numerator just sits in the tenths place, so 7/10 = 0.7 = 70%. Combined, the fifths and tenths cover any value that is a clean multiple of 10%, which makes them especially useful on rapid estimation questions.
The percent of a number SSAT question is the most common variant of percent problem on the test, and it follows a fixed two-word translation: "of" means multiply, and "is" means equals. Once you internalize those translations, every percent problem reduces to a one-line equation.
The English phrase "what is 30% of 80" becomes the equation x = 0.30 × 80 = 24. The phrase "12 is what percent of 50" becomes 12 = p × 50, which gives p = 0.24, or 24%. Once the equation is on paper, the calculation is mechanical. The hard part is consistently identifying the whole (the number after "of") and the part (the number before or after "is").
For round-number percents, the decimal form is fast (50% × 80 = 0.5 × 80 = 40). But for many SSAT problems, the fraction equivalent is faster: 25% of 60 is easier as (1/4) × 60 = 15 than as 0.25 × 60. The rule of thumb is to scan the percent first — if it is a known fraction equivalent, use the fraction; otherwise, use the decimal. This is where the equivalents chart pays off.
Reverse questions ask for the percent itself: "12 is what percent of 50?" or "What percent of 200 is 30?" Set up the same equation, but solve for the percent: percent = part ÷ whole. Then convert the resulting decimal to a percent by moving the decimal two places. So 12/50 = 0.24 = 24%, and 30/200 = 0.15 = 15%. Many students invert this fraction by mistake — always put the part on top and the whole on the bottom.
Worked Example
Setup: What is 60% of 45?
SSAT percent problems involving change come in two flavors: questions that give you an old and new value and ask for the percent change, and questions that give you a starting value plus a percent change and ask for the result. There is one formula and one shortcut. Master both and these questions become formulaic.
The percent change formula is (New − Old) ÷ Old × 100%. The result is positive for an increase and negative for a decrease. The most common student error is using the new value as the denominator instead of the old value — always divide by the original (starting) value. So a price moving from $25 to $30 is (30 − 25)/25 × 100% = 5/25 × 100% = 20%.
For applied problems that give you a percent change and ask for the resulting value, the multiplier shortcut beats the formula. A 20% increase means multiplying by 1.20. A 15% decrease means multiplying by 0.85 (since 1 − 0.15 = 0.85). A jacket priced at $80 with a 25% discount becomes $80 × (1 − 0.25) = $80 × 0.75 = $60 in a single multiplication. This method also avoids the most common percent-change mistake — adding the change back to the wrong base.
Compound percent changes do not cancel, and SSAT word problems often exploit that fact. A value of 100 raised by 50% becomes 150, and 150 reduced by 50% becomes 75 — not 100. Using the multiplier method makes this transparent: 100 × 1.50 × 0.50 = 75, or 75% of the original. Anytime two percent changes happen in sequence, multiply the multipliers; do not add or subtract the percentages.
Worked Example
Setup: A jacket originally costs $80 and is on sale for 25% off. What is the sale price?
Enter an original (old) value and a new value to compute the percent increase or decrease using the SSAT formula.
The hardest SSAT math practice problems on this topic blend fractions, decimals, and percents into a single multi-step scenario. The strategy is always the same: pick one form to work in, translate the words into an equation, and only convert at the very end if the answer choices demand it.
When a problem gives you "3/5 of the class scored above 80%," the fraction 3/5 and the percent 80% are talking about two different things — 3/5 is a portion of students, while 80% is a score on a quiz. Read carefully to identify which quantity each value refers to. Then pick one consistent form (usually fractions, since they keep arithmetic exact) and work through the steps. Resist the urge to convert everything to decimals out of habit; fractions are often cleaner.
SSAT word problems frequently shift the base of a percent mid-problem. "A store reduces a $100 item by 20%, then takes an additional 10% off the sale price" is not the same as "a store reduces a $100 item by 30%." The 10% is taken from the new $80 sale price, not from the original $100. After each step, write down the current value and check what the next percent is being applied to. Multipliers help here too: ($100 × 0.80) × 0.90 = $72.
Before doing exact arithmetic, scan the answer choices. If they are far apart (say, 10, 25, 50, 75, 100), a rough estimate is enough to pick the right one. If they are close together (say, 47, 48, 50, 52, 53), you will need exact computation. Estimating in fraction form is usually the fastest: "3/5 of about 30 is about 18" eliminates two or three wrong choices instantly.
Worked Example
Setup: In a class of 30 students, 3/5 scored above 80% on a quiz. How many students scored 80% or below?
SSAT upper level math test-takers consistently lose points on percent and conversion problems for a small set of recurring reasons. Knowing the error patterns in advance is half the cure — when you sense one of these traps, slow down for ten seconds and verify.
The fraction 1/3 is exactly 0.333… (a repeating decimal), not 0.33. The 0.003… difference is small in isolation, but it grows when you multiply or compound it. On a non-calculator test, the cleanest fix is to do thirds in fraction form all the way through, and convert to a decimal only when the final answer requires it. The same logic applies to sixths, ninths, and any fraction whose denominator includes a 3.
A tax that rises from 5% to 7% is a 2 percentage-point increase, but a 40% percent increase. The two phrasings sound similar, but they describe completely different quantities. SSAT problems sometimes use this distinction to set a trap. When a question asks for "percent change" or "percent increase," apply the formula (New − Old) ÷ Old × 100%. When the question simply asks for the difference, subtract.
The percent change formula always divides by the OLD value. A common error is dividing by the new value, or by the average of the two. So a price moving from $40 to $50 is a 25% increase ((50 − 40)/40 × 100%), not 20% ((50 − 40)/50 × 100%). Anchor on the rule "divide by where you started," and double-check the denominator before you compute.
Use this checklist to confirm you have covered every angle of fractions, decimals, and percents that the SSAT can throw at you. If you cannot tick all six items, go back to the relevant section above before moving on.
Yes. They appear throughout both Quantitative sections of the Middle and Upper Level SSAT as part of the Computation and Number Concepts content area. Expect direct conversion questions, percent-of-a-number problems, percent change word problems, and multi-step problems that mix all three forms. Because the SSAT does not allow calculators, fluency between fractions, decimals, and percents is essential for finishing on time.
No. Calculators are not permitted on any SSAT math section, so every fraction, decimal, and percent calculation must be done by hand or mentally. This is why memorizing the most common fraction-decimal-percent equivalents (halves, quarters, thirds, fifths, eighths, and tenths) is one of the highest-leverage prep activities for the quantitative sections.