ISEE fractions decimals percents questions show up on every level of the test, and they are the single highest-yield topic to practice because the same handful of conversions and shortcuts unlock dozens of questions across both math sections. Because the ISEE bans calculators, the students who win this topic are the ones who can convert between forms in under a second — and that is what this guide will train you to do.
ISEE Mathematics Achievement fractions, decimals, and percents questions are spread across two scored math sections, and the count varies by level. Knowing exactly where they appear lets you allocate prep time intelligently — the topic carries far more weight than its name suggests.
Mathematics Achievement tests direct calculations: convert this fraction, find this percent, compute this decimal. Quantitative Reasoning is more concept-oriented — word problems and quantitative comparisons that often contain a fraction or percent step inside a larger setup.
On Middle and Upper Levels, Mathematics Achievement gives you 47 questions in 40 minutes (42 scored, 5 experimental). Roughly 7-10 of those questions test decimals, percents, and fractions head-on. Add the fraction and percent skills hidden inside Quantitative Reasoning word problems, and the topic ends up driving close to a quarter of your total math score.
| ISEE Level | Math Achievement (Q / Time) | Quantitative Reasoning (Q / Time) | Approx. F-D-P Questions |
|---|---|---|---|
| Lower (Grades 5-6) | 30 Q / 30 min | Not separated — math is one combined section | 5-7 |
| Middle (Grades 7-8) | 47 Q / 40 min | 37 Q / 35 min | 7-10 in Math Achievement, plus more in QR word problems |
| Upper (Grades 9-12) | 47 Q / 40 min | 37 Q / 35 min | 7-10 in Math Achievement, plus more in QR word problems |
Calculators are banned on every section of the ISEE — which is why this topic rewards memorization so heavily. A student who can recognize 7/8 as 87.5% in one second has a real arithmetic advantage over a student who has to long-divide 7 by 8 on scratch paper. With about 50 seconds per question on Math Achievement, those instant recognitions buy time for the harder problems.
Every ISEE question that asks you to convert fractions decimals percents falls into one of six directions. The cheat sheet below walks through each direction with a worked example.
There are exactly six ways to move between the three forms — fraction to decimal, decimal to fraction, decimal to percent, percent to decimal, fraction to percent, and percent to fraction. Knowing the operation for each one is non-negotiable.
| From | To | Method | Example |
|---|---|---|---|
| Fraction | Decimal | Divide numerator by denominator (or scale to /10, /100, /1000) | 3/4 = 3 ÷ 4 = 0.75 |
| Decimal | Fraction | Read aloud → write that → simplify | 0.6 = six tenths = 6/10 = 3/5 |
| Decimal | Percent | Multiply by 100 (move decimal 2 places right) | 0.42 = 42% |
| Percent | Decimal | Divide by 100 (move decimal 2 places left) | 65% = 0.65 |
| Fraction | Percent | Divide, then × 100 — or scale denominator to 100 | 3/20 = 15/100 = 15% |
| Percent | Fraction | Write over 100, then simplify | 40% = 40/100 = 2/5 |
Use this quick decision rule. Scale when the denominator is a factor of 100: 2, 4, 5, 10, 20, 25, or 50. For example, 7/20 = 35/100 = 35% in one mental step. Memorize when the denominator is 3, 6, 8, 9, or 12 — these never scale cleanly, so commit the benchmarks to recall instead of long-dividing on test day. The eighth-fractions and the thirds are the two families that show up over and over.
Decimal-to-percent and percent-to-decimal are the same operation in opposite directions: shift the decimal two places. Move it right when going to a percent (multiplying by 100), move it left when going to a decimal (dividing by 100).
Worked Example
Setup: Convert 7/8 to a percent without long-dividing on test day.
If you only do one thing to prepare for ISEE fractions decimals percents, do this: drill the 14 rows in the table below until recall takes less than one second. Together they cover the vast majority of conversion answers on the test.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 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% |
| 1/3 | ≈ 0.333… | ≈ 33.3% |
| 2/3 | ≈ 0.666… | ≈ 66.7% |
| 1/10 | 0.1 | 10% |
Almost every student knows the halves and quarters, but it is still worth drilling them under time pressure to make recall reflexive. Fifths are easy to compute on the fly because the numerator times 20 gives the percent — 1×20=20, 2×20=40, 3×20=60, 4×20=80.
Eighth-fractions are the family that decides whether your conversion speed is competitive. Each step up adds 12.5%, so the four eighths to memorize are 1/8 (12.5%), 3/8 (37.5%), 5/8 (62.5%), and 7/8 (87.5%) — the even-numerator eighths reduce to halves and quarters, which you already know.
Thirds repeat: 1/3 = 0.333… = 33.3% and 2/3 = 0.666… = 66.7%. ISEE answer choices may show them as exact fractions, rounded percents, or repeating-decimal notation. Recognize all three forms so you do not get tripped up by formatting.
Use these two tools to drill conversions until they feel automatic. The calculator turns any fraction into its decimal and percent equivalents (and flags benchmark matches), and the lookup converter is a fast-recall trainer for the 14 benchmarks above.
Enter ANY fraction (numerator and denominator) and the tool returns the decimal, percent, and a benchmark-recognition note when the value matches a memorized equivalent.
Pick any benchmark fraction and instantly see its decimal and percent forms — drill these until recall is reflex.
ISEE percent word problems and ISEE percent change problems are where this topic stops being a vocabulary test and starts being a logic test. Most lost points here come from misreading the setup or applying the wrong formula — not from arithmetic errors.
Percent change always equals (new value − original value) divided by the original, multiplied by 100. The single most common mistake is dividing by the new value instead of the original. The denominator is always the starting point, not the endpoint.
Discount problems ask for a sale price after a percent reduction. The fastest formula is sale price = original × (1 − discount as decimal). For a 30% discount on $50, that is $50 × 0.70 = $35. Markup problems mirror this: new price = original × (1 + markup as decimal).
When two or more percent changes happen in sequence, you cannot add them. The second percent applies to the new total, not the original. Two consecutive 10% increases produce a 21% net change, not 20%. This is the trap on multi-step ISEE percent problems.
Worked Example
Setup: A jacket originally costs $80 and is on sale for 25% off. Then a second markdown takes another 20% off the sale price. What is the final price?
ISEE decimal practice questions and ordering questions ask you to compare values across all three forms. The clearest approach is to convert everything to decimals — that is the official ISEE practice guide recommendation, and it works.
When a problem mixes fractions, decimals, and percents, your first move should be to translate them all into decimals. From there, comparing becomes a place-value exercise — line up the decimal points and read across.
Worked Example
Setup: Order from least to greatest: 3/8, 0.4, 35%, and 2/5.
When a question asks you to compare just two fractions, cross-multiplication is faster than converting either to a decimal. To compare a/b versus c/d, calculate a×d and c×b. Whichever cross-product is bigger sits on the side of the bigger fraction — especially useful in Quantitative Reasoning quantitative-comparison questions.
ISEE answer choices love to include "almost-the-same" decimals — pairs like 0.7 and 0.07, or 0.125 and 0.0125. Always count the digits after the decimal point before committing to an answer. A single missing zero changes the value by a factor of ten.
The same six mistakes account for the vast majority of lost points on this topic. Once you can name a mistake, you stop making it. Drill the table below once a day and watch your accuracy climb without learning any new math.
| Mistake | Why It Happens | Quick Fix |
|---|---|---|
| Selecting 0.01 instead of 0.10 | Confusing decimal place value | Always count places: 'tenths is one place, hundredths is two' |
| 2/5 × 3/5 = 6/5 | Treating multiplication like addition (keeping denominator) | Multiply both tops AND both bottoms: numerators × numerators, denominators × denominators |
| Two 10% increases = 20% | Adding percents instead of compounding | Apply each percent to the new total — the second 10% is taken on a larger number |
| Forgot to simplify final fraction | Stopping calculation as soon as a number appears | Last step is always 'reduce' or 'match the answer-choice form' |
| Dividing by the new value in % change | Default to the most recent number | Percent change ALWAYS divides by the ORIGINAL value, no exceptions |
| Mistranslating 'x% of y' | Reading too fast | 'Of' = multiplication; convert percent to decimal first |
The classic error is choosing 0.01 when the right answer is 0.10. Both look like a "one with two zeros," but one is a hundredth and the other is a tenth — a tenfold difference. Slow down by half a second when shifting decimals: count "one place, two places" out loud (or in your head) every single time.
Research on rational-number errors found that 6th and 8th graders made wrong fraction-operation errors on 55% of fraction-division problems and 46% of multiplication problems. The most common mistake: writing 2/5 × 3/5 = 6/5 because the student kept the denominator the same the way they would in addition. Multiplication is different: numerators times numerators, denominators times denominators. The correct answer is 6/25.
Two consecutive 10% increases do not equal a 20% increase. The first one bumps 100 to 110; the second 10% applies to 110, not 100, giving 11 more — for a total of 121. That is a 21% net change. The cure is to apply each one in sequence to the running total.
The best strategy converts prepared knowledge into points under time pressure. Math Achievement gives you about 50 seconds per question (40 minutes ÷ 47 questions), so the techniques below are how you finish without rushing.
For percent questions, 10% is your secret weapon. Ten percent of any number is just that number with the decimal moved one place left — 10% of 60 is 6, 10% of 280 is 28. From there, 20% is double that, 30% is triple, and 5% is half. This single trick solves most ISEE percent problems faster than any formula.
When a percent problem uses unknown variables ("a number is increased by 25%, then decreased by…"), substitute 100 for the unknown. Every percent operation becomes a one-step calculation, and the variable cancels out, so the result is always correct.
Before grinding through a calculation, glance at the answer choices. If you can rule out two as obviously too big or too small, you have already cut your guess rate from 25% to 50%. Estimation also catches arithmetic mistakes — if your computed answer is not even close to your estimate, recheck before bubbling.
Use this checklist to confirm you have covered the highest-leverage skills before test day. Each item maps to a section in this guide, so you can return to the relevant table or worked example if anything feels shaky.