GMAT Fractions, Decimals and Percents

By Muntasir Aug 02, 2026 7 min read

TL;DR

Fractions, decimals and percents (FDP) are three ways to write the same value, and GMAT Quant Reasoning tests all three inside word problems. The Quant section runs 21 Problem Solving questions in 45 minutes, with no calculator allowed, so fast mental conversion matters. Memorize the common pairs: 1/2 equals 0.5 equals 50%, 1/4 equals 0.25 equals 25%, 1/8 equals 0.125 equals 12.5%. Watch three traps: a percent change often shifts to a new base, successive percent changes do not add, and percent of Y sits exactly 100 points above percent greater than Y. Compare fractions fast with cross-multiplication instead of finding a common denominator.

Fractions, decimals and percents describe the same underlying value in three different formats, and the GMAT switches between them constantly inside word problems. Quantitative Reasoning gives you 21 Problem Solving questions in 45 minutes, roughly two minutes per question, and no calculator is allowed on this section. Every second spent converting a fraction to a decimal by long division is a second lost.

This guide covers the conversion shortcuts worth memorizing, the percent traps most test-takers miss, a fast method for comparing fractions without a calculator, and how to combine these skills inside multi-step word problems. Every section pairs a rule with a short example you are able to reuse on test day. Two full worked problems close out the guide.

Fraction-Decimal-Percent Conversion Shortcuts

Memorize this table before test day. Recognizing 3/8 as 0.375 instantly saves the long division step mid-problem. The thirds, sixths and ninths repeat forever, so their decimals and percents below are rounded and marked approximate. Keep the fraction form for exact arithmetic and use the rounded values for recognition.

Fraction	Decimal	Percent
1/2	0.5	50%
1/3	0.333 (approx.)	33.3% (approx.)
2/3	0.667 (approx.)	66.7% (approx.)
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%
1/6	0.167 (approx.)	16.7% (approx.)
5/6	0.833 (approx.)	83.3% (approx.)
1/8	0.125	12.5%
3/8	0.375	37.5%
5/8	0.625	62.5%
7/8	0.875	87.5%
1/9	0.111 (approx.)	11.1% (approx.)
1/10	0.1	10%
1/100	0.01	1%

Why Memorization Beats Calculation

No calculator is allowed on the Quantitative Reasoning section, so any conversion not already memorized costs time on scratch paper instead. For fractions outside the standard table, divide the numerator by the denominator by hand, or find a nearby memorized fraction and adjust. mba.com recommends solving problems in writing on your whiteboard to avoid errors.

Converting Uncommon Fractions on the Fly

For a fraction like 7/20, convert the denominator to 100 first: multiply both parts by 5 to get 35/100, which equals 35%. This shortcut works whenever the denominator divides evenly into 10, 100 or 1,000. For denominators without a clean multiple, such as 7ths, divide the numerator by the denominator directly and round to three decimal places.

Percent-Change and Percent-Of Traps

Percent work sits in the arithmetic side of the section, and Quantitative Reasoning measures your arithmetic and elementary algebra foundational knowledge. The errors in percent questions are predictable once you know where to look. Three setups produce them: a percent change measured against the wrong base, successive changes added together instead of multiplied, and a percent-of question read as a percent-greater-than question. All three are worked out below.

The Percent Increase and Decrease Formula

Both formulas divide by the same number: the original value. Only the numerator flips, subtracting the smaller amount from the larger one in each direction. Anchoring the denominator to the starting value keeps the two straight under time pressure. Write the original value down first, then build the numerator around it.

Percent increase equals (new value minus original value), divided by the original value, times 100.
Percent decrease equals (original value minus new value), divided by the original value, times 100.
The denominator is always the original value, never the new value.

The Shifting Base Trap

A price rising 20% and then falling 20% does not return to its starting point, because each change applies to a different base. Consider a $100 item: a 20% increase brings it to $120. A 20% decrease off $120 removes $24, landing at $96, four dollars below the original price.

Successive Percent Changes Don't Add

Two successive percent changes never combine by simple addition. A 10% increase followed by another 10% increase produces a total gain of 21%, not 20%, because the second increase applies to the already-increased value. Multiply the two growth factors instead: 1.10 times 1.10 equals 1.21, a 21% total increase.

Percent Of Versus Percent Greater Than

Two phrasings sit one word apart and produce answers 100 percentage points apart. Read the preposition before you compute anything. The three rules below cover the whole family.

X is what percent of Y: divide X by Y, then multiply by 100.
X is what percent greater than Y: divide X by Y, multiply by 100, then subtract 100%.
P percent of Q percent of N: multiply the two decimals together, then multiply by N.

Set X at 150 and Y at 120. For the percent-of version, 150 divided by 120 equals 1.25, so 150 is 125% of 120. For the percent-greater-than version, subtract 100% from 125% to get 25%, so 150 is 25% greater than 120. One word moves the answer from 125 to 25, and both values sit in the answer choices.

The percent-of-a-percent setup stacks the same error. Taking 30% of 40% of N gives 0.30 times 0.40 times N, which equals 0.12N, or 12% of N. Adding the two percents to 70% is wrong, and so is dropping the decimal and reporting 12 of N. Check it with N equal to 200: 40% of 200 is 80, and 30% of 80 is 24, matching 0.12 times 200.

Comparing Fractions Quickly Without a Calculator

With no calculator on the Quant section, comparing fractions needs a technique faster than finding a common denominator by hand. Building a common denominator costs two multiplications and leaves you holding larger numbers on your whiteboard. Two moves replace it: cross-multiplication for an exact answer, and benchmarking against 1/2 for a fast sort. Start with the benchmark, then cross-multiply when both fractions land on the same side.

Cross-Multiplication Method

To compare two fractions without common denominators, cross-multiply. For 5/7 versus 7/10, multiply 5 by 10 to get 50, and multiply 7 by 7 to get 49. Since 50 is greater than 49, 5/7 is the larger fraction. This method works for any two positive fractions and skips finding a common denominator entirely.

Benchmarking Against 1/2

Before cross-multiplying, check whether each fraction sits above or below 1/2. A fraction is above 1/2 when the numerator, doubled, exceeds the denominator. For 5/9, doubling 5 gives 10, above 9, so 5/9 sits above 1/2. This benchmark eliminates wrong answer choices in seconds on multiple-choice questions.

Combining FDP Skills in Word Problems

GMAT Quantitative Reasoning measures arithmetic and elementary algebra knowledge through Problem Solving questions, and multi-step word problems blend fractions, decimals and percents inside a single scenario. A stem hands you a fraction of a total, applies a percent discount, then asks for a decimal answer. Switching formats mid-calculation is where the arithmetic slips. The two subsections below cover the format choice and the order of your scratch work.

Picking the Best Format for the Problem

No single format wins every problem, so pick the one matching the numbers in front of you. Fractions hold exact values, decimals add and multiply fast, and percents put unlike quantities on one scale. Read the answer choices before you commit, since they show the format the question expects at the end. The three rules below cover the common setups.

Use fractions when the problem describes parts of a whole and an exact answer is needed, such as ratios of ingredients or shares of a total.
Use decimals for quick addition, subtraction or multiplication steps inside a longer calculation.
Use percents to compare two quantities measured on different scales, since percent expresses both as parts of 100.

Working the Problem on Scratch Paper

Write out each piece of information in the same format before combining them. Mixing an unconverted percent with a decimal mid-calculation is a common source of arithmetic errors. Set up the entire equation with a single format, fractions or decimals, then convert the final answer to whatever format the question asks for.

Sample Problem Walkthroughs

Question: a store marks up a product's cost by 25% to set the retail price, then discounts the retail price by 20% during a sale. What percent of the original cost is the sale price?

Set the original cost at $100 for easy math. A 25% markup brings the retail price to $125. A 20% discount off $125 removes $25, leaving a sale price of $100. The sale price equals 100% of the original cost. The markup and discount cancel out exactly here.

Question: Class A has 40 students, and 5/8 of them pass an exam. Class B has 50 students, and 62% of them pass. Which class has more students who passed, and by how many?

Convert both to whole numbers. Class A: 5/8 of 40 equals 25 passing students. Class B: 62% of 50 equals 31 passing students. Class B has 6 more passing students than Class A, even though its pass rate looks close to Class A's 62.5%.

Practice these skills with our free Fractions & Decimals and Percents drills, each offering three difficulty levels with instant scoring and no signup required. For the full breakdown of the Quant Reasoning section, read our GMAT Quant Reasoning guide, and for FDP applied to interest and profit problems, see mixtures, interest and profit. Visit our GMAT prep page for the full library of mocks and section practice, or check your target score with our GMAT score calculator. You will find the same conversions in ratio and rate problems, in our GMAT ratios, rates and work guide.