Case Interview Fractions: The Complete Guide

Author: Taylor Warfield, Former Bain Manager and interviewer

Last Updated: July 15, 2026

 

Case interview fractions are the fastest way to do consulting math in your head, since turning awkward numbers into simple fractions lets you divide and find percentages in seconds with no calculator. This guide gives you the exact fractions to memorize, five speed techniques, and worked examples drawn from real case scenarios.

 

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Key Takeaways

 

Fractions are the single most useful shortcut in case interview math, because almost every percentage, ratio, and division problem becomes faster once you think in fractions.

 

  • Memorize fraction-to-percent conversions from 1/2 through 1/12, plus 1/20 and 1/25

 

  • Convert percentages into fraction division to skip long arithmetic, so 12.5% of 800 becomes 800 divided by 8

 

  • Simplify and cancel before you calculate so you always work with the smallest possible numbers

 

  • Estimate any messy division by snapping it to the nearest clean fraction you know

 

  • Sense check the size of your answer and state your rounding assumptions out loud

 

What Are Fractions in Case Interviews and Why Do They Matter?

 

In case interviews, fractions are a mental math tool you use to handle division, percentages, and ratios quickly with no calculator. Because consulting math allows no calculator, rewriting 37.5% as 3/8 or a division like 90 divided by 720 as 1/8 lets you reach an answer in seconds rather than minutes.

 

Across more than 200 practice cases I have reviewed from McKinsey, BCG, and Bain, roughly 90% of the math comes down to five skills: multiplication, division, percentages, fractions, and basic algebra. Fractions sit underneath three of those five, which is why fluency here speeds up almost every calculation in a case interview math problem.

 

The math itself is middle school level. The difficulty comes from doing it fast, under pressure, while an interviewer watches and you reason about a business problem at the same time.

 

Top firms test this on purpose. McKinsey, BCG, and Bain run live case interviews with pen and paper only, and McKinsey states in its own interviewing guidance that you solve problems without outside tools. Some online steps such as the McKinsey Solve assessment do allow a calculator, but the live case rounds never do.

 

Which Fractions Should You Memorize for Case Interviews?

 

Memorize every unit fraction from 1/2 through 1/12, plus 1/20 and 1/25, along with their percentage and decimal values. These cover the vast majority of conversions that come up in case math, and knowing them on sight saves you 20 to 30 seconds on every question where they appear.

 

Fraction

Percentage

Decimal

1/2

50%

0.5

1/3

33.3%

0.333

1/4

25%

0.25

1/5

20%

0.2

1/6

16.7%

0.167

1/7

14.3%

0.143

1/8

12.5%

0.125

1/9

11.1%

0.111

1/10

10%

0.1

1/11

9.1%

0.091

1/12

8.3%

0.083

1/20

5%

0.05

1/25

4%

0.04

 

Once you know the unit fractions, the multiples come for free. If 1/8 is 12.5%, then 3/8 is 37.5% and 5/8 is 62.5%, and if 1/5 is 20%, then 2/5 is 40%, 3/5 is 60%, and 4/5 is 80%. Knowing these on sight is the foundation of fast mental math.

 

These conversions belong on the same one page reference as the rest of your consulting math cheat sheet, so you can drill them daily until recall is instant.

 

How Do You Use Fractions to Do Fast Case Math?

 

Use fractions to replace slow operations with fast ones: turn percentages into division, cancel before you multiply, and snap messy divisions to a nearby clean fraction. These five techniques cover almost every calculation you will run into.

 

Technique 1: Convert percentages into fraction division

 

The fastest way to take a percentage of a number is to rewrite the percentage as a fraction and divide. To find 20% of 500, treat 20% as 1/5 and compute 500 divided by 5, which is 100. To find 12.5% of 800, treat it as 1/8 and compute 800 divided by 8, which is 100.

 

Technique 2: Simplify and cancel before you calculate

 

Always reduce a fraction to its smallest form before doing any arithmetic. A market share of 90 in a 720 market looks ugly until you cancel it to 90/720, then 9/72, then 1/8, which is 12.5%. Canceling first means you work with single-digit numbers instead of three-digit ones.

 

Technique 3: Divide using fraction shortcuts

 

Some divisions are faster as fraction multiplication. Dividing by 5 is the same as multiplying by 2 and dropping a zero, so 340 divided by 5 becomes 340 times 2, then drop a zero, giving 68. Dividing by 25 is multiplying by 4 and dropping two zeros, so 600 divided by 25 is 600 times 4, then drop two zeros, giving 24.

 

Technique 4: Estimate messy division with the nearest fraction

 

When a division does not resolve cleanly, snap it to the closest fraction you know. To estimate 107 divided by 13, recognize that 13 times 8 is 104, so the answer is just over 8, roughly 8.2. This gives you a number to keep moving with in a few seconds, which matters far more than a perfect decimal.

 

If you want a faster way to build this fluency, my case interview course drills these exact conversions and shortcuts until they become automatic in as little as 7 days.

 

Technique 5: Take a fraction of a fraction by multiplying

 

To find a fraction of a fraction, multiply the numerators and the denominators. If 1/3 of a workforce are engineers and 1/4 of those engineers leave, the share who leave is 1/3 times 1/4, which is 1/12 of the whole workforce. This pattern comes up constantly in segmentation and cohort math.

 

How Do Fractions Show Up in Real Cases?

 

Fractions appear most often in profitability, market share, and growth math, where a single clean fraction replaces a messy decimal. Here are three worked examples that mirror what you will see.

 

Example: A client earns $400 million in revenue and $50 million in profit. Profit margin is 50 divided by 400, which simplifies to 1/8, or 12.5%. Reading it as a fraction is faster than long division and easier to sense check.

 

Margin questions sit at the center of most profitability case interviews, where every answer is just profit expressed as a fraction of revenue.

 

Example: A firm sells $90 million in a market worth $720 million. Market share is 90/720, which cancels to 1/8, or 12.5%. The same shortcut works whether the numbers are in thousands, millions, or billions, as long as the units match.

 

This is also why fractions speed up market sizing, where you constantly scale one quantity up or down by a ratio.

 

Example: A factory needs 2 supervisors for every 15 workers and currently has 45 workers. Since 45 is 3 times 15, you need 3 times 2 supervisors, which is 6. Setting it up as a ratio and scaling by a whole number beats reaching for a formula.

 

What Are the Most Common Fraction Mistakes in Case Interviews?

 

The most common fraction mistakes are losing track of zeros, forgetting to simplify, and rounding so aggressively that the answer drifts off. Each one is avoidable with a simple habit.

 

  • Losing zeros: strip the zeros before you calculate, then add them back at the end, and write down how many you removed

 

  • Skipping simplification: cancel the fraction to its smallest form first so you never divide large numbers in your head

 

  • Over rounding: keep rounding under about 10% of the value, or your final answer can drift far enough to be wrong

 

  • Silent assumptions: say your rounding and conversions out loud so the interviewer can follow and correct you

 

Most of these errors disappear with reps, which is why timed math drills are the highest return practice you can do.

 

Tips for Getting Faster With Case Interview Fractions

 

Tip #1: Drill the conversions until they are automatic

 

You should know every fraction in the table on sight, with zero hesitation. Use flashcards or a timed quiz and practice daily until recall takes under a second.

 

Tip #2: Default to fractions over decimals

 

Whenever you see a percentage or an ugly division, convert it to a fraction first. Fractions cancel cleanly and keep your numbers small, which is exactly what you want under pressure.

 

Tip #3: Write your work down instead of holding it in your head

 

Keep a clean column of numbers on paper and box your final answer. Holding multiple steps in your head is where most errors creep in.

 

Tip #4: Always sense check the size of your answer

 

Before you say a number, ask whether it is roughly the right magnitude. A profit margin of 125% or a market share of 0.0125% should immediately tell you a decimal slipped.

 

Tip #5: Practice out loud with someone watching

 

The hard part is not the math, it is doing it while talking and being observed. Practicing live with a former interviewer through case interview coaching is the fastest way to get comfortable performing math under that kind of pressure.

 

Mastering case interview fractions comes down to two habits: memorizing the conversion table cold and defaulting to fractions every time you see a percentage or a messy division. Drill those conversions daily until they are automatic, and your case math will get faster and more accurate almost immediately.

 

Frequently Asked Questions

 

What fractions should I memorize for case interviews?

 

Memorize every unit fraction from 1/2 through 1/12, plus 1/20 and 1/25, with their percentage and decimal values. These cover almost every conversion in case math. Knowing them on sight saves 20 to 30 seconds on each question where they appear.

 

Is case interview math hard?

 

No. Case interview math is middle school level arithmetic, fractions, percentages, and basic algebra. The difficulty is speed and accuracy under pressure with no calculator, not the math itself.

 

Can I use a calculator during a case interview?

 

No. Live case interviews at firms like McKinsey, BCG, and Bain are pen and paper only. Some online assessments allow a calculator, but you should still build mental math fluency for the live rounds.

 

How do I convert a fraction to a percentage quickly?

 

Divide the numerator by the denominator and multiply by 100, or recall the value from memory. For example, 3/8 is 0.375, which is 37.5%. Memorizing the common conversions removes the division step entirely.

 

How do fractions make case math faster?

 

Fractions let you cancel and simplify before you calculate, so you work with small numbers instead of large ones. Rewriting 12.5% as 1/8 or 90 divided by 720 as 1/8 turns a slow calculation into an instant one.

 

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