Fractions on the Bocconi Test: Rules, Traps and Practice

Fractions are not a named topic on the Bocconi test. They still decide many math questions. You meet them inside percentages, ratios, unit conversions and word problems. This guide shows the fraction skills that matter, with worked examples and the mistakes we see most often.

TL;DR

• Bocconi’s official math syllabus does not list fractions as a heading. They appear inside other topics.
• Master five moves: simplify, compare, add and subtract, multiply and divide, convert to percentages.
• Most lost points come from the same few errors: adding denominators, inverting the wrong fraction, and misreading “of”.
• You have about 1.5 minutes per question on average, so speed with fractions matters.
• Practice under test timing. Check each mistake, then repeat the skill.

Table of Contents

• What fractions mean for the Bocconi test
• The five fraction moves you need
• Fraction word problems
• Common mistakes and how to avoid them
• Where fractions hide in other sections
• A practice plan for fractions
• Our view on fractions
• Practice with Prepadmit
• FAQ
• Sources

What fractions mean for the Bocconi test

We are sorry to say there is no “fractions” chapter to study. The official Online Bocconi Test page lists number properties, percentages, unit conversions and simple application problems in the math syllabus. Fractions are not a standalone heading.

That does not make them optional. A percentage is a fraction with 100 as the denominator. A ratio is a fraction in disguise. A unit conversion often means multiplying by a fraction. So fraction fluency lifts your score across the math section.

The same page gives the test structure: 50 multiple-choice questions. Of these, 24 are Mathematics, 11 Reading Comprehension, 6 Numerical Reasoning and 9 Critical Thinking. The simulation lasts 75 minutes, shows three questions per page, and does not let you go back after you advance.

Do the math on time. 75 minutes for 50 questions is 1.5 minutes per question on average. A fraction calculation that takes three minutes on paper costs you the time of two other questions. The goal is to be correct and quick.

The five fraction moves you need

Learn these until they feel automatic. Each one appears in many question types.

1. Simplify

To simplify, divide numerator and denominator by their greatest common divisor (MCD in Italian schools) until they have no common divisor other than 1. Treccani describes this rule. An Italian school handout gives a practical version: divide by any common factor, repeatedly, until none is left.

Example: simplify 84/126.

• Both are divisible by 2: 42/63.
• Both are divisible by 21: 2/3.

You do not need to find the MCD at once. Small steps are fine and often faster under stress.

2. Compare

The handout gives three rules:

• Same denominator: the larger numerator gives the larger fraction.
• Same numerator: the smaller denominator gives the larger fraction.
• Different denominators: convert to a common denominator first.

Example: which is larger, 5/8 or 7/12?

The smallest common denominator is 24. 5/8 = 15/24 and 7/12 = 14/24. So 5/8 is larger.

On the test, you can often skip the full conversion. Cross-multiply instead: 5 × 12 = 60 and 7 × 8 = 56. The larger product sits on the side of the larger fraction, so 5/8 wins. This only works when both denominators are positive.

Another quick tool is the decimal check. Compare 7/9 and 0.78. Since 7/9 = 0.777…, it is smaller than 0.78.

3. Add and subtract

With the same denominator, add or subtract the numerators and keep the denominator. With different denominators, use a common denominator, preferably the lowest common multiple (mcm). Then work on the numerators. Treccani states this procedure.

Example: 3/4 + 5/6.

• The mcm of 4 and 6 is 12.
• 3/4 = 9/12 and 5/6 = 10/12.
• Sum: 19/12, or 1 and 7/12.

Example with a negative result: 1/2 − 3/4 = 2/4 − 3/4 = −1/4.

4. Multiply and divide

Multiply numerators together and denominators together. To divide, multiply the first fraction by the reciprocal of the second. Treccani gives the same rule.

Reduce before you multiply. It keeps the numbers small.

Example: 14/15 × 25/21.

• 14 and 21 share 7: they become 2 and 3.
• 25 and 15 share 5: they become 5 and 3.
• Result: (2 × 5) / (3 × 3) = 10/9.

Example of division: 3/5 ÷ 9/10.

• Invert only the second fraction: 3/5 × 10/9.
• Reduce: 3 and 9 share 3, 10 and 5 share 5. You get 1/1 × 2/3.
• Result: 2/3.

5. Convert

To make an equivalent fraction, multiply or divide both terms by the same non-zero number. An apparent fraction, where the denominator divides the numerator, is really an integer. For example, 18/6 = 3.

For percentages, remember a few anchor values:

These values let you move between forms without long division. They also connect fractions to the ratio and proportion drills that Bocconi candidates need.

Fraction word problems

Bocconi questions are rarely bare calculations. They tell a short story. The skill is to turn words into a fraction expression, then use the five moves.

Translate the words

• “of” usually means multiply.
• “what is left” means 1 minus the parts used.
• “a third more” means multiply by 4/3.
• “a third less” means multiply by 2/3.

Worked example: what is left

A student spends 1/3 of a budget on rent and 1/4 on food. What fraction is left?

1 − 1/3 − 1/4 = 12/12 − 4/12 − 3/12 = 5/12.

If the budget is 1,800 euros, the amount left is 1,800 × 5/12 = 750 euros.

Worked example: a part of a part

In a class of 30, 3/5 are girls. One third of the girls study French. How many girls study French?

• Girls: 30 × 3/5 = 18.
• French students among them: 18 × 1/3 = 6.

The same answer comes from 3/5 × 1/3 = 1/5 of the class, and 1/5 of 30 is 6.

Worked example: fraction of a fraction

What is 2/3 of 3/4? Multiply: 2/3 × 3/4 = 6/12 = 1/2. Reduce first and you get it faster: the 3s cancel and you have 2/4.

A short method for any word problem

1. Read the question first. Know what you must find.
2. Write the whole as 1, or as a letter.
3. Write each part as a fraction of that whole.
4. Check that the parts add up to 1 when they should.
5. Compute. Then ask if the answer is reasonable.

Step 5 saves points. If you find that 5/12 of a budget is more than the budget, something is wrong.

Common mistakes and how to avoid them

We review many wrong answers. The same errors come back.

There are two more habits to avoid.

• Doing the full calculation when estimation is enough. Answer choices on multiple-choice tests are often far apart. Round the fractions, estimate, and pick.
• Skipping the check of units. If the question asks for minutes and you found hours, convert. Unit conversions are part of the official syllabus.

Also review how the test treats number rules. Divisibility, factors and multiples help you simplify fast. Our guide to Bocconi number properties covers them. Remainder questions use similar thinking, as shown in how the test uses remainders.

Where fractions hide in other sections

The math section is the obvious place. Fractions also show up elsewhere.

• Numerical Reasoning. Tables and charts give you shares, rates and changes. You compare parts of a whole. See what to expect in Numerical Reasoning.
• Percentages. An increase of 25% is a multiplication by 5/4. A decrease of 20% is a multiplication by 4/5.
• Ratios. A ratio of 3 to 2 means shares of 3/5 and 2/5.
• Critical Thinking. Some arguments rely on proportions. A larger number is not always a larger share.

Only 6 of the 50 questions are Numerical Reasoning, but the 24 math questions are the largest block. Strong fraction skills give you time for the harder items.

A practice plan for fractions

This plan fits into a normal week. It does not need extra books.

1. Day 1: Rules. Redo the five moves with 5 examples each. Write them without notes.
2. Day 2: Speed. Do 20 short calculations. Set a timer. Aim for under 45 seconds each.
3. Day 3: Word problems. Do 8 problems. Write the fraction expression before you compute.
4. Day 4: Mixed set. Include percentages, ratios and unit conversions.
5. Day 5: Timed block. Do 24 math questions in about 36 minutes, which matches the average pace for the math share.
6. Day 6: Error review. For each wrong answer, name the cause: rule, speed, reading or arithmetic.
7. Day 7: Rest or a light review.

Then repeat with new questions. Reviewing mistakes matters more than doing more questions. A wrong answer you understand is worth more than ten right answers you guessed.

For more drills, see targeted math exercises and timed mocks and three worked exercises with a 75 minute mock plan.

Official versus supplementary material

Use official material to learn the format and the timing. Use school handouts and worksheets to train the basic rules. Do not assume a worksheet matches the difficulty or style of the test. Check the format on the official page, and read the official 2026-2027 rules document. It says the test closes automatically when time expires and submits the answers you gave. So leave no question blank if you are close to the end.

If you want the wider picture of the exam, read what the online test involves and the format changes for 2026.

Our view on fractions

We built Prepadmit with experts from Bocconi and HEC. Here is how we see fractions.

Fractions are a tool, not a subject. Students who fail them rarely lack the rules. They lack automatic speed. They stop, doubt the rule, and lose a minute. Then the pressure grows on the next question.

We suggest three things. First, practice the rules in short bursts until you do not think about them. Second, practice in test conditions. Three questions per page and no way back changes how you work. Third, study your errors by type. If you add denominators once, you will do it again under stress unless you name it.

This is why our platform uses official past papers, detailed corrections and skill-specific modes. You can drill one skill, then return to a full simulation. Progress tracking shows if your weak spot is shrinking.

— quentin

Practice with Prepadmit

If you want to practice fractions in the real format, Prepadmit can help. The platform offers simulations based on official papers and on-demand tests. It also gives detailed answer corrections, skill-specific practice, progress tracking and ranking against other students. It is designed as an affordable alternative to private coaching, and it comes with a money-back guarantee.

You can access the full preparation and start with a timed math block. Then review each mistake and repeat.

FAQ

Are fractions on the Bocconi test?

Yes, inside other topics. The official math syllabus lists number properties, percentages, unit conversions and simple application problems. Fractions are not a separate heading, but you need them for most of these.

Can I use a calculator?

We do not state a calculator rule here. Check the official rules document for the current year before test day. Plan to do fraction work by hand, because that is the safest preparation.

How fast should I solve a fraction question?

The test has 50 questions in 75 minutes, so the average is 1.5 minutes each. Simple fraction operations should take well under a minute. Word problems can take longer, so save time on the easy ones.

What is the best way to compare fractions quickly?

First check if denominators or numerators match. If not, cross-multiply, or compare each to a known value such as 1/2. Use a common denominator only when needed.

Where can I find practice questions?

Start with the official Bocconi test page and its simulation. Add school worksheets for the basic rules. Then use timed mock tests to practice under real conditions.

Sources

• Online Bocconi Test, Bocconi University
• Online Admission Test rules, Bocconi University
• Frazione, Treccani
• Le frazioni, school handout

Recommended

• Bocconi Test Number Properties: Rules, Traps and Practice
• Three Questions at a Time: Bocconi Ratio and Proportion Drills
• Bocconi Remainders: How the Test Uses Them and How to Practice
• 4 Shortcuts That Halve Your Time on Bocconi Word Problems