vmbo havo vwo
Fraction calculator
Quick answer
Addition: same denominators, then add the numerators. 1/2 + 1/3 = 5/6.
Multiplication: numerator × numerator, denominator × denominator, then simplify. Division: multiply by the reciprocal. A denominator of 0 is not allowed.
Calculator
This is the fraction calculator (Dutch pages say breuken): choose +, −, ×, ÷ or simplify. The GCD is used inside the simplify step; you can also compute it alone on the GCD and LCM calculator.
What is a fraction?
A fraction is numerator / denominator: how many equal parts of a whole. 3/4 is three of four equal parts. The denominator may not be 0 — division by zero is undefined.
| Term | Meaning | In 3/4 |
|---|---|---|
| Numerator | How many parts you take | 3 |
| Denominator | How many equal parts the whole is split into | 4 |
Percentages are fractions with denominator 100. That is why this page sits next to the percentage calculator. Common denominators and simplifying use the GCD (Dutch: GGD); compute that alone on the GCD and LCM calculator.
Examples by level
The tabs use the Dutch school names once: vmbo is the more practical track, havo sits in the middle, vwo is the university-preparatory track. The same rules apply; the wording gets denser.
Simplify 12/18.
- GCDGCD(12, 18) = 6
- Divide12 ÷ 6 = 2, 18 ÷ 6 = 3 → 2/3
You divide numerator and denominator by the same number. The value stays the same.
1/2 + 1/3
- Least common denominatorLCM(2, 3) = 6 (Dutch: KGV)
- Rewrite3/6 + 2/6
- Numerators5/6
You only add the numerators once the denominators match.
(2/3) × (3/4) and (1/2) ÷ (1/4)
- Product2×3 / 3×4 = 6/12 = 1/2
- Quotient1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2
Dividing by a fraction is multiplying by its reciprocal.
Common mistakes
Wrong
1/2 + 1/3 = 2/5 (adding numerators and denominators).
Right
Same denominators first. 3/6 + 2/6 = 5/6.
Wrong
Dividing fractions by dividing numerators and dividing denominators separately.
Right
Multiply by the reciprocal: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
Wrong
Simplifying by dividing only the numerator, or by different numbers above and below.
Right
Same GCD on both. 12/18: divide both by 6 → 2/3.
Practice
vmbo 3/4 − 1/2.
1/4
3/4 − 2/4 = 1/4.
havo 2/3 × 3/4.
1/2
6/12 = 1/2 after simplifying with GCD 6.
vwo May the denominator be 0?
No. Division by 0 is undefined.
In class
Fractions run from vmbo through vwo in Dutch secondary school. GCD and LCM (Dutch: GGD and KGV) sit inside the simplify step and when you match denominators; compute them alone on the GCD and LCM calculator. Looking for a “calculator with fractions”? This is it.
Next step
- How does this work? The explanation and examples are further up this page.
- Test yourself Fraction practice, with an explanation after every answer.
- Video explanations On the Fraction practice page. YouTube only loads when you press play.
Learning path
- Next: Percentage calculator Percent of a number, part-whole, and percent change.
- Related: GCD and LCM calculator
Frequently asked questions
How do you add fractions?
Make the denominators the same, add the numerators, then simplify. 1/2 + 1/3 = 5/6.
How do you simplify a fraction?
Divide the numerator and the denominator by their GCD (greatest common divisor; Dutch: GGD). 12/18 = 2/3.
What is the difference between numerator and denominator?
The numerator is how many equal parts you take; the denominator is how many equal parts the whole is split into. In 3/4, 3 is the numerator and 4 is the denominator.
Related tools
Percentage calculator
A percentage is a fraction with denominator 100.
Online calculator
General sums; fractions with steps stay on this page.
GCD and LCM calculator
Simplifying divides numerator and denominator by their GCD.
Numbers and ratios
Hub that places fractions after percentage and before GCD/LCM and map scale.