vmbo havo vwo
Numbers and ratios
What belongs here
Numbers and ratios is arithmetic without x: how much of a whole, how a fraction works, what two integers share, and how 1 : n fits a map. Four tools: percentage, fractions, GCD/LCM and scale. On the Dutch site this topic is called Getallen en verhoudingen.
In which order do you build this?
- Percentage: part of a whole, or the reverse
- Fractions: the same ratio, different notation
- GCD and LCM: simplify and find a common denominator
- Scale: ratio on a map, 1 : n
Start with the percentage calculator when the sum is about “part of”, discount, a mark or BTW (Dutch VAT): 15 of 60 is 25%. Move to the fraction calculator when numerator and denominator are in view: add with equal denominators, simplify with the GCD. That GCD (and the LCM for the least common denominator) sits alone on the GCD and LCM calculator. Open the scale calculator only for 1 : n on a floor plan or map — that is not a percentage.
Which tool do you pick?
| You see in the sum… | Open |
|---|---|
| %, discount, mark, BTW, “part of” | Percentage calculator |
| Numerator/denominator, +, −, ×, ÷ or simplify | Fraction calculator |
| Two integers, GCD or LCM asked | GCD and LCM |
| Map, floor plan, 1 : n | Scale calculator |
What you meet per level
On this hub: which numbers tool fits which kind of sum. No separate exam rules here; the current program is on Examenblad. Dutch secondary tracks are named once: vmbo, havo and vwo.
On vmbo: discount and marks (percentage), pizza in slices (fractions), “what fits both” (GCD), classroom floor plan 1 : 50 or 1 : 100 (scale). Keep one unit first; 4 cm × 50 = 200 cm, convert to meters only at the end.
On havo you combine tools: simplify first (GCD), then a percentage of that simplified fraction, or find the LCM as least common denominator. Scale 1 : 25 000 needs the km step: 4 cm × 25 000 = 100 000 cm = 1 km. Percent change and 21% BTW belong on percentage, not on GCD or scale.
On vwo the same four tools inside a larger sum: growth factor next to percentage, simplify until irreducible, GCD of more than two numbers as GCD(GCD(a,b),c), and the same 1 : n in a bigger scale problem. No extra calculation laws on this hub.
Tools
Percentage calculator
Part of a whole, the reverse, or percent change. Start here when you see %.
vmbo havo vwoFraction calculator
Add, subtract, multiply, divide and simplify with a common denominator.
vmbo havo vwoGCD and LCM
Euclid for the GCD, then LCM = |a × b| ÷ GCD (Dutch: GGD and KGV).
vmbo havo vwoScale calculator
Map → real, reverse, or find n for 1 : n. Not a percentage.
Topics by level
- vmbo, havo and vwo: Percentage calculator · Fraction calculator · GCD and LCM calculator · Scale calculator
- Math A or math B in havo or vwo? Difference between math A and B