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A 2 to 3 ratio table

A 2:3 ratio table multiplies both parts by the same scale. At multipliers 1, 2, 3 and 4 the pairs are 2:3, 4:6, 6:9 and 8:12; every row has the same quotient because neither side is scaled independently.

The first side of the base ratio. Decimals are converted to whole-number parts before the ratio is simplified.

The second side. Both parts must be positive because a zero-part mixture has no useful scale table.

A multiplier of 0.5 makes half the base quantities; 1 makes the base row itself.

The distance between adjacent scale rows. It does not change the ratio.

Simplified ratio
2:3
Both decimal parts are first written as integers, then divided by their greatest common divisor.
Rows generated
12
Last multiplier
6.000000
First quantity in last row
12.000000
Second quantity in last row
18.000000

Equivalent ratio table

10.511.5
2123
31.534.5
4246
52.557.5
6369
73.5710.5
84812
94.5913.5
1051015
115.51116.5
1261218
What to take away
  1. At half scale the pair is 1 and 1.5, which is still exactly 2:3.

  2. The twelfth default row uses a multiplier of 6 and gives 12 to 18.

  3. Dividing either quantity by its base part recovers the same multiplier.

How it works

The formula

multiplier[row] = start + (row - 1) x step

firstQuantity[row]  = firstPart  x multiplier[row]
secondQuantity[row] = secondPart x multiplier[row]

To simplify decimal parts:
  write both parts as base-10 integers over powers of ten
  cross-multiply to one common denominator
  divide both resulting integers by their greatest common divisor

The same multiplier is always applied to both parts.

What it assumes

  • Both base parts and both multiplier controls are positive. A zero-part relationship can be written, but it does not make a useful scale table and is refused here.
  • Parts are dimensionless until the visitor assigns a unit. A row can mean grams, litres, pixels or people only when both columns are interpreted consistently.
  • The simplified headline is exact for the decimal spelling accepted by the number control. Table quantities use JavaScript numbers and are shortened to twelve significant digits to remove binary display tails.
  • A ratio names quantities alongside each other. A ratio of 1:4 contains five total parts; it does not mean one part out of four total.

Common questions

Is 4 to 6 the same ratio as 2 to 3?

Yes. Both parts of 2:3 were multiplied by two, and 4:6 simplifies back to 2:3 by dividing both parts by two.

Can equivalent ratio rows contain decimals?

Yes. Multiplying 2:3 by one half gives 1:1.5. Decimal quantities do not make the relationship approximate when the same exact multiplier is applied to both sides.

Sources

The full method, worked example and every assumption behind this figure are on Ratio Table Maker.