EVERYDAY MATH / THE HOW & THE WHY

Read ratios as relationships, not totals

Simplify positive ratios, preserve units, and turn a part-to-part ratio into shares of a whole.

THE IDEA AT A GLANCEa : b → a/(a+b) and b/(a+b)
01

Say what each side represents

A ratio such as 2:3 compares two quantities in a stated order. Two parts concentrate to three parts water is not the same mixture as three parts concentrate to two parts water.

Bring measurements into the same unit before simplifying: 50 centimeters to 2 meters is 50:200, which simplifies to 1:4. The calculator does not perform that unit conversion automatically.

02

Clear decimals, then reduce

You may multiply both ratio values by a power of ten to obtain integers, then divide by their greatest common divisor. Scaling both sides together preserves the relationship.

The ratio tool reads positive finite decimals exactly within its documented limits. Zero or negative quantities require different interpretations and are outside this particular tool’s supported ratio model.

03

Convert a ratio into a share

For a two-part ratio a:b, the whole contains a+b parts. The first share is a/(a+b), not a/b. The latter compares the first part directly with the second.

If a total is supplied, divide it by the sum of the ratio parts to find one part, then multiply by each ratio number. Check that the allocated quantities add back to the total.

LET’S WORK IT THROUGH

Share 90 units in the ratio 2:3.

  1. There are 2 + 3 = 5 equal parts.
  2. Each part is 90 ÷ 5 = 18 units.
  3. The shares are 2 × 18 = 36 and 3 × 18 = 54.

THE ANSWERThe two shares are 36 and 54.

YOUR TURN

A small check for understanding.

Simplify 1.2 : 1.8.

Reveal the answer

2 : 3. Multiply by 10, then divide both values by 6.

Now try your own numbers.

The simplify a ratio includes input guidance and the limits of its supported calculations. Use it alongside the method above.

Open Simplify a ratio ↗

A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.