Mathematics · Middle school

The divided water tank

Make the tank’s parts finer: the water stays put while the fraction’s name changes. See equivalent fractions.

In the learning section below the figure, predict, try, complete the tasks and check yourself with short questions.

Fig. 1The divided water tank

Pull the lever: the parts get finer, the water stays put

1/2 · 50%

Starting fraction (×1)

Numerator

parts filled

Denominator

number of parts

Split lever (factor)

Split every part into how many pieces?

Same amount

Water level: 50%

Pull the lever and watch the water: the numerator and denominator grow together.

Simplest form: 1/2

Learn

Progress is kept on this page only; no points are given.

1Predict
2Try
3Explain

The tank is 1/2 full. If you pull the lever to ×3 and split every part into 3 pieces, what happens to the water level?

The height from the tank’s floor up to the “1 whole” line is split into as many equal parts as the denominator, and the water fills as many parts as the numerator. When the lever splits every part into k equal pieces, both the denominator and the number of filled parts are multiplied by k, so the water level (numerator ÷ denominator) does not change: a/b = (a × k)/(b × k), k ≠ 0. Adding the same number to the top and bottom does change the level.

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