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Grade 5 · Fractions

Community-park layout: take a fraction of a fractional area

A unit-square design for a community-park design uses 7/10 of the width and 4/10 of the height. Change the controls and explain what the animation reveals.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
Community-park layout: take a fraction of a fractional area. Intersection squares now: 0. Exact final product: 28/100. Final value: 0.287/10 × 4/10 = 28/1000 hundredths currently belong to both selections.
The quantities are invented for this investigation. Controls change the model rather than real-world records. Displayed decimals are rounded; whole-number counts are exact.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Intersection squares now
0
Exact final product
28/100
Final value
0.28

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

A unit-square design for a community-park design uses 7/10 of the width and 4/10 of the height. Taking a fraction of a fraction is represented by the overlap of two selections. A ten-by-ten square has one hundred equal small squares, so the overlap can be counted in hundredths of the whole. The overlap contains 28 hundredths. It is at most either original fraction because both selections are between zero and one.

A relationship to keep

7/10 × 4/10 = 28/100

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Read the starting situation

    A unit-square design for a community-park design uses 7/10 of the width and 4/10 of the height. Identify what each number measures before changing a control; the worked example refers to these starting values.

  2. STEP 2

    Follow the mathematical change

    Select columns first, then reveal the chosen rows. Count only the squares belonging to both selections. Pause on an intermediate frame and compare the picture with the live readouts.

  3. STEP 3

    Explain and test the relationship

    The overlap contains 28 hundredths. It is at most either original fraction because both selections are between zero and one. Change one input, predict its effect, and test whether the same relationship still works.

Your turn to explain

Make a prediction. Test your reasoning.

Community-park layout: use the original situation. A unit-square design for a community-park design uses 7/10 of the width and 4/10 of the height. What exact fraction of the unit square belongs to both selections?

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

28/100 = 7/25. Multiply the selected column and row counts, keeping the full 100-square whole.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 5 · Algebra

Take a fraction of a fraction

Interpret fraction multiplication as selecting part of a part.