Grade 5 · Take a fraction of a fractional area · 513 of 750
Take a fraction of a fractional area: tenths selected across: 4; tenths selected vertically: 3
A unit-square design for a classroom activity uses 4/10 of the width and 3/10 of the height. Find the exact fractional area of the overlap, explain the calculation, and check a related question.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A unit-square design for a classroom activity uses 4/10 of the width and 3/10 of the height. First find the exact fractional area of the overlap. Then answer: What exact fraction of the unit square belongs to both selections?
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A starting point
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.
Work through the reasoning
Step 1
Identify the quantities and the task
A unit-square design for a classroom activity uses 4/10 of the width and 3/10 of the height. The first task is to find the exact fractional area of the overlap. 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.
Step 2
Calculate the original result
4/10 × 3/10 = 12/100. The overlap contains 12 hundredths. It is at most either original fraction because both selections are between zero and one.
Step 3
Complete the follow-up calculation
What exact fraction of the unit square belongs to both selections? 12/100 = 3/25. Multiply the selected column and row counts, keeping the full 100-square whole.
The answer
4/10 × 3/10 = 12/100. The overlap contains 12 hundredths. It is at most either original fraction because both selections are between zero and one. Follow-up: 12/100 = 3/25. Multiply the selected column and row counts, keeping the full 100-square whole.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
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Watch the relationship
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The mathematical idea
A unit-square design for a classroom activity uses 4/10 of the width and 3/10 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 12 hundredths. It is at most either original fraction because both selections are between zero and one.
4/10 × 3/10 = 12/100
03 · Reflect and transfer
Explain what changes and why.
Select columns first, then reveal the chosen rows. Count only the squares belonging to both selections. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.