Grade 3 · Subdivide quarters without changing them · 35 of 750
Subdivide quarters without changing them: shaded quarters: 3; smaller pieces per quarter: 6
At a classroom activity, 3/4 of a strip is selected and every quarter is divided into 6 smaller equal pieces. Find the selected-piece count and total-piece count after the stated subdivision, 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
At a classroom activity, 3/4 of a strip is selected and every quarter is divided into 6 smaller equal pieces. First find the selected-piece count and total-piece count after the stated subdivision. Then answer: If every quarter were divided into 7 pieces instead, what equivalent fraction would result?
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A starting point
Equivalent fractions rename the same amount. Subdivide selected and unselected parts by the same factor; changing only the numerator would alter the amount instead of its name.
Work through the reasoning
Step 1
Identify the quantities and the task
At a classroom activity, 3/4 of a strip is selected and every quarter is divided into 6 smaller equal pieces. The first task is to find the selected-piece count and total-piece count after the stated subdivision. Equivalent fractions rename the same amount. Subdivide selected and unselected parts by the same factor; changing only the numerator would alter the amount instead of its name.
Step 2
Calculate the original result
3/4 = 18/24. There are 18 selected small pieces among 24 in the whole. Both counts grew by the factor 6.
Step 3
Complete the follow-up calculation
If every quarter were divided into 7 pieces instead, what equivalent fraction would result? 21/28. Multiply both 3 and 4 by 7.
The answer
3/4 = 18/24. There are 18 selected small pieces among 24 in the whole. Both counts grew by the factor 6. Follow-up: 21/28. Multiply both 3 and 4 by 7.
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.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
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From experiment to screen.
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The mathematical idea
At a classroom activity, 3/4 of a strip is selected and every quarter is divided into 6 smaller equal pieces. Equivalent fractions rename the same amount. Subdivide selected and unselected parts by the same factor; changing only the numerator would alter the amount instead of its name. There are 18 selected small pieces among 24 in the whole. Both counts grew by the factor 6.
3/4 = 18/24
03 · Reflect and transfer
Explain what changes and why.
Compare the two equal-length strips as the extra cuts appear. Their colored lengths remain aligned throughout the construction. 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.