Grade 4 · Multiply every expanded place-value part · 536 of 750
Multiply every expanded place-value part: three-digit amount: 623; equal copies: 7
At a classroom activity, 7 identical supply sets each contain 623 counters. Find the number of objects in all the original sets, 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, 7 identical supply sets each contain 623 counters. First find the number of objects in all the original sets. Then answer: How many objects would one additional identical set contribute, and what would the new total be?
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A starting point
Distributivity lets a multi-digit factor be split into hundreds, tens, and ones. Every part occurs in every set, so every place-value part must be multiplied by the same copy count.
Work through the reasoning
Step 1
Identify the quantities and the task
At a classroom activity, 7 identical supply sets each contain 623 counters. The first task is to find the number of objects in all the original sets. Distributivity lets a multi-digit factor be split into hundreds, tens, and ones. Every part occurs in every set, so every place-value part must be multiplied by the same copy count.
Step 2
Calculate the original result
623 × 7 = 4361. 600 × 7, 20 × 7, and 3 × 7 account for all 4361 objects.
Step 3
Complete the follow-up calculation
How many objects would one additional identical set contribute, and what would the new total be? It contributes 623; the new total is 4984. A new copy repeats all the place-value parts.
The answer
623 × 7 = 4361. 600 × 7, 20 × 7, and 3 × 7 account for all 4361 objects. Follow-up: It contributes 623; the new total is 4984. A new copy repeats all the place-value parts.
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
At a classroom activity, 7 identical supply sets each contain 623 counters. Distributivity lets a multi-digit factor be split into hundreds, tens, and ones. Every part occurs in every set, so every place-value part must be multiplied by the same copy count. 600 × 7, 20 × 7, and 3 × 7 account for all 4361 objects.
623 × 7 = 4361
03 · Reflect and transfer
Explain what changes and why.
Reveal the hundreds, tens, and ones products separately. Recombine those nonoverlapping contributions to recover the total. 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.