Division Problem: Finding Remainder When 73 Dancers Form 10 Equal Groups

Division with Remainder Finding

There are 73 people in a dance group.

If the dancers are divided into 10 groups of 10 dancers, then how many dancers will be left without a group?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

There are 73 people in a dance group.

If the dancers are divided into 10 groups of 10 dancers, then how many dancers will be left without a group?

2

Step-by-step solution

To solve this problem, we'll proceed with the following steps:

  • Step 1: Perform division to find how many groups of 10 dancers can be formed.
  • Step 2: Calculate the remainder to find how many dancers are left ungrouped.

Let's go through the steps:

Step 1: Divide 73 (total dancers) by 10 (dancers per group). We calculate:

73÷10=7 remainder 3 73 \div 10 = 7 \text{ remainder } 3

This division tells us that we can form 7 complete groups of 10 dancers each, with a remainder indicating the number of dancers left ungrouped.

Step 2: The remainder from the division is 3, indicating there are 3 dancers left without a group.

Therefore, the solution to the problem is 3\mathbf{3} dancers remain without a group.

3

Final Answer

3 3

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: Total divided by group size gives quotient and remainder
  • Technique: 73÷10=7 remainder 3 73 \div 10 = 7 \text{ remainder } 3 means 7 complete groups
  • Check: Verify: 7×10+3=70+3=73 7 \times 10 + 3 = 70 + 3 = 73

Common Mistakes

Avoid these frequent errors
  • Confusing quotient with remainder
    Don't give the quotient (7) as the answer when asked for leftover dancers = wrong! The quotient tells you how many complete groups you can make, not how many are left over. Always identify what the remainder represents.

Practice Quiz

Test your knowledge with interactive questions

If we have 67 blocks in total, how many blocks will remain if we remove 5 tens and 4 ones?

FAQ

Everything you need to know about this question

What's the difference between quotient and remainder?

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The quotient is how many complete groups you can make (7 groups of 10). The remainder is what's left over after making those groups (3 dancers).

Why can't I just subtract 70 from 73?

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That actually works perfectly! 7370=3 73 - 70 = 3 gives the same answer. Division with remainder and subtraction are just different ways to solve the same problem.

What if the question asked for groups of different sizes?

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The method stays the same! Divide the total by the new group size. The remainder will tell you how many people don't fit into complete groups.

Can the remainder ever be bigger than the divisor?

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No! The remainder must always be smaller than what you're dividing by. If it's not, you can make another complete group.

How do I check my division with remainder?

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Multiply: (quotient × divisor) + remainder = original number. For this problem: (7×10)+3=73 (7 \times 10) + 3 = 73

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