Solve the Division Problem: (100+1) ÷ 25

Mixed Number Division with Remainders

100+125= ? \frac{100+1}{25}=\text{ ?}

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Step-by-step written solution

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1

Understand the problem

100+125= ? \frac{100+1}{25}=\text{ ?}

2

Step-by-step solution

Let's first solve the addition exercise in the numerator:

100+1=101 100+1=101

Note that the result we will get if we divide 25 by 100 will have a remainder.

Let's now check what the closest number to 101 is, by which we can then divide 25 without a remainder:

10025=4 \frac{100}{25}=4

Finally we add the remainder to get the answer:

4125 4\frac{1}{25}

3

Final Answer

4125 4\frac{1}{25}

Key Points to Remember

Essential concepts to master this topic
  • Order: Always simplify the numerator before dividing by denominator
  • Division: Find whole part first: 101÷25=4 101 ÷ 25 = 4 remainder 1
  • Check: Verify: 4×25+1=101 4 \times 25 + 1 = 101

Common Mistakes

Avoid these frequent errors
  • Dividing numerator terms separately
    Don't divide 100÷25 and 1÷25 separately = wrong approach! This ignores order of operations and gives 4+125 4 + \frac{1}{25} which isn't the same as 4125 4\frac{1}{25} . Always simplify the entire numerator first, then divide by the denominator.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do I add 100 + 1 first instead of dividing each part?

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Order of operations requires us to do operations inside parentheses first! 100+125 \frac{100+1}{25} means we must calculate 100 + 1 = 101 before dividing by 25.

How do I know when my answer should be a mixed number?

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When dividing gives you a remainder, convert to a mixed number! If 101 ÷ 25 = 4 remainder 1, then the answer is 4125 4\frac{1}{25} (4 whole parts plus 125 \frac{1}{25} ).

What's the difference between 4 + 1/25 and 4 1/25?

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They're the same value but different notation! 4125 4\frac{1}{25} is the proper mixed number format, while 4+125 4 + \frac{1}{25} shows the addition explicitly.

How can I check if my mixed number is correct?

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Convert back to improper fraction: 4125=4×25+125=10125 4\frac{1}{25} = \frac{4 \times 25 + 1}{25} = \frac{101}{25} . This should equal your original expression!

Why isn't the answer just 5?

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Because 101 ÷ 25 doesn't divide evenly! 25×5=125 25 \times 5 = 125 , which is bigger than 101. The closest whole number is 4, with 1 left over.

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