How to Solve Word Problems on Dividing Whole Numbers by Unit Fractions

Dividing a whole number by a unit fraction asks how many of those parts fit inside the whole, which is why the answer is always larger than the number you started with. Below: why the rule multiplies by the reciprocal, two worked word problems, and practice questions.

Dividing Whole Numbers and Unit Fractions: Word Problems

Example 1:

A chocolate bar is divided into sections, each representing \( \frac{1}{4} \) of the bar. If there are 8 sections in total, how long is the entire chocolate bar?

Solution Process:

To find the length of the whole chocolate bar, divide the number of sections (8) by the size of each section (\( \frac{1}{4} \)).

Answer:

The chocolate bar is 2 times as long.

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Example 2:

A rope is cut into pieces, each measuring \( \frac{1}{3} \) of a meter. If there are 9 pieces, how long was the rope originally?

Solution Process:

To find the original length of the rope, divide the number of pieces (9) by the length of each piece (\( \frac{1}{3} \)).

Answer:

The rope was originally 3 meters long.

Word problems involving the division of whole numbers by unit fractions help bridge the gap between abstract math concepts and real-world applications. By understanding the context and using systematic division, you can solve these problems with ease. Whether you’re planning a party, dividing resources, or just curious about everyday scenarios, these skills will come in handy. So, the next time you’re faced with a word problem involving division by unit fractions, approach it methodically and confidently, knowing you have the tools to find the solution!

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Practice Questions:

1. A book has chapters, each \( \frac{1}{5} \) of the total pages. If there are 10 chapters, how many pages are in the book?

2. A cake is sliced into pieces, each representing \( \frac{1}{6} \) of the cake. If there were 12 slices, how big was the cake?

3. A tank is divided into sections, each holding \( \frac{1}{8} \) of the total water. If there are 16 sections, what’s the tank’s total capacity?

4. A playlist has songs, each \( \frac{1}{7} \) of the total duration. If there are 14 songs, how long is the playlist?

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Answers:

1. 2 pages

2. 2 cakes

3. 2 tanks

4. 2 hours (or whatever unit of time is being used)

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