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

In real-life scenarios, we often encounter situations where we need to divide whole numbers by unit fractions. These word problems help us understand the practical applications of such divisions. Let's explore some word problems that involve dividing whole numbers by unit fractions.

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

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 (\( \frac{1}{4} \)).


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 (\( \frac{1}{3} \)).


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!

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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1. 2 pages

2. 2 cakes

3. 2 tanks

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

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